XYZ is a small leather shoes manufacturing company. The market for the brand of
ID: 1227949 • Letter: X
Question
XYZ is a small leather shoes manufacturing company. The market for the brand of shoes produced by XYZ is highly competitive, currently selling for $100 per pair. XYZ's total and marginal cost functions are as follows: C(Q) = 1,000,000 + 0.01Q2 MC = 0.02Q Where Q is number of pairs of shoes produced per year. a. How many pairs of shoes will the firm produce in order to maximize profit (minimize loss)? b. How much profit (loss) will the firm earn? c. Analyze the firm’s position in terms of the shutdown condition. Should XYZ operate or shut down in the short-run? (Hint: The company’s fixed and variable costs can be derived from the TC equation)
Explanation / Answer
a.
Profit would be maximum or loss would be minimum where MC = P
0.02Q = 100
Q = 5,000
Answer: The firm will produce 5,000 pairs of shoes for maximizing profit or minimizing loss.
b.
Profit = TR – TC
= (5,000 × $100) – (1,000,000 + 0.01Q^2)
= 500,000 – (1,000,000 + 0.01 × 5,000)
= 500,000 – 1,000,050
= - 500,050
Answer: The profit is -$500,050
c.
The firm will shutdown if AVC is not recovered.
Fixed cost (FC) is the constant number of TC, 1,000,000
TVC = TC – FC = (1,000,000 + 0.01Q^2) – 1,000,000 = 0.01Q^2
AVC = TVC / Q = (0.01Q^2) / Q = 0.01Q
Since the quantity is 5,000 here, AVC = 0.01 × 5,000 = $50
Answer: Since the price $100 is higher than AVC $50, the firm should not go for shutdown now. It should increase the production to recover the fixed cost too.
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