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 = 80 – .5p, and the marginal cost of production is $100.
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

Answer:

A. 15 units

B. $130

Explanation:

In order to solve this, we need to use the profit maximization condition for monopoly.

MR = MC will give us the optimal quantity and price for the monopolist.

The consumer's demand for the product is:

Qd = 80 - 0.5P

Therefore, we have:

P = (80 / 0.5) - (Qd / 0.5)

P = 160 - 2Qd

Recall that, Total Revenue:

TR = P * Q

So, in this case TR = 160Q - 2Q^2

MR = d(TR) / dQ = 160 - 4Q

Now, MR = MC

160 - 4Q = 100

4Q = 160 - 100

4Q = 60

Q = 60 / 4

Q = 15 units.

Now, P =160 - 2Q

P = 160 - 2(15)

P = 160 - 30 = 130

The optimal number of units to be placed in a package will therefore be 15 units while the firm should charge $130 for this package.