Question

5 Purrfect sells deluxe cat toys. The deluxe cat toy market is highly competitive, with toys currently selling for ¥10, 000 each. Purrfect's total and marginal cost curves are: TC = 200000 + 4q^ МС 8q where q is the number of toys manufactured each year (a) Write down Purrfect's revenue function. Write down Purrfect's profit function (b) Calculate Purrfect's profit-maximizing quantity. Is the firm earning a profit? (c) Analyze Purrfect's position in terms of the shutdown condition. Should Purrfect operate or shut down in the short run? Be explicit about what criteria are most important to the decision. Page 2 (d) In light of your answer to (c), how would you advise Purrfect to proceed in the long run? Use no less than one and no more than two complete sentences to clearly articulate your main insights

Answer 1

Q5) a)

Revenue function TR = P*q = 10,000q

Profit function π = TR - TC

π = 10,000q - 200,000 - 4q²

B) dπ/dq= 10,000 - 8q = 0

q* = 10,000/8 = 1250

π = 10,000*1250 - 200,000 - 4*1250²

= 6050000

Yes Firm earning π

C) shut down price in Short run , when P = Min of AVC

AVC= 4q

Min AVC = 0

So if Price > 0, then continue to produce in Short run

D)

Min AC

AC = TC/q = 200,000/q + 4q

dAC/dq= -200,000/q² +4 = 0

q = √50,000

q* = 223.607

P = min AC = 1788.854

So continue Production in long run .