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 = 60 - 0.25P, and the marginal cost of production is $80.

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

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

Answer 1

(a)

In order to maximize profit a firm produces that quantity at which Marginal Revenue(MR) = Marginal Cost(MC)

MR = d(TR)/dQ and TR = PQ = (1/0.25)(60 - Q)Q = 4(60 - Q)Q , Here Qd = Q

=> MR = 240 - 8Q

MC = 80

MR = MC => 240 - 8Q = 80 => Q = 20

Hence,  the optimal number of units to put in a package = 20 units

(b)

When Quantity = 20 consumers are willing to pay P = (1/0.25)(60 - Q) = 4(60 - 20) = 160

Hence he should charge Price = $160.

Hence,  the firm should charge $160 for this package.