02 Jun Question Try your best at each problem. Problems sets will
Question
Try your best at each problem. Problems sets will be graded on e?ort as well as correctness.
Write clearly.
Show all your work and label graphs!
If you choose to work in groups, each student must hand in their own problem set.
When I say “brie?y”, I mean one or two sentences. I don’t expect (or want) an essay.
1.1 Perfect Competition
Problem
Nucky Thompson is a bootlegger in Atlantic City area, where he sells bootlegged alcohol to local underground speakeasies on the boardwalk. There are a total of N = 10 identical speakeasies which have the cost function C(q) = 10 + 5q + q 2 , where q is the total number of bottles of booze sold at an individual bar per night. The overall demand for alcohol in AC per night is given by the inverse
demand curve P (Q) = 511 ? 2Q, where Q is the total quantity demanded. Assume that the market is perfectly competitive at the speakeasy level.
(a) Find the marginal cost for each speakeasy (M C(q)). (Hint: use di?erentiation)
(b) Write down the speakeasy’s pro?t function, ?(q).
(d) Solve for the short-run optimal quantity of bottles sold by each speakeasy (q?).
(e) Solve for the short-run equilibrium market price and total quantity (P ?, Q?).
(f) Solve for each speakeasy’s pro?t.
(g) Is the market in long-run equilibrium? Why or why not? What will happen to the number of speakeasies on the boardwalk in the long-run?
(h) Calculate producer, consumer, and total surplus (Hint: the market supply curve (i.e., marginal cost) is given by M C(Q) = 5 + Q ).
1.2
Reality Check
Please state possible reasons for and against the following markets being perfectly competitive. That is, what assumptions of perfect competition hold in these markets and what assumptions fail?
(a) Agricultural markets (e.g., the market for corn).
(b) The food cart market in a large city (e.g., DC) .
(c) A large online platform for di?erent sellers to sell their product (e.g., Amazon marketplace).
2.1
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