Question

Suppose that MUB is the only producer of electricity in the little town of Microeconomica. The faces a demand curve of the form: P = 210 – 4Q, where P (measured in dollars) and Q (measured in kilowatts) stand for the unit price and quantity of electricity produced, respectively. Suppose that in producing electricity for the town, MUB incurs production costs that total C(Q) = 5Q.

a. What is MUB’s marginal cost function?

b. How many kilowatts of electricity should MUB produce to maximize its profits.

c. What is the firm’s resulting optimal price?

d. At the profit-maximizing price, what is MUB’s total revenue?

e. Now suppose that because of technological issues, MUB’s marginal cost increases to $20. Calculate the new optimal quantity, price, and revenue.

Answer 1

P = 210 – 4Q

Total revenue(TR)= 210Q-4Q²

Marginal revenue(MR)= Differentiation of TR wrt Q= 210-8Q

Total C(Q) = 5Q

a.

Marginal cost= MC= Differentiation of TC with respect to Q= 5

b.

Profit of MUB= P x Q - TC

Profit= (210-4Q)Q-5Q

Differentiate wrt Q:

dProfit/dQ= 210-8Q-5= 0

8Q= 205

Q= 205/8= 25.625 Optimal quantity for maximum profit

c.

Optimal price:

P= 210-4Q= 210-4(25.625)= 210-102.5= 102.5 Optimal price

d.

Total revenue= P x Q= 25.625 x 102.5= 2626.56

e.

New MC= MC'= 20

Optimal condition:

MC= MR

20 = 210-8Q

8Q= 190

Q= 23.75 New optimal quantity

P= 210-4(23.75)= 210-95= 115 New optimal price

TR= P x Q= 2256.25