Question 8: Given TC = 100 + 60Q - 12Q2 + Q3. Find

a. The equations of the TVC, AVC, and MC functions.

b. The level of output at which AVC and MC are minimum, and prove that the AVC and MC curves are U-shaped.

c. Find the AVC and MC for the level of output at which the AVC curve is minimum.

Question 9: Answer the same questions as in the above problem if:

TC = 120 + 50Q - 10Q2 + Q3

Question10: If the demand function faced by a firm is:

Q = 90 - 2P

TC = 2 + 57Q - 8Q2 + Q3

Determine the level of output at which the firm maximizes the profit.

Question 11: Determine the best level of output for the above question by the MR and MC approach.

Question 12: Determine the best level of output for a perfectly competitive firm that sells its product at P = $4 and faces TC = 0.04Q3 - 0.9Q2 + 10Q + 5. Will the firm produce this level of output? Why?

Question 13: Suppose that the production function is given as follows:

TPL = 10L + 5L2 + L3

Find the total product, Marginal product and average product when L = 5.

Question 14: Find the optimum level of output and profit from the cost function

TC = 50 + 6Q2

and price

P = 100 - 4Q

Also derive marginal cost and marginal revenue.