A firm is the only seller of specialized tool. The fixed costs are $1000. The variable costs are 50q (so marginal cost is equal to 50). The firm faces an inverse demand of p = 250 .5q, so the marginal revenue is 250 q).

(a) Calculate the price and output that maximizes the firm's profits (the monopoly price and quantity).

(b) Calculate the firm's total profit at the profit-maximizing price.

(c) Draw a graph of the firm's inverse demand, marginal revenue, and marginal cost. Label the intercepts on the vertical axis. Label the producer surplus, the consumer surplus, and the dead weight loss