Two weeks ago, I posted the first half of the honors exam that I administered last spring at Oberlin college. I am following up today with the second half. Once again, I’ve translated some of the questions from economese to English, but am fairly confident that nothing significant has been lost in the translation. This starts with Question 6:
Question 6. When Eve works, she produces exactly one apple per hour. Adam is completely unproductive and can produce nothing at all. Eve’s income is taxed at a flat percentage rate, with the proceeds delivered to Adam. What determines the optimal tax rate? What does “optimal” mean here, and what philosophical justification would many economists give for adopting this tax rate?
To make the problem concrete, you can assume that both Adam and Eve, if it were both possible and necessary, would be willing to work up to 1 hour for 1 apple, up to 2 hours for 4 apples, up to 3 hours for 9 apples, and up to x hours for x2 apples. Now what is the optimal tax rate? (Your answer should be a number.)
Question 7. Jack and Jill play a game. First, each flips a coin. After seeing their own coins (but not each others’), each player (separately) says either “Red” or “Black”. If they name opposite colors, then the Black-sayer gets $4 and the Red-sayer gets nothing. If both say Black, then they both get either $5 (if both flipped heads) or $10 (otherwise). If they both say Red, then they both get either nothing (if both flipped heads) or $20 (otherwise). Assume both players play optimally. If Jack flips heads, what is the probability that he says “Black”? What if Jack flips tails?
Edited to add (in response to a comment from Ron): Assume that neither Jack nor Jill says either Red or Black with probability zero.
Question 8. The five Dukes of Earl are scheduled to arrive at the royal palace on each of the first five days of May. Duke One is scheduled to arrive on the first day of May, Duke Two on the second, etc. Each Duke, upon arrival, can either kill the king or support the king. If he kills the king, he takes the king’s place, becomes the new king, and awaits the next Duke’s arrival. If he supports the king, all subsequent Dukes cancel their visits. A Duke’s first priority is to remain alive, and his second priority is to become king. Who is king on May 6?
Question 9. Suppose the government mails every taxpayer a check for $300. Under a variety of assumptions, discuss the short run and long run effects on a variety of economic variables such as output, employment, the interest rate and the trade balance.
Question 10. Suppose you want to study the effect of education on wages. You have wage data for 100 pairs of siblings, where one member of each pair attended college and one didn’t. Based on these data, you make some estimates. Now you learn that all 100 pairs of siblings are in fact twins. Does this increase or decrease your confidence in your results? Make some arguments in both directions.