Suppose the market for T-Shirts in the country of Argonia is perfectly competiti
ID: 1189229 • Letter: S
Question
Suppose the market for T-Shirts in the country of Argonia is perfectly competitive, and the price of a T-Shirt is $20. A producer in this market has the following total cost and marginal cost functions:
TC (q) = 500 + 0.1q2 MC (q) = 0.2q
a) What part of the total cost function represents fixed costs?
b) Write the equation for the firm's average variable cost.
c) Compute the number of T-Shirts the firm will produce to maximize profit.
d) Compute the average total cost of producing the profit-maximizing quantity of T-Shirts.
e) What is the average variable cost of producing the profit-maximizing quantity of T-Shirts?
f) What's the firm's profit?
g) What's the firm's profit is Q=O. Should the firm operate at Q found in part c?
Explanation / Answer
TC (q) = 500 + 0.1q2 MC (q) = 0.2q
a) fixed costs $ 500
b) TVC/Q or 0.1q2 /q
c) Profit maximization condition P=MC
.2Q =20
Q =100
d) . 500 + 0.1q2 /q
on subtituting the value of q as 100
AC =15
e)AVC = 0.1q2 /q
=1000/100
=$10
f) Profit = TR-TC
= 20*100 -1500
=2,000-1,500
=$500
g) Firm will suffer loss if q=0
firms Should operate at Q found in part c since it is earning profit.
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