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 ( 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).