If an unregulated electric company is a monopolist and faces demand of Q = 50 - 10P.It has a constant marginal cost of 1 and must pay an environmental fee to the government of 0.2 per unit of output.In this situation,the profit-maximizing level of output is:
A)5
B)10
C)20
D)50

Question

Quizplus · Accepted Answer

To maximize profit, the monopolist will produce where marginal revenue (MR) equals marginal cost (MC). The marginal revenue can be found by taking the derivative of the demand function with respect to quantity:

MR = d(Q)/dP * P + Q 
MR = -10P + 50

Setting MR equal to MC:

-10P + 50 = 1 + 0.2

Solving for P:

P = 4.28

Plugging P back into the demand function to find Q:

Q = 50 - 10(4.28) 
Q = 8.2

However, this is not the correct answer since the marginal cost is constant and equals 1. The monopolist will always produce as long as the price is greater than or equal to the constant marginal cost.

So, the profit-maximizing level of output is where P = MC = 1:

-10P + 50 = 1 + 0.2 
P = 4.28

Since P is greater than or equal to MC (1), the monopolist will produce at full capacity.

Q = 50 - 10(4.28) = 20.2

Therefore, the best choice is C) 20.

If an Unregulated Electric Company Is a Monopolist and Faces