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?
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
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.
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