Question

Consider the following perfectly competitive market. The relationship between total product and cost for each individual producer is as follows: Total Product Marginal Cost Average Variable Cost Average Total Cost 3 5.00 8.00 16.00 4 6.00 7.50 13.00 5 7.00 7.00 11.25 6 8.00 7.25 11.00 7 9.00 7.33 10.50 8 10.00 7.67 10.00 (a) (i) Determine the shutdown quantity for the firm in this market. (ii) Determine the shutdown price for the firm in this market. Suppose the initial market price is equal to $8.00 (b) Determine the level of profit-maximizing output when the market price is equal to $8.00. (c) Determine the level of economic profit when the market price is equal to $8.00. Suppose the market demand curve is given by the following equation: QD = 52 – 2 * P (d) Determine the market equilibrium quantity when the market price is equal to $8.00. (e) How many firms currently operate in this market? (f) Do you expect the number of firms that operate in this market to increase, decrease, or remain constant? (g) Determine the long-run equilibrium market price. (h) Determine the long-run equilibrium market quantity. (i) How many firms operate in the market in the long-run equilibrium?

Answer 1

a (i) Shutdown quantity = 5
As we see in the table above, MC = AVC = 7 when output = 5. (price= MC in a competitive market) the firm will not produce when the price falls below AVC. Hence, shutdown quntity = 5.

(ii) Shutdown price = $7.
When output = 5, MC = 7 (which is also the price). This is the shutdown price.

b. When price= $8, profit maximizing output = 6
As price = MC, the firm will produce 6 units when MC = 8.

c, Economic profit = -$18 (loss)
When price= $8, output = 6 units
from the table above, when price= MC = 8, output = 6 units. So, total revenue = 8*6 = 48
ATC = 11 at this level. So, total cost = 11*6 = 66
Profit = total revenue - total cost, or 48 - 66 = -18 (loss)

MARKET EQUILIBRIUM:

Demand:Qd = 52 - 2P; so inverse demand: P = 26 - 0.5Q

d. Market equilibrium quantity = 36
26 - 0.5Q = 8; so, Q = 18/ 0.5 = 36

e. number of firms in the market = 6
Firm's output at price = $8 is 6 units
Market output when price = $8 is 36 units
So, number of firms in the market = 36/ 6 = 6

f. The number of firms will decrease (loss making firms that cannot sustain the loss will exit the industry).

g. long run equilibrium market price = $10 (Long run condition: price = MC = ATC; i.e. 10)

h. long run equilibrium market quntity = 8 units (from the table when MC = ATC = 10, output = 8)

i. Number of firms in the long run = 4
Firm's output when price = $10 is 8 units (from the table price = MC = ATC= 10)
Market output when price = $10 is 32 units (26 - 0.5*Q = 10; So, Q = 32)
So, number of firms = 32/ 8 = 4