Suppose that you estimate the following cost function for your company, which is a monopolistically competitive firm:

TC = 80Q - 4Qsquared + 0.25Qthird

and the following demand curve for your product:

P = 80 - 2Q

a. Compute and plot the average cost and marginal cost.

b. Over what range of output does economies of scale exist? Diseconomies of scale?

c. How many units of output will you produce and what price will you charge for each unit? (Hint: A monopolistically competitive firm produces where MR=MC. First find the level of output by setting MR=MC, then substitute the value of Q into the price equation above to find the value of P.)

d. Is the company making a profit or loss at the suggested output level? How much?

Could I please have explanations for each question? Thank you!