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 -
5Q**^{2}**where TC is total
cost (in dollars) and Q is hourly output.**

**What output maximizes profit?****What is the firm’s economic profit at this output?****What is the firm’s average cost at this output?****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 - 5Q^{2}

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 - 5Q^{2} )

= (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.

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