Question

A monopolist faces a demand curve of Q = 164 – P, where P is price and Q is the output produced by the monopolist. What choice of output will maximize revenue?

Group of answer choices

70

74

82

86

if monopolist produces good X and faces a demand curve X = 112 - 2P, where P is price. What is the monopolist's marginal revenue as a function of good X?

Group of answer choices

44 - X

56 - 0.5X

56 - X

44 - 0.5X

Answer 1

The demand function is given as:

Q = 164 - P which can also be written as P = 164 - Q

The total revenue can be calculated by multiplying the price with quantity demanded.

Total Revenue = (P)(Q) = 164Q - Q​​​​​​2​​​

The marginal revenue is the additional revenue received when one more unit of a good is sold. It can be calculated by differentiating the total revenue function with respect to quantity.

Marginal Revenue = 164 - 2Q

The obtain the level of output at which the revenue is maximum, the marginal revenue should be equal to zero. So,

164 - 2Q = 0

2Q = 164

Q = 82

So, the revenue is maximum when 82 units re produced. Therefore, the correct answer is 'Option C'.

The demand curve is given as:

X = 112 - 2P which can also be written as P = 56 - 0.5X

The total revenue function is:

Total Revenue = (X)(P) = 56X - 0.5X2

​​​​​​The marginal revenue function can be calculated by differentiating the total revenue function with respect to X.

Marginal Revenue = 56 - X

So, the correct answer is 'Option C'.