Question

If a monopolist supplies goods at a price; P = 170 - Q, with marginal cost; MC = 52. Find the quantity and price

Answer 1

Answer:

Quantity = 59 units

Price = $111

Step-by-step explanation:

The Demand function is given by

$P = 170 - Q$

The Marginal cost is given by

$MC = 52$

We are asked to find the quantity and price of goods.

Firstly, obtain the Marginal revenue function from the demand function

The Total revenue is given by

$TR = P \times Q \\\\TR = (170 - Q) \times Q \\\\TR = 170Q - Q^2$

The Marginal revenue is the derivative of the Total revenue,

$MR = \frac{d}{dQ} (TR) = 170Q - Q^2 \\\\MR = \frac{d}{dQ} (TR) = 170 - 2Q$

Assuming that the monopolist maximizes profits,

$MR = MC \\\\170 - 2Q = 52\\\\2Q = 170 - 52\\\\2Q = 118\\\\Q = 118/2\\\\Q = 59$

Therefore, the quantity is 59 units.

The price of each good is

$P = 170 - Q \\\\P = 170 - 59 \\\\P = 111$

Therefore, the price is $111.