Suppose that a competitive firm's marginal cost of producing output q is given by MC(q) = 3 + 2q. Assume that the market price of the firm's product is $9.

a. What level of output will the firm produce? b. What is the firm's producer surplus?

c. Suppose that the average variable cost of the firm is given by AVC(q) = 3 + q. Suppose that the firm's fixed costs are known to be $3. Will the firm be earning a positive, negative, or zero profit in the short run?

2. A firm produces a product in a competitive industry and has a total cost function C = 25 + 2q + q2 and a marginal cost function MC = 2 + 2q. At the given market price of $10, the firm is producing 5 units of output. Is the firm maximizing its profit? What quantity of output should the firm produce in the long run?

3. Suppose the same firm's cost function is C(q) = 4q2 + 16.

a. Find variable cost, fixed cost, average cost, average variable cost, and average fixed cost. (Hint: Marginal cost is given by MC = 8q.)

b. Show the average cost, marginal cost, and average variable cost curves on a graph.

c. Find the output that minimizes average cost.

d. At what range of prices will the firm produce a positive output?

e. At what range of prices will the firm earn a negative profit?

f. At what range of prices will the firm earn a positive profit?