Question

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 + 40? MC = 84 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

Solution

Price: ¥10000

Total Cost: 200000 + 4q^{​​​​​2}

Marginal Cost: 8q

(a)

Revenue function = Pq = 10000*q

Profit Function (π) = Revenue - Cost

= 10000q - 200000 -4q²

^(b)

On differentiating profit Function with respect to q

dπ/dq = 10000 - 0-8q

dπ/dq = 0

10000 - 8q =0

8q = 10000

q = 10000/8 = 1250

Total Revenue (R) = pq = 10000*1250 =12500000

Total Cost = 200000 + 4q² = 20000 +4(1250)² =6450000

π = R - C = 12500000 - 6450000 =6050000

Yes the firm is earning profit.

(c)

In short run a firm's shut down condition is given by

P > AVC

AVC = 4q² /q =4q

AVC_|q=1250 = 4*1250=5000

P = ¥10000

The firm should continue to operate as P>AVC

(d)

As it is clear from the above calculation shown that

P> AVC. Therefore,firm must continue to operate in long run as well as price is greater than AVC