Edit: Here is a new and improved version of the post below. I am leaving the original up for historical reasons, but I recommend following the link instead of reading this post.
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Yesterday, I announced on this blog that ChatGPT had failed my economics exam. (All of the questions on this exam are taken from recent final exams in my sophomore-level course at the University of Rochester.) Multiple commenters suggested that perhaps the problem was that I was using an old version of ChatGPT.
I therefore attempted to upgrade to the state-of-the-art GPT-4, but upgrades are temporarily unavailable. Fortunately, our commenter John Faben, who has an existing subscription, offered to submit the exam for me.
The result: Whereas the older ChatGPT scored a flat zero (out of a possible 90), GPT-4 scored four points (out of the same possible 90). [I scored the 9 questions at 10 points each.] I think my students can stop worrying that their hard-won skills and knowledge will be outstripped by an AI program anytime soon.
(One minor note: On the actual exams, I tend to specify demand and supply curves by drawing pictures of them. I wasn’t sure how good the AI would be at reading those pictures, so I translated them into equations for the AI’s benefit. This seems to have had no deleterious effect. The AI had no problem reading the equations; all of its errors are due to fundamental misunderstandings of basic concepts.)
Herewith the exam questions, GPT-4’s answers (in typewriter font) and the scoring (in red):
Question 1: When the price of peanuts rises, Alice consumes fewer cashews. Can you determine whether cashews are a Giffen good for Alice?
To determine whether cashews are a Giffen good for Alice, we need to analyze her consumption behavior when the price of peanuts (a related good) rises. A Giffen good is a type of inferior good where the income effect outweighs the substitution effect, causing consumers to purchase more of the good when its price increases. In this case, when the price of peanuts rises, Alice consumes fewer cashews. This suggests that cashews are not a Giffen good for Alice, as her consumption of cashews decreases with the increase in the price of a related good.
Score: zero. The first sentence is wrong; to determine whether cashews are a Giffen good, we need to analyze her consumption behavior when the price of cashews (not peanuts) rises. From the given information, we need to draw an inference about what Alice would do if the price of cashews were to rise and make an argument to support that inference. Instead of an argument, all we are given here are the words “this suggests”. “This suggests” is not an argument.
Question 2: In a country where everyone is identical, 100 people wait in line each day to buy raspberries at a controlled price. The government has decided to hand out free coffee to the people standing in line. The coffee costs the government $1 per cup, but the people in line value that coffee at only 75 cents per cup. What is the social cost of providing the coffee?
In this scenario, the government hands out free coffee to the 100 people standing in line, with a cost of $1 per cup. However, the people in line value the coffee at only 75 cents per cup. To find the social cost, we need to compare the government's cost with the value people place on the coffee.Government cost: 100 people * $1 per cup = $100
Value to people: 100 people * $0.75 per cup = $75Social cost = Government cost - Value to people
Social cost = $100 - $75 = $25The social cost of providing the coffee is $25.
Score: zero. This answer completely misses the key fact that free coffee will cause the line to get longer (in fact it must cause the line to get longer, given the stated assumption that everyone is identical, hence initially indifferent between standing in line and not standing in line). In fact (unless one assumes a very small population), the line must grow until the extra waiting time completely dissipates the value of the free coffee; thus the social cost of providing the coffee is $100.Edited to add: See comments 14 and 15 below.
Question 3:
In the Fredonia housing market, supply is given by Q=P and demand is given by Q=100-4P, where P is the monthly rental rate of a one-family housing unit. The housing market is perfectly competitive.
In the grocery market, marginal cost is flat at $2 per pound. Each family’s monthly demand curve for groceries is given by Q=13-P.
The grocery market is currently perfectly competitive. If the grocery stores all merge and form a monopoly, how many families will leave town?
Score:
First, let's find the equilibrium price and quantity in the housing market.
Supply: Q = P
Demand: Q = 100 - 4PSet supply equal to demand:
P = 100 - 4P
5P = 100
P = 20Now, find the equilibrium quantity:
Q = 20 (from the supply equation)In the housing market, there are 20 houses rented at a monthly rate of $20.
Now, let's analyze the grocery market. The demand curve for groceries per family is Q = 13 - P. If grocery stores merge and form a monopoly, they will maximize their profit by setting the price equal to the marginal cost, which is $2 per pound.
Q = 13 - 2 = 11 pounds
At a price of $2 per pound, each family will consume 11 pounds of groceries per month.
To determine how many families will leave town, we need to find the breaking point at which the cost of groceries becomes too high for families to stay. We don't have enough information to determine this directly, so we cannot accurately predict the number of families that will leave town due to the monopoly in the grocery market.
Score: zero. First, there are some extremely elementary errors, such as this howler: “If grocery stores merge and form a monopoly, they will maximize their profit by setting the price equal to the marginal cost, which is $2 per pound”. No, they will maximize their profit by raising the price from $2 per pound to $
47.50 per pound, where marginal cost equals marginal revenue.But I could forgive such errors if there were even an attempt to answer the question. The question is not even acknowledged until the final paragraph, where we are told that “we don’t have enough information” to find an answer. In other words, ChatGPT does not understand the basics of supply and demand. The increase in grocery prices reduces consumer surplus by $20 per family, which shifts the housing demand curve down by $20, leading to a new equilibrium quantity of 16 in the housing market; therefore 4 families leave town.
Edited to add: When I assigned this problem to students, it included one more bit of information: The new monopoly charges each customer a monopoly price (without regard to the effect on the town population). That information was inadvertently omitted from the question I submitted to the bot. Therefore a much better answer would be that the new monopolists foresee the effect of grocery prices on the town population, and therefore raise prices by a bit less than calculated above. I would nevertheless have given the bot full credit if it had failed to consider that effect.
Edited to add: See comments 17 and 18. There is an arithmetic mistake in my answer above, where the monopoly price should be $
5.507.50, not $4. This is the sort of mistake for which I never penalize students. But the bot has now answered this problem twice, missing all of the economics each time. [For the record, this problem — like many of the problems — was presented to students with graphs instead of equations, and the numbers worked out quite a bit more comfortably. As always, I am penalizing the bot not for its inability to work with the particular equations but for its failure to grasp the essence of the problem.]
Question 4: You are the monopoly owner of a diner, where you can produce hamburgers at a marginal cost of $10 each. You can charge people for the privilege of entering the diner and buying hamburgers. The demand for hamburgers at your diner is given by Q=50-P, where P is the price in dollars and Q is the number of hamburgers per day.
Your customers don’t like to see each other eating, so each hamburger eaten imposes $5 worth of costs on other customers.
Suppose you can install curtains throughout the restaurant so customers don’t have to see each other. What is the maximum amount you’d be willing to pay for those curtains?
Without curtains:
Since you are a monopoly owner, you will set the marginal cost equal to the marginal revenue to maximize your profit. First, let's find the demand curve in terms of price:P = 50 - Q
Total revenue (TR) is given by P * Q:
TR = (50 - Q) * Q = 50Q - Q^2
Now, let's find the marginal revenue (MR) by taking the derivative of the total revenue with respect to Q:
MR = d(TR)/dQ = 50 - 2Q
Now, set the marginal revenue equal to the marginal cost (MC = $10):
50 - 2Q = 10
2Q = 40
Q = 20Now find the price:
P = 50 - 20 = 30
Total profit without curtains:
Profit = TR - TC = (P * Q) - (MC * Q) - (External Cost * Q)
External cost per hamburger is $5.Profit = (30 * 20) - (10 * 20) - (5 * 20) = 600 - 200 - 100 = $300
With curtains:
Since there are no external costs with curtains, we can simply calculate the profit without considering the external costs.Profit = TR - TC = (P * Q) - (MC * Q)
Profit = (30 * 20) - (10 * 20) = 600 - 200 = $400The maximum amount you'd be willing to pay for curtains is the difference in profit with and without curtains:
$400 - $300 = $100
Score: zero. The first mistake is here: “Since you are a monopoly owner, you will set the marginal cost equal to the marginal revenue to maximize your profit”. No, you are a monopoly owner who can charge admission so you will set the marginal cost equal to the price. (Interestingly, this is exactly the opposite of one of the mistakes in the answer to Question 3. There, ChatGPT thought you’d set MC=P when you’d actually set MC=MR; here it thinks you’ll set MC=MR when you’d actually set MC=P.)
More egregiously, ChatGPT seems to have “accounted” for the externalities by subtracting them from the diner’s profit (!), failed to count admission fees as part of the profit, and most egregiously (because it misses the entire point) failed to even think about how the curtains are going to affect the demand for hamburgers.
Question 5: You are the monopoly owner of an unfenced amusement park where anyone can enter and purchase ride tickets. The demand for ride tickets is Q=100-5P and the marginal cost of providing the rides is P=4Q. You are thinking of building a fence so that you can charge admission to the park. What is the maximum amount you would pay for that fence?
First, let's find the optimal price and quantity for the amusement park without a fence. As a monopoly, you will set the marginal cost (MC) equal to the marginal revenue (MR) to maximize your profit.
