Question

2) The cost function for Acme Laundry is C(q) = 10 + 10q+q?, where q is tons of laundry cleaned. Assume that the market is perfectly competitive. a. What q should the firm choose to maximize its profit if the market price is p? How much does it produce if p=50? b. Assume that the government imposes a per unit tax of r =2. How much should the firm produce to maximize its after-tax profit if the market price is p? How much does it produce if p=50?

Answer 1

a) Profit is given by π = revenue – cost

π = pq – 10 – 10q – q^2

Profit is maximum when π’(q) is 0

p – 10 – 2q = 0

q = 0.5p – 5

Hence profit maximizing quantity is q = 0.5p – 5

When p is 50, q is 50*0.5 – 5 = 20 units

b) Now cost is C = 10 + 10q + 2q + q^2 OR C = 10 + 12q + q^2

Profit is changed to π = pq – 10 – 12q – q^2

Profit is maximum when π’(q) is 0

p – 12 – 2q = 0

q = 0.5p – 6

Hence profit maximizing quantity is q = 0.5p – 6

When p is 50, q is 50*0.5 – 6 = 19 units