Consider a perfectly competitive firm with total costs = + + 2

where , , and are positive number and is quantity of output the firm produces.

a) Identify the fixed cost , and the variable cost of this firm, ().

b) Find the average cost (), and the marginal cost ().

c) Find the minimum of the () curve. Use this minimum of the () to describe the firm's long-run supply curve.

d) Use your results from part (a) to find the average variable cost () function and the minimum of the (). Use this minimum of the () to describe the firm's short-run supply curve.