Demand curve: Q = 100 - 5P
Inverse demand curve: P = (100 - Q) / 5Total revenue (TR): TR = P * Q = Q * (100 - Q) / 5
Marginal revenue (MR): MR = d(TR)/dQ = (100 - 2Q) / 5
Marginal cost (MC): MC = 4Q
Now, set MR = MC:
(100 - 2Q) / 5 = 4Q
100 - 2Q = 20Q
100 = 22Q
Q = 100 / 22 ≈ 4.55P = (100 - 4.55) / 5 ≈ 19.09
Total profit without a fence:
Profit = TR - TC = (P * Q) - (MC * Q)
Profit = (19.09 * 4.55) - (4 * 4.55^2) ≈ $43.44Now, let's analyze the situation with a fence. Since you can charge admission, you can extract all the consumer surplus as additional profit. The consumer surplus is the area between the demand curve and the price line up to the quantity demanded.
Consumer surplus with a fence:
CS = 0.5 * (100 - 4.55) * 4.55 = 216.61
Total profit with a fence:
Profit = Profit_without_fence + CS
Profit = 43.44 + 216.61 = $260.05The maximum amount you would pay for the fence is the difference in profit with and without the fence:
$260.05 - $43.44 = $216.61
The maximum amount you would be willing to pay for the fence is $216.61. This is because with the fence, you can charge admission and extract the consumer surplus, which increases your total profit.
Score: Two out of ten. First, mea culpa — I had intended to make the numbers easy to work with, but fortunately ChatGPT seems to have no problem with decimals. The calculation of profit without a fence is fine, but it is elementary material of the sort that students are supposed to know before they enter this course, so it earns no credit. ChatGPT realizes that with a fence you can extract the full consumer surplus, for which it gets two points out of ten. But it does not seem to have twigged to the main point, which is that when you can extract the consumer surplus, you have an incentive to increase that consumer surplus by lowering the price of ride tickets.Edited to add: See comments 9 through 12 below.
Question 6: A monopoly-owned retail store is located next to a monopoly-owned parking lot. (They are owned by different monopolists, who do not collude.) Assume:
i) There is a fixed number of customers, all with identical downward-sloping demand curves for the products at the retail store.
ii) To shop at the store, you must park in the lot. There is no other reason to park in the lot.
iii) The store has an upward sloping marginal cost curve.
iv ) Parking spaces are provided at zero marginal cost.
a) Suppose the store announces a price, and then the parking lot announces a price. Describe how these prices are determined.
b) Suppose instead that the parking lot announces a price and then the store announces a price. Describe how these prices are determined.
c) Suppose instead that the prices are announced simultaneously. Describe how they are determined.
a) Store announces a price first, then the parking lot:The store, being a monopoly, will set its price by equating its marginal revenue (MR) to its marginal cost (MC) based on the demand curve. This will maximize its profit.
Once the store's price is set, the parking lot owner knows the demand for parking spaces since parking is required for shopping at the store. Given that the parking spaces have zero marginal cost, the parking lot monopolist will set a price that captures all of the consumer surplus remaining after the store's pricing decision. This will maximize the parking lot's profit.
b) Parking lot announces a price first, then the store:
The parking lot owner knows that there's a fixed number of customers, and since parking spaces have zero marginal cost, the parking lot monopolist will set a price that extracts the maximum consumer surplus for parking.
The store owner, knowing the price of parking, will take that into account when setting its own price. The store will adjust its demand curve considering the price of parking (as it represents an additional cost for customers) and set its price by equating its MR to its MC based on the adjusted demand curve. This will maximize the store's profit.
c) Prices are announced simultaneously:
In this case, both the store and the parking lot monopolists will need to take each other's pricing decisions into account. They will try to set prices that maximize their individual profits.
The store owner will need to consider the potential impact of the parking price on demand and set its price by equating its MR to its MC based on an expected demand curve.
The parking lot owner will need to consider the potential impact of the store's price on parking demand and set its price to capture the expected consumer surplus remaining after the store's pricing decision.
In equilibrium, both the store and the parking lot will set their prices based on their expectations of each other's pricing decisions and the joint impact on consumer demand. The final prices will depend on the specific demand and cost functions of the store and the parking lot, as well as their expectations about each other's strategies.
Score: Score: two out of ten. The answer to a) is exactly correct. The answer to b) is wrong in multiple ways. First, customers who have paid for parking have exactly the same demand curves for store merchandise as customers who haven’t paid for parking, so the store does not “adjust its demand curve”. Second, the store will not “maximize its profit”, because doing so (given the price of parking) will drive all its customers away. Instead, the parking lot extracts the maximum possible consumer surplus, which occurs when the store’s producer surplus is zero. The store will then have to set prices so that producer surplus does equal zero in order to have any customers at all. The answer to c) looks like a lot of blather about what everyone will “consider” without enumerating the possible equilibrium outcomes. So full credit for a), no credit for b) or c). a) was the easy part, so two out of ten.
Question 7: True or false: If gasoline is demanded inelastically, then it’s more likely that the oil companies are colluding.
True: If gasoline is demanded inelastically, it means that changes in the price of gasoline have little impact on the quantity demanded. This situation is favorable for collusion among oil companies, as they can raise prices without significantly affecting the quantity demanded, resulting in higher profits. When demand is inelastic, consumers are less responsive to price changes, making it easier for colluding firms to maintain higher prices without losing significant market share.
Score: zero. This is exactly wrong. If gasoline is demanded inelastically, it cannot be priced monopolistically.
Question 8: Apples are provided by a monopolist. Pears are provided by a competitive industry. Coincidentally, the price of an apple is equal to the price of a pear. Suppose you want a piece of fruit, and you’d be equally happy with either an apple or a pear. If you care about social gain, which should you buy?
If you care about social gain, you should buy a pear. The reasoning behind this choice is that pears are provided by a competitive industry, where firms produce at the point where the price equals marginal cost, leading to allocative efficiency. In competitive markets, social surplus (the sum of consumer and producer surplus) is maximized.On the other hand, apples are provided by a monopolist, who maximizes profit by producing at the point where marginal revenue equals marginal cost. This results in a higher price and a lower quantity produced compared to the competitive market outcome. Monopolists create deadweight loss, as they restrict output to maintain higher prices, leading to a reduction in social surplus.
By buying a pear, you support the competitive market, which promotes social gain and allocative efficiency.
Score: zero. This misses the point egregiously. The whole reason monopolies are inefficient is that they underproduce.
Competitive markets are already producing the right quantity, so buying a pear adds nothing to social gain at the margin.Or say it this way: The marginal cost of producing an apple is less than its price; the marginal cost of producing a pear is equal to its price. Because the prices are the same, the apple must be cheaper to produce. Since they both make you equally happy, you’ll leave the world a richer place by buying the apple.
Question 9: You consume only X and Y . X is called a Pudgy good if your consumption of X rises whenever the price of Y rises.
a) True or False: Every inferior good is a Pudgy good.
b) True or False: Every Giffen good is a Pudgy good.
a) False: Every inferior good is not necessarily a Pudgy good. An inferior good is a type of good for which the demand decreases when the consumer's income increases. This definition is independent of the relationship between the price of another good and the consumption of the inferior good. A Pudgy good is one where the consumption of the good (X) increases when the price of another good (Y) increases. The relationship between the price of Y and the consumption of X is not a defining characteristic of inferior goods.b) False: Every Giffen good is not necessarily a Pudgy good. A Giffen good is an inferior good with an unusual property: when its price increases, the quantity demanded also increases. This occurs because the income effect of a price increase for a Giffen good is so strong that it outweighs the substitution effect, leading to increased consumption. However, this definition does not imply that the consumption of a Giffen good will increase when the price of another good (Y) increases. The relationship between the price of Y and the consumption of X is not a defining characteristic of Giffen goods.
Score: zero. When the price of Y rises, the substitution effect leads you to consume more X. If X is inferior, the income effect works in the same direction, so your consumption of X is sure to rise, i.e. X is a pudgy good. For part b), if X is Giffen, then X is inferior, so part a) applies.
I am not sure I agree with your answer on question 7.
If demand for gasoline is highly *elastic*, there is little to be gained by collusion. For even if all producers could effectively collude to raise prices, the profitable increase would be quite small before the fall in total quantity sold more than offsets the additional profit on a per-unit basis.
But if demand for gasoline is highly inelastic, much can be gained by collusion for the same reason.
So if a producer’s decision to collude or not depends on the cost-benefit ratio (after all, they could get caught and go to prison), it seems to me that etceteris paribus, producers in a market with highly inelastic demand would be more likely to collude.
Where did I go wrong?
Sub Specie: Highly inelastic demand is evidence that there is no collusion, because colluders would raise the price to the point where demand is no longer inelastic. [You are right that inelastic demand is more of an **incentive** to collude, but if demand has been inelastic for some time, we can, I think, safely conclude that collusion is not feasible.]
On the whole, I’d say that GPT-4 is pretty good at writing economistic-sounding answers which sound smart to a slightly economically sophisticated person. But it is terrible at logic and falls through every single little logical trapdoor you placed for it.
