1. In a given industry located in the town of Teahupo’o all firms have access to the same technology. The cost curve for Tikei’s firm is: TC = 3q2, where q is the output of Tikei’s firm. Marginal cost is MC = 6q.
Initially, there are 60 firms in the industry (Tikei’s firm + Mako’s firm + Moana’s firm + Vanea’s firm + 56 other firms). The 60 firms in the industry are identical in every way.
a) Find the supply curve of Tikei’s firm and of the entire industry in the Short Run. Hint 1: Tikei’s firm supply curve should be of the form q = f(P) (please see footnote). Hint 2: The industry supply curve should be of the form Q= f (P). Be thorough to get full credit. Make sure you show: (a) How to go from the firm’s MC curve to the firm’s supply curve. (b) How you go from one firm’s (Tikei’s firm) supply curve to the industry’s supply curve (i.e., the town of Teahupo’o’s supply curve).
b) If the demand curve for the industry is: Q = 504 - 2P find the short run competitive equilibrium price, quantity supplied by Tikei’s firm, and total industry supply. Find the producer surplus and consumer surplus for the market level graph (both graphically and numerically).
c) The government of Teahupo’o decides to intervene in the market by buying 72 units no matter what the price is. The demand faced by the industry is now Q = 576 -2P. Find the new short run equilibrium price, quantity supplied per firm, and industry supply. Graph the market equilibrium. Make sure to label your axes, your curves, and find the relevant intercepts and intersections. Also point out how much the government buys and how much consumers buy on your graph.
q=f(P) means it is of a form where q is equal to some function of P. For example, the supply curve could look like this: q=88P or q=66+P or q= P/30 or q=80+3P2, etc. These are not the answer to the question but examples of what q=f(P) means.
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