Question

Question 1. We assume that a firm is in a perfectly competitive industry. The relations between the firm’s total cost (T C), marginal cost (MC) and quantity produced

(Q) are given by:

T C=$1,000,000+$20Q+$0.0001Q2

MC= ∂T C ∂Q =$20+$0.0002Q

Total cost includes a normal profit.

(1). What are the levels of optimal output and profit if price is equal to $60 each? (5 points)

(2). If the total fixed cost is $1,000,000, check that the firm’s marginal cost is greater than average variable cost at every point along the firm’s marginal cost curve. (5 points)

(3). If the firm is typical in the industry, calculate the firm’s long-run equilibrium output, price, and economic profit levels. (10 points

Answer 1

(1) A perfectly competitive firm produces at following point in short run:

P = MC

=> 60 = 20 + 0.0002Q

=> 0.0002Q = 60 -20

=> 0.0002Q = 40

=> Q = (40 / 0.0002)

=> Q = 200,000

Profit = TR - TC

=> Profit = PQ - (1,000,000 + 20Q + 0.0001Q²)

=> Profit = (60 * 200,000) - (1,000,000 + 20 * 200,000 + 0.0001 *(200,000)²)

=> Profit = 12,000,000 - 9,000,000

Profit = 3,000,000

Optimal output level of each firm is 200,000 and profit is $3,000,000

---------

(2) Marginal cost (MC) intersects average variable cost (AVC) at its minimum point and after that minimum MC ins above AVC.

TC = 1,000,000 + 20Q + 0.0001Q²

TVC = 20Q + 0.0001Q²

AVC = (TVC / Q)

=> AVC = 20 + 0.0001Q

Set MC = AVC

=> 20 + 0.0002Q = 20 + 0.0001Q

=> 0.0002Q - 0.0001Q = 20 -20

=> 0.0001Q = 0

=> Q = 0

At Q = 0, MC intersects AVC.

So, MC will be above AVC for all the quantity level above quantity of 0 units

------------------------------

(3)

A perfectly competitive firm produces at following point in long run:

P = MC = AC

TC = 1,000,000 + 20Q + 0.0001Q²

AC = (TC / Q)

=> AC = (1,000,000 /Q) + 20 + 0.0001Q

Set, MC = AC

=> 20 + 0.0002Q = (1,000,000 /Q) + 20 + 0.0001Q

=> 20 + 0.0002Q - 20 - 0.0001Q = (1,000,000 /Q)

=> 0.0001Q = (1,000,000 /Q)

=> Q² = (1,000,000 / 0.0001)

=> Q = (1,000,000 / 0.0001)^0.5

=> Q = 100,000

Firm's long run equilibrium output is 100,000 units.

P = MC
=> P = 20 + 0.0002Q

=> P = 20 + 0.0002(100,000)

=> P = 20 + 20

=> P= 40

Long run equilibrium price is $40

Economic profit = TR - TC

=> Economic profit = PQ - (1,000,000 + 20Q + 0.0001Q²)

=> Economic profit =(40 * 100,000) - (1,000,000 + 20 * 100,000 + 0.0001 *(100,000)²)

=> Economic profit == 4,000,000 - 4,000,000

=> Economic profit =0

Economic profit of each firm in long run will be 0