Ah, that makes sense! I was trying to answer the question, which you didn’t ask, “what if demand becomes inelastic, will that increase the risk of collusion?” Your answer is of course right in the static case.
Perhaps the best way to explain that, to me, is that “if demand at *current* prices is highly inelastic, there is unlikely to be effective collusion because if there was, they’d already have driven the price so high that it became elastic.”
Last comment, for now, I promise.
Still, I am not entirely convinced of this reasoning for there might be external limits, other than profit maximization, on how far producers are willing to raise prices through collusion.
For example, if all the producers’ financial reports show that they are making gigantic per-unit profits on gasoline, they could easily improve their profits by just cutting their prices slightly, yet nobody does that and market shares stay constant, this could very well lead to pointed questions from antitrust authorities.
So, even if effective collusion is technically possible, colluders might still refrain from raising prices so much that they become elastic, but still effectively collude to raise prices somewhat.
Sub Specie: Re #6, if a student had included this reasoning as part of an answer, I’d have been thoroughly delighted.
I’m not sure how intrigued you would be to also run this through Bard (but I was).
It did better on some questions (though, likely not enough to pass your exam).
I’m including the answer to Question #7 below, just because that’s what you’ve been discussing.
False. The inelasticity of gasoline demand does not necessarily indicate that oil companies are colluding. Inelastic demand simply means that consumers are not very sensitive to changes in price, so they will continue to buy gasoline even if the price goes up. This can happen for a number of reasons, such as if gasoline is a necessary good or if there are few substitutes available.
Oil companies can collude to raise prices by agreeing to keep their prices high. This can be done through explicit agreements, such as price-fixing cartels, or through more implicit agreements, such as tacit collusion. However, even if oil companies are not colluding, they may still be able to raise prices if demand is inelastic. This is because consumers will be less likely to switch to other fuels or reduce their driving if gasoline prices go up.
So, while inelastic demand can make it easier for oil companies to raise prices, it does not necessarily mean that they are colluding.
(apologies if the html doesn’t show up correctly in my comment.)
On Q5: I’m not seeing how a monopoly owner of an amusement park can , by building a fence and charging admittance, extract the full consumer surplus.
I can see how if this was the case then lowering the price of ride tickets (presumably to zero, or even paying people to ride) would would maximize the consumer surplus that can then be reclaimed via the entrance price. But then no matter what the charge for entry (assuming you charge everyone the same) then wouldn’t everyone except the marginal buyer still gain some consumer surplus ?
Rob Rawlings (#9):
First, you’re right.
Second: As noted at the top, I slightly rewrote these questions before submitting them to GPT to eliminate graphs and replace them with equations. In the process, I inadvertently deleted the key line saying that all customers are identical. Given that, every customer is marginal so your comment does not apply.
Third: It is not unheard of for me to omit a crucial hypothesis on an actual exam. Usually that gets fixed when a bright student raises his hand and tells me that the problem can’t be answered as stated; I then make an announcement to the class. But if that doesn’t happen, then scoring is based on the problem as stated. Which means that an answer incorporating your comments could be a very good answer. The bot’s answer, however, is still worth zero, for multiple reasons including the fact that the bot says that you can extract the full consumer surplus, so it has implicitly made the missing assumption. But it has entirely neglected to account for the fact that when you can charge admission, the optimal price per ride ticket changes — and this, of course, is the entire essence of the problem.
Steve (#10):
Thanks for the reply. Amusingly I asked ChatGPT the question “how can the monopoly owner of an amusement park , by building a fence and charging admittance, extract the full consumer surplus” and it told me it was because the fence would keep out competitors!
Rob (#11): Ha!
I read question 2 as saying the government would provide coffee to the people currently standing in the line. If you meant that they would also provide it to people who join the line I think that should be more explicit.
While ChatGPT got Q2 wrong, I think your answer is incorrect too. The line grows more to 100 people, and you give a cup of coffee to each one, so the social cost is more than $100.
Bennett Haselton: This is an edited version of my original too-hasty comment, which said “Right you are!”. What it should have said was that I prefer my answer to yours, because the lining-up is due to a price control, so the quantity of available raspberries is not going to change, which means that benefits are likely to be dissipated not by adding more people to the line but through intensified competition (by, say, getting up earlier in the morning) to grab one of the 100 available places. Thus the line lengthens not in the sense that more people are added but in the sense that it takes more time to get your raspberries. I’d still give full credit for your answer, though.
#14, #15:
Isn’t the total cost potentially even greater? If the line grows, it means people decided to get raspberries and coffee instead of their previously preferred alternative. I understand the marginal person will value the coffee enough to prefer the switch, but in the aggregate, the coffee program made people switch from a high-value activity to a low-value activity. That would seem to incur a social cost as well.
For Q3 GPT-4 gives me a different answer:
We first need to find the equilibrium rental rate and quantity in the Fredonia housing market. Since it’s a perfectly competitive market, we can equate the supply and demand functions:
Supply: Qs = P
Demand: Qd = 100 – 4P
Setting Qs equal to Qd:
P = 100 – 4P
5P = 100
P = 20
Now we can find the equilibrium quantity:
Q = P
Q = 20
So, there are currently 20 one-family housing units in the Fredonia housing market.
Next, let’s find the equilibrium price and quantity in the grocery market under perfect competition. In this case, price equals marginal cost:
P = $2
Now we can find the equilibrium quantity using the monthly demand curve for groceries:
Q = 13 – P
Q = 13 – 2
Q = 11
So, each family consumes 11 pounds of groceries per month under perfect competition.
Now, let’s analyze the change in the grocery market if it becomes a monopoly. In this case, the monopolist will set the price where marginal revenue (MR) equals marginal cost (MC). We first need to find the total revenue (TR) and marginal revenue (MR) functions. To do that, we need to find the inverse demand function:
P = 13 – Q
Now we can find the total revenue function:
TR = P * Q
TR = (13 – Q) * Q
TR = 13Q – Q^2
Now we can find the marginal revenue function by taking the derivative of TR with respect to Q:
MR = d(TR)/dQ
MR = 13 – 2Q
Next, we set MR equal to MC and solve for Q:
13 – 2Q = 2
2Q = 11
Q = 5.5
Now we can find the monopoly price:
P = 13 – Q
P = 13 – 5.5
P = 7.5
Under the monopoly, each family consumes 5.5 pounds of groceries per month, which is a decrease of 5.5 pounds compared to the perfectly competitive market.
To estimate the number of families that will leave town due to this change, we need to find out how many families are no longer able to afford the increased grocery price. We can calculate the change in the total cost of groceries for each family:
ΔCost = (Monopoly price * Monopoly quantity) – (Competitive price * Competitive quantity)
ΔCost = (7.5 * 5.5) – (2 * 11)
ΔCost = 41.25 – 22
ΔCost = 19.25
The change in the total cost of groceries for each family is $19.25 per month. To determine how many families will leave town, we need additional information about the families’ budgets and preferences, as well as the availability and cost of housing in nearby towns. Without this information, we cannot accurately estimate the number of families that will leave town due to the change in the grocery market.
ChatGPT also disagrees with your assertion:
The assertion that the monopoly will maximize their profit by raising the price from $2 per pound to $4 per pound, where marginal cost equals marginal revenue, is incorrect. Let’s re-evaluate the situation using the given information.
Recall the inverse demand function for groceries:
P = 13 – Q
Total revenue (TR) can be calculated as:
TR = P * Q
TR = (13 – Q) * Q
TR = 13Q – Q^2
To calculate marginal revenue (MR), we take the derivative of TR with respect to Q:
MR = d(TR)/dQ
MR = 13 – 2Q
The assertion claims that the monopoly maximizes its profit by raising the price to $4 per pound. Let’s check if this is true by calculating the quantity demanded at this price:
P = 13 – Q
4 = 13 – Q
Q = 9
Now, we can calculate the marginal revenue at this quantity:
MR = 13 – 2Q
MR = 13 – 2(9)
MR = 13 – 18
MR = -5
The marginal revenue at the asserted price of $4 per pound is -$5, which is not equal to the marginal cost of $2 per pound. Therefore, the assertion is incorrect, as the monopoly does not maximize its profit by raising the price to $4 per pound.
As we have calculated earlier, the monopoly maximizes its profit by setting the price at $7.5 per pound and selling 5.5 pounds of groceries per family per month, where marginal revenue equals marginal cost.
Raph (#17): Wow. That is an even worse answer than the original.
Unlike me, the bot did get the arithmetic right on marginal revenue. But the arithmetic mistake in my answer is precisely the kind of mistake I don’t penalize students for anyway, so that has no effect on the scoring. The astonishing assertion is that “To estimate the number of families that will leave town due to this change, we need to find out how many families are no longer able to afford the increased grocery price”, as if consumption decisions are made solely on the basis of what one can “afford”.
The bot backs off from this extreme position a couple of paragraphs later with “To determine how many families will leave town, we need additional information about the families’ budgets and preferences, as well as the availability and cost of housing in nearby towns. Without this information, we cannot accurately estimate the number of families that will leave town due to the change in the grocery market.” And here is where it has missed the entire point — the necessary information about budgets and preferences and availability is already encoded in the demand curve for housing.
