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.

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

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

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