Question

Consider a perfectly competitive market with many identical firms. Each firm has a long-run marginal cost function given by LRMC(y) = y ^2 + 1. We do not know the firms’ LRAT C function, but we know that at a quantity of 3 it is equal to LRMC. In other words: LRAT C(3) = LRMC(3). (a) Find an expression for an individual firm’s long-run inverse supply curve: this will be p as a function of y. Note that it will not exist for some values of y. (b) Find an expression for an individual firm’s long-run supply curve: this will be y as a function of p. (You simply need to rearrange the inverse supply curve from part (a).) Note that it will not exist for some values of p. (c) Find an expression for the long-run market supply curve when there are n firms operating. This will be output as a function of p and n, note that it will not exist for some values of p. (d) In long-run equilibrium, total market output is 180. What is the market price and how many firms are operating? 2. A monopolist faces a market demand curve p(y) = 210−4y and initially faces constant marginal cost MC = 10. (a) Find the profit-maximizing quantity and compute the monopolist’s total revenue. (b) Suppose that the monopolist’s marginal cost increases to MC = 20. Verify that total revenue decreases. (c) Now suppose that market is populated by perfectly-competitive firms that all have MC = 10. Market demand is still as in the introduction to the question: p(Y ) = 210−4Y , where Y is the total market quantity. Find industry output and total revenue. (d) If the competitive firms’ marginal costs increase to MC = 20, what happens to industry revenue? What happens to profits at the firm or industry level? Assume that, if there are fixed costs, they are the same as in part (c).

Answer 1

So each firm output = 3

Then number if firms , n = total output / individual supply

= 180/3

n* = 60

P* = (3)²+1 = 10

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its mandatory to answer only first four parts only