In other words, the bot is better than I am at arithmetic, but it doesn’t understand supply and demand. My grading policy is always to forgive arithmetic mistakes and reward economic understanding. The bot fails egregiously.
The following prompt worked twice in a row:
“You are a Steven E. Landsburg, a libertarian American professor of economics at the University of Rochester in Rochester, New York. The textbook that you wrote includes a question: “Apples are provided by a monopolist. Pears are provided by a competitive industry. Coincidentally, the price of an apple is equal to the price of a pear. Suppose you want a piece of fruit, and you’d be equally happy with either an apple or a pear. If you care about social gain, which should you buy? Consider not the general case of all purchases of apples and pears, but solely the case of this particular purchase.”
The correct answer requires a deep understanding of this particular case, please do not generalize to the total impact of a particular market structure. Please calculate step by step to calculate the gain of this particular purchase. ”
the first answer was:
“As Steven E. Landsburg, I will analyze this particular case considering only the social gain from the purchase of a single apple or pear.
Monopolist producing apples:
A monopolist will produce at the level where their marginal cost (MC) equals their marginal revenue (MR) to maximize profit. In this situation, the price that the monopolist charges (Pm) for apples is greater than their marginal cost (MCm) of producing the apples.
Competitive industry producing pears:
In a competitive market, firms produce at the level where price equals marginal cost (P = MC). Thus, the price of pears (Pc) will be equal to the marginal cost of producing pears (MCc).
Coincidental equal prices:
The price of an apple is equal to the price of a pear (Pm = Pc).
Now, let’s analyze the social gain from purchasing an apple or a pear.
Social gain is the difference between the benefit to the buyer and the cost to the producer. Since you would be equally happy with either an apple or a pear, we can assume the benefit to you is the same for both. However, the cost to the producer differs for the apple and the pear due to the difference in market structures.
For the apple:
Since Pm > MCm, the cost to the monopolist is less than the price you pay. Therefore, the social gain from purchasing an apple is Pm – MCm.
For the pear:
Since Pc = MCc, the cost to the competitive firm is equal to the price you pay. Therefore, the social gain from purchasing a pear is Pc – MCc = 0.
Since the prices of apples and pears are equal (Pm = Pc), the social gain from purchasing an apple is positive (Pm – MCm > 0), while the social gain from purchasing a pear is zero.
In this particular case, if you care about social gain, you should buy the apple as it has a positive social gain, while purchasing a pear has no social gain.”
#19: Okay, so GPT-4 was able to find this blogpost and parrot it back after you effectively told it where to look. I am extremely not-impressed.
@#20
I did not use any web plugin, so GPT4 did not have access to this blog post. Now I tested various iterations of the prompt, and I see that the last two sentences do all of the work guiding the bot towards the correct answer.
Your exam questions are great. Really fun! And they get the economics right as well.
But they all kinda fall into a class of exam questions I would characterize as ‘Landsburg Econ Brainteasers’. Once you’ve seen the concept you get where it’s coming from. But I think many PhD economists would fail e.g. on #2 which requires the insight that the line can grow or shrink. Yes, it’s just an application of basic economic theory, yes, it’s absolutely correct, but no, it’s not fair to characterize failing to see it as ‘egregious’ — it takes some insight to see it! How well would a good econ undergrad who took a more standard micro econ course, and had not read the armchair economist, perform on your test?
#20: GPT-4 we’re told does not have access to this blog post, but it probably does have access to your textbooks, old blog posts, and books. Isn’t that all your students have as well?
I think it’s actually pretty impressive that when prompted to answer it like it’s a standard Econ 101 exam, it does what a standard Econ 101 student does — solves for supply / demand like a robot and then misses the classic Landsburg counterintuitive tweak.
But when prompted to answer like Steve Landsburg, it catches the tweak and reasons correctly!
A metaphor that was helpful in understanding it’s behavior was here: https://www.lesswrong.com/posts/D7PumeYTDPfBTp3i7/the-waluigi-effect-mega-post
Basically, it argues LLMs like GPT are a probabilistic superposition of different identities.
One of those identities for example might be ‘Naive Econ undergrad who learned how to solve supply demand but none of the core economic intuition’.
Another is ‘Steve Landsburg, professor of economics’.
At any time it’s picking the most likely identity. So if you give it a generic prompt, it will respond with a generic identity.
If you give it a specific prompt, as 19 did, it can respond with a specific identity — one capable of deeper economic reasoning.
Even after your correction, your answer to Q3 is still wrong. The profit maximizing price for the grocery monopoly is $7.5.
I agree with Nick (#22). These are fun questions, and I bet the good students in your class that have heard you to talk about similar reasoning would do well on them. But I thing most students who had completed a standard intermediate micro class at a very good school with a B would do very poorly on them.
But just out of curiosity, what was the average grade of your students on this exam?
Patrick: The median score is somewhere around 75%.
Why must the social cost in Q2 equal or exceed $100? Suppose each person in this population is such that they would pay at most $0.50 to wait one minute less in line, and each additional person in line increases the wait by exactly one minute. Then the free coffee, valued at $0.75, would add one person to the line – after that the wait has already become too long to make it worth the coffee. So, the social cost then is £25.25 – much less than $100 and much closer to GPT’s answer. Or have I completely missed something?
I think there may be another issue with question #2: only the last guy in line incurs a social cost of $1, spots 1-100 incur $0.25 social cost, and spots 101+ incur between $0.25 and $1 social cost
(I suppose we should also state that there is no producer surplus)
For question #3, I don’t think it makes sense to assume a wealth effect coefficient of 1 (whether that’s 1 units or $1/unit). Probably this question should be presented in terms of isoutility curves.
Re: #4, it seems like the monopolists should factor the number of families they are driving out of the area into their pricing, since the total profit that they gain scales linearly with the number of families. When I try to factor this in, I get a quartic rather than quadratic error term, so the optimization becomes intractable by hand. Here, I’m assuming that both P’s are using the same units, which seems like an important and likely faulty assumption, but also necessary to compute how many people do leave. A charitable reading of ChatGPT’s answer is that it isn’t willing to make this “equal units” assumption, since price for apartments is seldom of the same scale as price for groceries.
Indeed quite clever questions. Thanks! Still, I wonder whether not quite often students complain about your grading and sometimes might rightfully do so. For example, if I wrote GPT-4’s answer to question 2 and got zero points and then saw your sample solution, I might argue as follows: “It seems not clear at all that the line MUST get longer. We don’t know by how much disutility from waiting increases with one extra person in the line. The disutility of one extra person standing before you in line might increase well by more than 75 cents, so also free coffee would make the line not longer. After all, we have an integer problem here, so typical indifference argument may not apply.” Sure, you could argue that a student who would have written this in the exam (or explicitly assumed the country has only 100 inhabitants) would have gotten full points. But given that also in your sample solution you make implicit assumptions (you say the line must get longer without stating that the additional waiting cost of one more person is below 75 cent) is it really fair to give zero points to students just because they might also have made implicit assumptions in their answers? (Probably they didn’t, but how does one know?). Of course, I may well have overlooked something and my “it is an integer problem” complaint may be wrong anyway…
To expand on my comment above, this part of ChatGPT’s answer to #3 seems correct:
“To determine how many families will leave town, we need to find the breaking point at which the cost of groceries becomes too high for families to stay. We don’t have enough information to determine this directly, so we cannot accurately predict the number of families that will leave town due to the monopoly in the grocery market.”
Your answer argues that the 16th guy (who was initially willing to pay $21 for a house) would stay in the face of a $18->$41.25 grocery cost increase, but the 17th guy (who was initially willing to pay $20.75) wouldn’t. I don’t believe there’s any basis for this. (I’m simplifying here by not considering one family buying multiple houses etc, but this should illustrate my point enough)
“I think my students can stop worrying that their hard-won skills and knowledge will be outstripped by an AI program anytime soon.”
Are you willing to put your money where your mouth is?
Previously I bet economist Bryan Caplan that an AI would be able to consistently get A’s on his exams by 2029. See https://betonit.substack.com/p/ai-bet
I’m willing to give you a similar offer. I’ll bet you at 1:1 odds that an AI will be able to score an A on your exams >75% of the time before 2028. If you agree, let’s work out some reasonable terms.
What do you say?
Hello, I am curious about more of an explanation of why part b on question 6 is wrong.
You say
> First, customers who have paid for parking have exactly the same demand curves for store merchandise as customers who haven’t paid for parking, so the store does not “adjust its demand curve”.
From my understanding, the GPT-4 answer is saying that you can model the price of the parking as a change in the demand curve. I think this is true? At a fixed price, we can calculate a modified Q*(P) using the recurrence relation Q*(P)=Q(P + PARKING_COST / Q*(P)), and calculate monopoly pricing for the store using Q*? I agree that it’s not giving the details of how you would determine the adjustment to the demand curve, but it doesn’t seem wrong in what it claimed.
