4. Suppose that you estimate the following cost function for your company, which is a firm operating in a perfectly competitive market:

TC=100Q-4Q²+Q³

The market demand and supply equations are as follows.

Q^D=134-3P+2Y

Q^S=24+2P-2PI

where Y= Income = 100 and P_I = Price of inputs = 120.

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?

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