Question

The White Company is a member of the lamp industry, which is perfectly competitive. The price of a lamp is $50. The firm’s total cost function is TC = 1,000 - 20Q - 5Q² where TC is total cost (in dollars) and Q is hourly output.

1. What output maximizes profit?
2. What is the firm’s economic profit at this output?
3. What is the firm’s average cost at this output?
4. If other firms in the lamp industry have the same cost function as this firm, is the industry in equilibrium? Why or why not?

Answer 1

Answer- a) Given, the firm is perfectly competitive, we use this rule P = MC to find the output.

Firstly, we have to minimize the total cost to find MC

TC = 1000 - 20 Q - 5Q²

MC = 20 +10 Q

Now,

P = MC

50 = 20 + 10 Q

50 - 20 = 10 Q

30 = 10 Q

Q = 30 / 10

Q = 3

Output is 3 maximises profit

b) Profit = TR - TC

            = (Price * Quantity) - (1000 - 20 Q - 5Q² )

            = (50 * 3 ) - ( 1000 + 20(3) + 5 (3)² )

           = 150 - (1000 + 60 + (5 * 9))

          = 150 - (1000 + 60 + 45)

          = 150 - 1105

          =    - 955

Firms economic profit at this output is $ - 955 or firm is in loss , because profit is negative.

c) Average Cost = Total Cost / Output

                       =   1105 / 3

                       = 368.33

Firm's average cost is $ 368.33.

d) None other firm in the lamp industry have the same cost function as this firm because firm is experiencing a big losses relative to revenue, so the industry cannot be in equilibrium.