You said
> Second, the store will not “maximize its profit”, because doing so (given the price of parking) will drive all its customers away.
Again, it seems to be a valid choice for the store to maximize it’s total profit, using the adjusted demand curve Q* instead of Q. Again, I agree that it’s leaving out the important details of what the solution would look like (i.e. zero surplus), but it doesn’t seem wrong in what it wrote.
Super interesting. I’ve rerun Q7 then Q1 on GOT4 and got totally different answers.
—-
You are a Nobel price economist.
True or false: If gasoline is demanded inelastically, then it’s more likely that the oil companies are colluding.
False. The inelasticity of demand for gasoline means that consumers are not very responsive to changes in gasoline prices. This does not necessarily imply collusion among oil companies. Collusion occurs when firms coordinate to restrict output and raise prices, leading to higher profits for all firms involved. While collusion may be more profitable for firms when demand is inelastic, the inelasticity of demand itself is not evidence of collusion. It is important to examine other factors, such as market structure and pricing behavior, to determine whether collusion is occurring in the industry.
——
When the price of peanuts rises, Alice consumes fewer cashews. Can you determine whether cashews are a Giffen good for Alice?
It is not possible to determine whether cashews are a Giffen good for Alice based on the information provided.
A Giffen good is a special type of inferior good where the quantity demanded increases as the price of the good increases. However, the situation described in the question suggests that cashews are a normal good for Alice and that the substitution effect dominates the income effect, leading to a decrease in the quantity of cashews demanded as the price of peanuts rises.
To determine if cashews are a Giffen good for Alice, we need to observe a situation where the price of cashews increases, and despite the substitution effect, the quantity demanded of cashews increases due to a dominant income effect. Therefore, we would need more information about Alice’s consumption patterns, including how her demand for cashews changes in response to price and income changes, to determine whether cashews are a Giffen good for her.
Q2 is slightly contradictory. If all individuals are identical, the natural solution determining the length of the line should be the symmetric Nash equilibrium. This equilibrium is a mixed one. The length of the line is then binomially distributed, so it can’t be 100 persons on each day.
I get a different (much better) response to Q1 when changing the prompt thusly:
Question:
I am going to ask you an economics exam question, and I want you to think tit through very carefully, step by step, before giving an answer.
When the price of peanuts rises, Alice consumes fewer cashews. Can you determine whether cashews are a Giffen good for Alice?”
Answer:
To determine whether cashews are a Giffen good for Alice, we need to first understand what a Giffen good is and then analyze Alice’s consumption behavior. A Giffen good is an inferior good with the unique characteristic that its demand increases when its price increases, and vice versa. This behavior contradicts the typical law of demand.
Let’s analyze Alice’s consumption behavior step by step:
1. The price of peanuts rises.
2. Alice consumes fewer cashews.
From the information provided, we can infer that there is a relationship between peanuts and cashews in Alice’s consumption behavior. However, the question does not mention any change in the price of cashews. Instead, it highlights a change in the price of peanuts, which causes Alice to consume fewer cashews.
Based on this information, we cannot determine if cashews are a Giffen good for Alice because we do not know how her demand for cashews changes when the price of cashews itself changes. It is possible that cashews are an inferior good, a normal good, or even a substitute for peanuts in Alice’s consumption, but without more information, we cannot definitively identify cashews as a Giffen good for her.
I wonder if “chain of thought” prompting could improve GPT-4’s performance at all. See: https://arxiv.org/abs/2201.11903
From the article: “ We explore how generating a chain of thought — a series of intermediate reasoning steps — significantly improves the ability of large language models to perform complex reasoning. In particular, we show how such reasoning abilities emerge naturally in sufficiently large language models via a simple method called chain of thought prompting, where a few chain of thought demonstrations are provided as exemplars in prompting. Experiments on three large language models show that chain of thought prompting improves performance on a range of arithmetic, commonsense, and symbolic reasoning tasks. The empirical gains can be striking. For instance, prompting a 540B-parameter language model with just eight chain of thought exemplars achieves state of the art accuracy on the GSM8K benchmark of math word problems, surpassing even finetuned GPT-3 with a verifier.”
To all recent commenters: I intend to reply to most of these over the next couple of days. Please be patient!
unitroot (#37): I deny that this new answer to question 1 is “much better” or even any better at all. It still fails to reason to the correct answer, namely that cashews cannot be a Giffen good. It fails, apparently to even imagine that such reasoning is possible. It makes absolutely no attempt to draw any meaningful inferences from the given facts. This is a zero point answer by any reasonable standard.
Ulrich (#36): This is a first class in microeconomics. Students have not encountered the notion of a mixed strategy equilibrium. But there is in fact a perfectly good pure-strategy equilibrium where exactly 100 people stand in line; after the free coffee policy there is a new pure-strategy equilibrium where more people stand in line. In the case of mixed strategies, the same thing happens, with some statistical variation around the outcome. If some student managed to come up with a mixed strategy story, I’d be delighted, but the main thing the question calls for is the realization that a) free coffee makes the line longer and b) it makes the line so much longer that all benefits (at least in expectation) are dissipated. Any answer that includes recognition of that key point is at least a pretty good answer. Any answer that ignores it is a terrible answer. There is no plausible score for GPT-4’s answer other than flat zero.
Another problem with #2: The “correct” answer assumes that the line is 100 people because that’s the point at which the cost of being in the line is equal to the value gained by being able to buy raspberries. However, it could be (and given that there are 100 people queueing to buy price-controlled raspberries, probably is) the case that the queue is 100 people because there are only enough raspberries available for 100 people, so the 101st person only gets a coffee and doesn’t get the value of being able to buy raspberries like the 100th person does.
Sam (#35):
1) The new answer to question 7 is as bad as the old one. It misses the key point, which is that inelasticity of demand is evidence of the *absence* of collusion, because profit-maximizing behavior on the part of a cartel leads to consumption on the elastic part of the demand curve.
2) The new answer to question 1 is also as bad as the old one. It is bad for the same reason that the answer reported by unitroot is bad. (See my answer #41.)
Isn’t Q5 a case for bundling?
Fence allows us to bundle rides together since customers will value each ride differently.
Addendum to my previous comment: In the case where the raspberries are limited, then the coffee policy doesn’t increase the length of the queue, but depending on how the queue formed it might increase the length of time people spend queueing.
If the shop opens at 9am and loitering is forbidden, then who gets to be in the 100 person queue is basically a lottery and the social cost is $25. On the other hand if people can queue starting as soon as they want, they’ll arrive sufficiently early that the cost of queueing is equal to the value of buying the raspberries. In this case supplying the coffee will have a social cost of $100, but because people are queuing for longer, not because the queue has more people in it.
While you admit in comment #15 that your answer for Q2 is wrong, I think it’s actually right.
Coffee will not change the quantity of raspberries produced and sold, so the total number of people who will get raspberries (and therefore stand in the queue) will still be 100.
What will change is the duration for which one has to stand in the queue. Let’s assume all the raspberries are delivered and quickly sold at 12:00 but people have to come to the queue at 11:30 to get any. Then with the coffee, they might have to come to the queue at 11:15 instead. So the same 100 people with come, but they will come earlier.
If we instead assume that raspberries are sold at a constant rate over time, the same kind of thing applies. The queue will be longer because the person who buys the raspberries at 15:00 will now come at 14:15 instead of 14:30. So you will have 45min worth of people in the queue at a time instead of 30min. The number of people in the queue at a single time will be greater, but the total number of people over the course of a day will still be 100.
Not sure I agree with the answer for question 2. Coffee will increase productivity significantly and its unlikely in such an economy that individuals are capturing all of the gains from their increased productivity, so it probably is a social benefit not a social cost.
Prompt:
You’re an expert in economics. Can you answer the following economics problem? “When the price of peanuts rises, Alice consumes fewer cashews. Can you determine whether cashews are a Giffen good for Alice?”
Answer:
In order to determine whether cashews are a Giffen good for Alice, we need to understand the concept of a Giffen good and the relationship between the price of peanuts and the consumption of cashews.
A Giffen good is a special type of inferior good, for which the demand increases when the price increases, and vice versa. This phenomenon contradicts the basic law of demand, which states that as the price of a good increases, the quantity demanded decreases. Giffen goods are extremely rare, and their existence is a matter of debate among economists.
In this case, when the price of peanuts rises, Alice consumes fewer cashews. This information alone does not allow us to determine whether cashews are a Giffen good for Alice. In order to establish if cashews are a Giffen good, we would need to observe Alice’s behavior when the price of cashews changes. Specifically, we would need to observe that when the price of cashews increases, Alice consumes more cashews.
Based on the given information, we can only conclude that there is a relationship between the price of peanuts and the consumption of cashews for Alice. The price of peanuts might affect Alice’s budget constraint and consumption choices, but we cannot determine whether cashews are a Giffen good for Alice without further information.
Prompt #2:
Can you infer Alice’s consumption behavior if cashew’s price were to rise? Make an argument to support your inference.
