Question

A monopoly is considering selling several units of a homogeneous product as a single package. A typical consumer’s demand for the product is Qd = 120 - 0.5P, and the marginal cost of production is $150.

a. Determine the optimal number of units to put in a package. units

b. How much should the firm charge for this package? $

Answer 1

Demand Function

Qd = 120 - 0.5P

Marginal Cost

$150

To find the optimal number of units or profit-maximizing quantity we need to equate marginal revenue and marginal cost because at profit-maximizing quantity both are equal.

MC is given so we need to find MR

To find MR there are certain steps

1) Convert demand function in terms of price also known as inverse demand

Qd = 120 - 0.5P

P = 240 - 2Qd

2) Now marginal revenue is the same as demand function only coefficient of Q becomes twice.

P = 240 - 2Qd

MR = 240 - 4Qd

Now we have marginal revenue so we will equate MR and MC to find profit-maximizing quantity.

MR = MC

240 - 4Qd = 150

Qd = 22.5

So the optimal number of units to put in a package is 22.5

The firm will charge 195 for this package

P = 240 - 2Qd

P = 240 - 2(22.5)

P = 195