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SportsMart is a sports apparel department store in Hayward. The manager has estimated that weekly demand...

SportsMart is a sports apparel department store in Hayward. The manager has estimated that weekly demand can be approximated by P = 25 – 0.001Q, where P is price and Q is output per week. The firm’s cost function C = 25,000 + 13Q + 0.002Q2, where C is total cost.

a) What is the firm’s profit maximizing price and output?

b) A former employee decides to sue SportsMart for employment discrimination, and management settles in court. The settlement requires SportsMart to pay the employee $10,000 per month for the next year. What is the profit maximizing price and output for the firm under these new conditions?

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Answer #1

Answer a) Firm profit maximization level of output and price are:

P= 25-0.001Q

PQ= 25Q-0.001Q 2

TR= 25Q-0.001Q 2

MR = 25-0.002Q

TC= 25000+13Q+0.002Q 2

MC = 13+0.004Q

Profit maximization level of output is

MR=MC

25-0.002Q=13+0.004Q

12= 0.006Q

Q= 2000 units

P= 25-0.001(2000)= 25-2=$23

B) If employee has been sue and the sports firm has to paid the $10,000 per month than the fixed cost of the firm has been increased for one year. But the variable cost is remain unaffected. This means that the profit maximization level of output and price remain the same. It means MR=MC and output is 2000 units and price is $23.

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