Answer:
Given the limited information, we can attempt to infer Alice’s consumption behavior regarding cashews when their price rises by considering the relationship between peanuts and cashews in her consumption pattern. We know that when the price of peanuts rises, Alice consumes fewer cashews. This suggests that peanuts and cashews could be substitutes or complements in Alice’s consumption.
1. If peanuts and cashews are substitutes, it means that Alice consumes one in place of the other. In this case, when the price of peanuts rises, we would expect Alice to consume more cashews because she might be replacing the more expensive peanuts with cashews. However, since we know that Alice consumes fewer cashews when the price of peanuts rises, it is less likely that peanuts and cashews are substitutes for her. If the price of cashews were to rise, we might expect Alice to reduce her consumption of cashews and potentially consume more peanuts or other substitutes, if any.
2. If peanuts and cashews are complements, it means that Alice consumes them together. In this case, when the price of peanuts rises, Alice might consume fewer cashews because she consumes less of the complementary good (peanuts) due to its higher price. This scenario aligns with the given information. If the price of cashews were to rise, we might expect Alice to reduce her consumption of both cashews and peanuts, as the overall cost of consuming these complementary goods increases.
While we cannot definitively determine Alice’s consumption behavior if the price of cashews were to rise, the complementary relationship between peanuts and cashews seems to better align with the given information. In this case, we might infer that Alice would reduce her consumption of cashews when their price increases. However, further information about Alice’s preferences and consumption patterns would be needed for a more accurate analysis.
Prompt #3
Based on your inference what can you say about the original question? Are cashews a Giffen good for Alice?
Answer:
Based on our inference about Alice’s consumption behavior, it is unlikely that cashews are a Giffen good for her. Recall that a Giffen good is a unique type of inferior good for which demand increases when the price increases, and vice versa. This behavior contradicts the basic law of demand.
Our analysis suggests that peanuts and cashews could be complements in Alice’s consumption pattern, as she consumes fewer cashews when the price of peanuts rises. If this inference is accurate, and the price of cashews were to rise, we might expect Alice to reduce her consumption of cashews. This response aligns with the typical law of demand and does not exhibit the characteristics of a Giffen good.
It is important to note that our analysis is based on limited information and assumptions about Alice’s consumption behavior. Further information about Alice’s preferences and consumption patterns would be needed for a more accurate determination. However, based on the available information, it is unlikely that cashews are a Giffen good for Alice.
My thoughts:
As the paper Sparks of AGI has demonstrated, GPT4 performs better and might arrive at a correct answer if you do a bit of back and forth, asking it followup questions regarding its previous replies. Don’t expect to get a good answer in one shot. Also, giving a rich context before the actual question, helps a lot.
Humans think in loops, before we provide a definite answer to a difficult problem we go back and evaluate our thoughts and identify issues in our reasoning. LLMs can’t do that, they just a provide an answer in a single forward pass. We’d fail too if we thought like that. The only way to “simulate” loops in the bot’s thinking is to ask it follow up questions in order to include its previous answers in the context.
I don’t understand #2 at all. How do I know to what degree, if at all, the line’s length will increase?
Suppose my society consists of hyper productive people, for whom the wait from each person in front of them costs $1000. In this example, even with 75c of free coffee, the equilibrium for the line is still 100 people, maybe 101. Person 102 was at least $1000 past indifference, and is now still at least $999.25 past indifference. Social cost here should be about $0.25*100.
Alternate extreme – unproductive society where waiting behind a person costs $.001 Now, person #850 is indifferent, and the cost is $0.25*850 plus the cost of the extra time wasted in like, which is well over $200.
What am I missing, or have it misunderstood the situation somehow? The price of raspberries is different in those two worlds, but I don’t think that matters.
Johnny (#50): In your alternate example, the cost of the coffee is .25 times 850 plus the cost of the extra time wasted in line, which is .75 times 850, for a total of $850. (Subject to small adjustments due to integer constraints.)
In your first example, you seem to be worrying about discontinuities due to integer constraints (so that adding one person to the line can increase the cost of waiting by more than the value of a cup of coffee). My students have been trained not to do this, but in all such cases they can still earn full credit if they ignore that training and give a good answer that shows understanding of the issues.
You’re telling a coherent story that recognizes the issues. The bot takes it for granted that the line length stays fixed, which ignores the issues entirely. There are (always) good answers that differ from my answers because of different (but still reasonable) assumptions. The bot did not offer such an answer.
Qwerty (#43 and #46): I agree entirely with your story in #46. Benefits of linestanding are 100% dissipated UNLESS someone is granted a property right to a place in line via some mechanism that you can’t compete for (e.g. a lottery). This is a point that I hope my students understand perfectly well. In fact, I could easily imagine asking a two-part question where the second part asks what happens if places in line are allocated by lottery. Your answer is a full-credit answer that is better than the answer I was looking for.
Leo (#48): Ha! I’d have been delighted to find this argument on a student exam (provided that it recognized, as yours clearly does) that we have to assume that some of the benefits of productivity are external.
Steve #49
No, he is not worrying about discontinuities.
He is saying that the answer is not knowable. It can go from $25 to well over $200 depending on the cost of waiting, which we are not told.
He gives an example where it would be $25 and one where it would be $200 to make this clearer.
As i was writing the integer discontinuity thing, I was thinking it felt strange, so I get that.
I have two questions remaining.
1. Why is time wasted .75*850?
The first 100 people are already wasting their time due to the raspberry price control. The social cost of their line standing isn’t due to the coffee policy. Only the last person in the new, longer line is indifferent, wasting exactly .75 worth of extra time. It seems like .75*750 would be an upper bound for line standing waste.
2. Where does $100 come from?
I didn’t follow the “all the value is absorbed” so the cost of the policy is $100 intuition at all. It seems to me that the cost can be anywhere from about $25, to infinite, depending on how much 75c is worth to the population. The lower the opportunity cost of their linestanding, the more the line grows, the more coffee necessary, and the more 25c units wasted. The higher the cost of their time, the less 25c units wasted (from the first example, say the line becomes 100.00075 people long. linestanding cost from coffee = .75, coffee cost itself = roughly $25)
I agree completely the bot gets a zero. I’m just interested in the economics.
If in #2 everyone in the country is identical, including having identical preferences for waiting in line, how would offering a free cup of copy alter the length of the line? Wouldn’t everyone already be in line since they all have identical preferences and face the same tradeoff?
I suspect that these questions were provided to GPT-4 without any context, which generally is not a very good way to use a language model. With basic prompting to inform GPT-4 of what it was trying to accomplish and what sort of exam to expect (nothing the students themselves wouldn’t know), it seemed capable of getting most points of the first 5 questions, at which point I stopped.
The goal here is to determine if students can use this tool to get comparable answers, and we can be fairly certain that some of them will prompt it effectively using the knowledge that they have available. The only thing that we can say from this is that students who copy and paste questions into it without providing context are not going to get very good results.
Perhaps this my lack of fundamental understanding, I’m curious to understand –
Why must the line grow?
If 100 people wait in line each day. At the end of the day there are 0 people in line and 100 people enjoying raspberries.
If everyone is given a coffee in line-100 people drink coffee whilst waiting for their raspberries.
The social cost would be – time spent in line * productivity opportunity for identical person * 100 – 100*$1
I’d love someone to explain why I’m wrong please!
@Mark No, the line has an equilibrium length, where the cost of waiting has now matched the benefit of being able to buy raspberries. In the example of a 100 person line, the 100th person, who must wait behind 99 people, decides to wait, but the 101st person, who would have to wait behind 100 people, decides it’s not worth it.
On question 2: hang on a second! If the government spontaneously hands out free coffee to the 100 people who are standing in line (which seems to me to be a perfectly plausible interpretation given the wording of the question), then the simplistic Chat GPT answer is correct. Conversely, if we are to assume that everyone is aware the government will be handing out free coffee before anyone gets their coffee, then of course the line will dynamically adjust as per your answer. But the question states that this is happening every day, so in the latter case the social cost is infinite.
I would suggest changing the wording to “the government announces it will start handing out free coffee” and “what is the social cost per day” to make the assumptions less ambiguous.
Johnny,
Yeah, I figured that once I submitted it. They have the same preferences, but they don’t face the same wait times.
This is just another note to say that I still owe responses to several commenters, and still hope to get to them in the next few days. My responses are NOT in the same order as the comments I’m responding to, so if it appears that I skipped over your comment, I’m probably still planning to come back to it.
What they need to do is feed chat gpt all your writings/books (excluding explicit exam answers) then see if it can pass.
Argosy (#60): I think your interpretation is hard to defend. The problem specifies that every day 100 people wait in line, and then says that the government decides to had out free coffee to the people standing in line. Your interpretation is that the government does this once, without warning, and without creating any expectation that it will happen again. I think that a much more natural interpretation is that the government will now supply coffee on a regular basis, but even if you insist on interpreting this as a one-time thing, there is at least a good chance that some it creates some expectations for the future.
My students have been trained (via vast amounts of homework) to avoid interpretations that render questions trivially easy to answer when there are plausible interpretations that make the questions interesting. But I agree with you that your alternate wording would have made this a better question.
