Question

Consider a market that faces the following market supply and demand functions

Q S = 2 + p

Q D = 10- 1/2 p

where identical firms face the total cost function of T C = 4 + q + q²

a) What is the market price?

b) Derive the average variable cost, average total cost, and marginal cost functions.

c) In the short run, how much does each firm produce?

d) In the short run, how much economic profit or loss will be obtained?

e) Based on the results in part (d), will firms want to enter or exit the market? Why?

 

Answer 1

a) At equilibrium, QD = QS

10 - p/2 = 2 + p

10 - 2 = p + p/2

8 = 3p/2

16 = 3p

p = 16/3

p = 5.33

b) TC = 4 + q + q²

Total variable cost = q + q² (TVC is the cost which changes with the change in output)

AVC = TVC/q = (q + q²)/q = 1 + q

ATC = TC/q = 4/q + 1 + q

MC = dTC/dq = 0 + 1 + 2q = 1 + 2q

c) Q = 2 + p = 2 + 5.33 = 7.33

Q = 7 units

d) Profit = TR - TC = pq - (4 + q + q²) = 5.33 x 7 - 4 - 7 - 7x7 = 37.31 - 60 = - 22.69

e) Firm will exit the market because firm suffered loss.