Suppose there are N firms who produce an identical product and face the demand curve P = 170 - 3Q, where P is the price of the good (in dollars) and Q is the total quantity supplied by the firms. The marginal cost of production per firm is $20; there are no fixed costs.

a If there is only one firm in the market (a monopolist), what is this firm's optimal output?

b If there are four firms in the market (N=4), what is the symmetric Nash equilibrium output per firm?

c What is the price in this market as N tends towards infinity?