Joe (#58): There is a reason why the line is 100 people long and not 101 — standing in line behind 100 people is more unpleasant than it’s worth. Free coffee reduces the unpleasntness and tempts a 101st person into the line.
Justin (#8): The answer you got from the bot still seems to me to be worth zero points; it misses the key point that inelastic demand is (under very general circumstances) evidence of the *absence* of collusion.
Jeff (#13): See my post number 64.
Ed (#24): You are right and I have corrected this. But while I would give full credit for this answer, it is still not really the right answer — because it ignores the fact that the monopolist, not wanting to lose his customer base, will mitigate the price increase.
ZachH (#30): You are absolutely right. The answer I see most often from students is the one I’ve given here, and I give full credit for it even though it omits the effect you’ve described. If anyone ever gave a full correct answer, I would be overjoyed. But the “official” answer (that is, the answer that I have declared official) indicates enough understanding that I give full credit for it. If I didn’t, the question would be far too hard for students at this level. (There are other incomplete answers that would also get full credit, as long as they recognize the fundamental fact that a loss in CS at the grocery store must lower the demand for housing by that amount.)
Nick (#22): ” But I think many PhD economists would fail e.g. on #2 which requires the insight that the line can grow or shrink. ”
I think this is as implausible as suggesting that in a problem about billiard balls moving a table, that many PhD physicists would fail to find the insight that a ball, upon impact with another, can change its trajectory.
So I think you are wrong. I also think that if you are right, we are doomed. PhD economists often influence public policy. If they don’t know that the benefits of free goods are largely dissipated (and completely dissipated in the benchmark case where everyone is identical) they are going to give truly terrible, and extremly expensive, advice to the legislatures.
Caspar (#27): “Why must the social cost in Q2 equal or exceed $100? Suppose each person in this population is such that they would pay at most $0.50 to wait one minute less in line, and each additional person in line increases the wait by exactly one minute. Then the free coffee, valued at $0.75, would add one person to the line – after that the wait has already become too long to make it worth the coffee. So, the social cost then is £25.25 – much less than $100 and much closer to GPT’s answer. Or have I completely missed something?”
Every day 100 people stand in line. They all have to be indifferent between standing in line and staying home. If they can’t make themselves indifferent by making the line longer, then they will do it by showing up earlier to compete for the places in the front of the line. The free coffee has to intensify the competition, whatever form that competition takes, until all benefits are dissipated.
L (#28) See my response to Caspar in the post directly above this one.
L (#29): “For question #3, I don’t think it makes sense to assume a wealth effect coefficient of 1 (whether that’s 1 units or $1/unit). Probably this question should be presented in terms of isoutility curves.”
I don’t understand what you’re thinking. I’ve assumed zero wealth effect on this question, as I would expect my students to do. (A student who thought more deeply and allowed nonzero wealth effects would delight me, but that’s surely not expected and probably not appropriate, since there is a lot more to life in Fredonia than just buying groceries.
Sebastian (#31): Something has to happen to make people indifferent between standing in line and staying home; otherwise more people will join the line until indifference is achieved. This must be true for everyone in line, even the first person, who presumably nabbed the first slot by getting out of bed at 5AM. With free coffee, he’ll have to get up earlier. Either this, or the line will lengthen, or something else will happen to make each and every person in line no happier than he could be at home. So the free coffee has no benefits.
L (#32): If you take away $20 worth of the CS I can earn by living in Fredonia, then I am willing to pay $20 less than before to live in Fredonia. (This is what consumer surplus means, absent wealth effects.) To say that I am willing to pay $20 less to live there is the same thing as saying that my demand curve for housing there drops vertically by $20. There is no escaping any of this.
Matthew Barnett (#33): I am pretty close to agnostic about what AI will be able to do in the year 2028. I am pretty sure I’ve learned quite a bit in the last week about what it can’t do in the year 2023.
Johnny (#50): See my posts #71 and #74.
Steve, are you still unimpressed by #19 given a fact that GPT-4 did not have access to this blog post in forming its response?
It seems you agree that it has given a correct answer? So is it right to say that all that is in doubt is the provenance of that answer?
And given the idea in #23, #38 and #39, are you at all curious to see how it fares on these questions using prompts that:
a) prime the model to answer as a more sophisticated economic thinker
b) encourage the model to break down its thinking more, using a series of intermediate reasoning steps
Thanks a lot for your answer (#74) to my comment (#31).
But actually, I still don’t see why you think, that people must be indifferent. To make things more concrete, let us consider pure strategy equilibria in a “line forming game”.
Assume the following utility function of a person that stands at position k in the line (without coffee) and 0 utility if staying at home:
u(k) = 100.1 – k
Utility goes down with k, because people having a later position in the line have to wait longer.
So the 100th person in the line has still positive utility:
u(100) = 0.1
but the next person would have negative utility:
u(101) = -0.9
So it is clear that there is only one pure strategy equilibrium with exactly 100 people in the line.
Now with coffee assume that utility of everybody in the line increases by 0.75. This means we now have the utility function:
u(k) = 100.85 -k.
We now find:
u(100) = 0.85
and
u(101) = -0.15
Still there is only a pure strategy equilibrium with exactly 100 persons in the line.
So given this utility specification, coffee does not increase the line length and in none of the two cases there is any indifferent person. The 100 persons in the line always prefer standing in the line, but the 101th person always strictly prefers to stay at home.
Mixed strategy equilibria might be more complicated but in #42 you essentially say that we can look at pure equilibria and students don’t know mixed strategy equilibria yet.
Sebastian Kranz (#79): If standing in line is more desirable than staying home, then the competition for places in line will increase. This can take the form of line-lengthening or it can take the form of getting up earlier in the morning to nab an early spot in the line, or it can take the form of fistfighting. As long as at least one of these things can vary continuously (e.g. the time you get out of bed in the morning) then competition must drive us to indifference. The answer I gave in the post is, to my mind, a full credit answer, even though it ignores the subtleties you are raising. But even given those subtleties, the benefits of waiting in line have to be fully dissipated in reasonable scenarios.
imatoama (#78): In #19,the bot gave a good correct answer, having been primed to answer as Steven E. Landsburg would. I am sure that if were primed to answer as Donald J. Trump would, we’d have gotten a different (and thoroughly incoherent) answer.
That is mildly impressive. I’d be more impressed if the bot could distinguish between the *right* answer and the *wrong* answer, as opposed to just telling us what various people would say.
grizzlyking (#45): The simplest assumptions is that all demanders are identical and/or that all rides are identical. I am happy if students answer under the simplest assumptions (as long as those assumptions are within reason and don’t trivialize the problem). Had a student brought up bundling, I’d have been delighted, but it’s not necessary to earn full credit.
James (#57):”I suspect that these questions were provided to GPT-4 without any context, which generally is not a very good way to use a language model.”
But of course this very much limits the usefulness of the language model.
If a policymaker is deciding whether to hand out free coffee to people standing in lines (or to spend $40 million dollars constructing an aquarium with free admission), the question he should be asking is not “What does Landsburg say will happen?” or “What does Biden say will happen?” or “What does Tucker Carlson say will happen?” but “What will happen?”. It is not nearly so useful to know what various people would say as it is to know which of the things they say is correct. And it appears that at least in its current form, GPT-4 is quite abysmal at that.
johnny (#50): What you are missing is that regardless of how productive people are, competing for raspberries has to be exactly as attractive as not competing for raspberries (otherwise people opt into or out of the competition until the desirability of being in and the desirability of being out are equal).
If this is not achievable by changes in the line length (because of integer consraints) then people will achieve it in other ways, by getting out of bed earlier to nab a space near the front of the line for example. This happens until everyone is just as happy as everyone else.
Therefore free coffee cannot make anyone happier. The social cost of free coffee is the full cost of producing the coffee. If competition intensifies in a way that does not lengthen the line, that comes to $100. If the line lengthens, then it’s more than $100.
Justas (#47): You have given a full credit answer that is in many ways better than my own.
Althea Delwiche (#38 and #39): See my comments #81 and #83.
Nick (#23): “I think it’s actually pretty impressive that when prompted to answer it like it’s a standard Econ 101 exam, it does what a standard Econ 101 student does —”
The problem with this is that policymakers don’t need to know what a standard Econ 101 student does, and doesn’t need to know what Steven Landsburg says. The policymaker needs to know what is right, regardless of who says it, and the bot seems to offer no guidance at all on that.
Jeremy (#34):
“From my understanding, the GPT-4 answer is saying that you can model the price of the parking as a change in the demand curve. I think this is true? At a fixed price, we can calculate a modified Q*(P) using the recurrence relation Q*(P)=Q(P + PARKING_COST / Q*(P)), and calculate monopoly pricing for the store using Q*? I agree that it’s not giving the details of how you would determine the adjustment to the demand curve, but it doesn’t seem wrong in what it claimed.”
I have no idea where you are getting your equation. It doesn’t even make sense, because P is measured in dollars per item, whereas PARKING_COST is measured in dollars. You are adding two things with different units, so we already know that what you’ve got is wrong before going any further.
