Question

Suppose the market of carpets is competitive. The demand for and the supply
of tables have been estimated as follows:
Q = 370 – 10P
Q = 80P +10
A typical firm producing tables has a total cost function of C = 64 +?^{​​​​​2}/4
a. Find the equilibrium market price and quantity. (2 marks)
b. Derive MC and AC functions of a typical firm. Then find the efficient scale of output of the firm. Show your steps clearly. (5 marks)
c. Find the profit maximizing output level and profit/loss level of a typical firm. Show your steps clearly. (4 marks)
d. Use side by side diagrams to illustrate the equilibrium market price, equilibrium quantity in the market, as well as the profit maximizing output level and profit/loss of a typical firm. (5 marks)
e. What will happen over time to the market and to the firm in the long run? Explain briefly in words.

Answer 1

(a)

In equilibrium, market demand equals market supply.

370 - 10P = 80P + 10

90P = 360

P = $4

Q = (80 x 4) + 10 = 320 + 10 = 330

(b)

MC = dC/dq = 2q/4 = q/2

AC = C/q = (64/q) + (q/4)

At efficient scale, AC is minimized. Average cost is minimized when dAC/dq = 0

dAC/dq = -(64/q²) + (1/4) = 0

64/q² = 1/4

q² = 256

q = 16

(c)

Profit is maximized when P = MC.

q/2 = 4

q = 8

Total revenue (TR) = P x q = $4 x 8 = $32

C(q) = 64 + (8 x 8 / 4) = 64 + 16 = $80

Profit ($) = TR - C(q) = 32 - 80 = -48 (Loss)

(d)

In following graph, D & S are market demand and supply curves intersecting at point A with price P0 (= $4) and quantity Q0 (= 33). The firm being a price taker, accepts P0 as its own price and equates P0 with its own MC at point B, producing output q0 (= 8). At this output level, AC is higher than P0, so there is a loss equal to area P0BCD.

P, Cest MC AC 0 0 Marckat) (Firm)

(e)

In long run, short run loss will make some firms to exit the market, lowering market supply and increasing market price. This will start decreasing the loss by each firm until new long run equilibrium is restored when each firm is earning zero economic loss.