1. Suppose you are given the following information about a particular industry 1000 - p Market demand C(y) = 100 + yz Each firm's cost function 1.1 [7 points] Given an output price of p, find the profit-maximizing quantity of output for a perfectly competitive firm in this industry. (That is, derive the individual supply function.) 1.2 [8 points] Assume that there are 20 identical firms active in this industry and that no firm can enter the industry. Find the output supplied by each firm, the profit of each firm, the equilibrium price, and the equilibrium quantity. (Hint: you need to use the individual supply function you found in 1.1 and the market clearing condition, that is, total supply must be equal to total demand.) 1.3 [8 points] Assume now that there are no barriers to entry, so that the market is characterized by perfect competition. New entrants are identical to incumbent firms. What is the long-run equilibrium price? The total industry output? The output of each firm? The number of firms? The profits of each firm? (Hint: you need to use the individual supply function you found in 1.1, the market clearing condition, that is, total supply must be equal to total demand, and the zero-profit condition.) 1.4 [5 points] Compute the average cost and the marginal cost of each firm in the long-run equilibrium. (Hint: First derive an expression for the average cost and the marginal cost, as a function of the individual output y; then, replace y with the equilibrium value of the individual output you found in 1.3.) 1.5 [2 points] How do the average and marginal cost you computed in 1.4 compare? Is this a coincidence