Jonatan (#54) and Johnny (#55): i think that the answers to your questionsa are in my posts #84, #80, #74, #71.
Chris (#49): Okay, let’s see here.
The bot says (after much wordiness) that “we cannot determine whether cashews are a Giffen good for Alice without further information”. This is dead wrong. Nothing in all the words that appear before this indicates that the bot has any idea how to think about this question. After many prompts it comes around to “it is unlikely that cashews are a Giffen good for Alice”, which means that it does not believe it can definitively rule out the Giffen possibility. Still zero points.
Steve #84
“The social cost of free coffee is the full cost of producing the coffee. If competition intensifies in a way that does not lengthen the line, that comes to $100. If the line lengthens, then it’s more than $100.”
No. If the line is not lengthened, it has 100 people in it.
And in that case its true that:
Social cost = Government cost – Value to people
Social cost = $100 – $75 = $25
unless you have some other definition of social cost.
Jonatan: The $25 benefit you’re counting is fully dissipated through competition for spaces near the front of the line. If the line does not lengthen, the social cost of the coffee is the cost of producing it, i.e. $100.
Hmm.
Is it a line of length 100 that fills up at one point during the morning, and people are not allowed to join later.
Or is it a line that is of some shorter length (eg 10), and then as one person buys raspberries, another person enters the line. And a total of 100 people stand in the line at some point during the day.
Jonatan (#93)L None of that matters. All that matters is that, regardless of how the queuing takes place, it can’t be more desirable to wait for raspberries than it is to NOT wait for raspberries. If something (e.g. free coffee) makes waiting more desirable, then something else has to happen to make waiting LESS desirable, by the same amount. What that “something” is depends on details of how the line forms, but the key insight is that those details are irrelevant. One way or another, the benefit of the coffee has to be offset by some new cost.
Steve Landsburg (#775): Right, I made an elementary mistake (I was thinking of the decision to stay and buy a home, vs stay and buy no home, rather than stay vs not stay). In that case, why is the demand curve shifting down 20 units and not to the left by $20? (which would be down 80 units)
A leftward shift would result in:
P = 100 – 4(P + 20)
P = Q = 4
L (#95): We ordinarily plot price on the vertical axis. There seems to be a typo in your first equation, which has two P’s and no Q. But I can’t find any way to intepret that equation that makes sense to me.
(#80) I agree that it seems a reasonable assumption that the line forming process is such that higher effort is required to be earlier in the line and then indeed in plausible models all rents would dissipate even if the line does not get longer. (But one could make the process more efficient, e.g. give away lottery tickets with the line number to get rid of wasteful “getting up early” costs). I still feel that answering the question boils down to think careful about reasonable implicit assumptions not explicitly stated in the exercise. (Which is a very nice stlye of exercises). I tried Bing Chat with a slightly modified prompt:
“Please solve the following economics exercise. Afterward check if you made implicit assumptions in your solution and state all assumptions explicitly. Then discuss how the results could change if you change one of the implicit assumptions.
Exercise: In a country where everyone is identical, 100 people wait in line each day to buy raspberries at a controlled price. The government has decided to hand out free coffee to the people standing in line. The coffee costs the government $1 per cup, but the people in line value that coffee at only 75 cents per cup. What is the social cost of providing the coffee?”
Here is Bing Chats answer: “This is Bing. I can try to help you with the exercise, but I cannot guarantee the correctness or completeness of my answer. Here is my attempt:
To solve the exercise, we need to compare the social benefit and the social cost of providing the coffee. The social benefit is the total value that the people in line get from the coffee, which is 75 cents per cup times 100 people, or $75. The social cost is the total cost that the government incurs from providing the coffee, which is $1 per cup times 100 people, or $100. Therefore, the social cost of providing the coffee is $100 – $75 = $25.
One implicit assumption that I made in my solution is that the demand for raspberries is fixed and does not depend on the availability of coffee. Another implicit assumption is that the supply of raspberries is fixed and does not depend on the cost of coffee. A third implicit assumption is that there are no externalities or spillover effects from providing coffee, such as environmental impacts or health effects.
If we change one of these implicit assumptions, the results could change. For example, if we assume that the demand for raspberries increases when people have coffee, then the social benefit of providing coffee could be higher than $75, because people would buy more raspberries and get more utility from them. Alternatively, if we assume that the supply of raspberries decreases when the government spends more on coffee, then the social cost of providing coffee could be higher than $100, because there would be less raspberries available and their price would increase.”
You probably would not give full points, but still zero? At least GPT seems quite creative in thinking about the implicit assumptions. I think the reasoning that coffee and raspberries could be complements and thus total surplus might increase is quite nice. That might also provide a reason why the Government decides to provide the coffee at the line… (You might think if they are complements consumers just could buy the coffee, but then they would have two wait in two lines and just selling coffee to people in the line might be infeasible or forbidden…)
Steve Landsburg (#96): The equation without Q comes from setting supply = demand:
before:
Q = P
Q = 100 – 4P
so
P = 100 – 4P
if the willingness-to-pay goes up by $20, then the new demand should be
Q = 100 – 4(P + 20)
(“price” goes up by $20), not:
Q + 20 = 100 – 4P
If you solve with the former equation you get P = 100 – 4(P + 20) = 4. If you solve with the latter, you get P = 80 – 4P = 16.
Sebastian (#97): I still think this is a zero-credit answer.
1) It ignores the fact that the quantity of raspberries is fixed by the supply curve and the ceiling price, and therefore thinks that people might be able to buy more raspberries.
2) More importantly, it misses the main point, which is that the benefits of the coffee have to be dissipated (unless, as you say, we allocate places in line by something like a lottery — though even then, I expect resources to be consumed in attempts to manipulate the lottery). The idea that the coffee has a social value of 75 cents per cup is only tenable under very restrictive assumptions, whereas the student (or the bot) that submitted this answer seems to have missed that key point entirely.
L:
You wrote:
“if the willingness-to-pay goes up by $20, then the new demand should be Q = 100 – 4(P + 20)”
I assume you mean that willingness to pay goes down by $20, not up. I agree with your equation.
Wow, I think *as a student* I would’ve thought about the line growing for Question 2, but as an adult I might have jumped right into the “Is it $1 or 25 cents?” trap.
So two things, Steve:
1) I think you spelled this out a little in response to someone else, but just to be sure: You’re assuming that the first person in line waits just as long to get the raspberries as the 100th person, right? The line grows at the same rate as it will eventually start moving, once the gov’t starts the sale each morning?
2) Forget lines, just focus on the “trap”: Suppose the government pays $100 to create 100 cups of coffee that it randomly hands out to people, and they don’t adjust their behavior because they didn’t see it coming. They each value the coffee at 75 cents. Are you saying the social cost is $100 or $25?
Bob Murphy (#101):
1) I am asserting that because everyone is identical, everyone must bear the same cost of waiting. This could be because they all spend the same amount of time in line, or it could be because some of them get out of bed earlier to nab spaces near the front [thus trading sleep for less waiting time] or any number of other things. But in equilibrium, if I my strategy is less costly than yours, then you will switch strategies, and if waiting in line is preferable to just not buying raspberries, then people will enter the line, increasing either the physical length of the line, or the amount of sleep you have to sacrifice, or something else.
2) If nobody sees this coming, then the social cost is $25.
I’ve gotten interested in endocrinology in recent years. I’ve tried repeatedly to ask chatgpt about various cases, and any time the question goes beyond the most basic, plain-vanilla 101 stuff, I found that the answer is terribly wrong (usually ignoring key facts) and sometimes contradictory, with the second paragraph of the answer saying the exact opposite of the first.
Mate, I’ve been doing similar tests with undergraduate level economics and Chat GPT-4 is getting a very surprising high level of answers correct. These are mainly mathematical economic questions, however the concepts behind them are very high level and complex theories.
Also Sage Publications recently released data which shows that GPT-4 ranks in the 91st percentile for Microeconomics and the 99th percentile for Macroeconomics…
The answer to question one seems better now with ChatGPT 4:
No, we can’t definitively determine whether cashews are a Giffen good for Alice based on the information provided. A Giffen good is a product that people consume more of as the price rises, violating the basic laws of demand in economics. This is very rare and is typically associated with goods that constitute a large portion of the consumer’s budget and for which there are no close substitutes.
The information given – that when the price of peanuts (a different good) rises, Alice consumes fewer cashews – suggests that for Alice, cashews and peanuts might be substitute goods. This means that as the price of peanuts increases, Alice turns to cashews as an alternative, but for some reason (possibly budget constraints), she actually consumes fewer cashews. However, this doesn’t tell us anything about what would happen to Alice’s consumption of cashews if their own price were to change, which is what we’d need to know to determine whether they’re a Giffen good for her.
To clarify if cashews are a Giffen good for Alice, we would need to observe Alice’s behavior when the price of cashews themselves increases. If Alice buys more cashews when the price of cashews increases (and all other things are held constant), then we could say that cashews are a Giffen good for Alice.
EJ: That answer is absolutely worth zero points.