Question

A drug company has a monopoly on a new patented medicine. The product can be made in either of two plants. The marginal costs of production for the two plants are MC1 = 20 +2Q1 and MC2 = 10 + 4Q2 The firm's estimate of demand for the product is P=20-3(Q1 +Q2). How much should the firm plan to produce in each plant? At what price should it plan to sell the product? (Round your responses to two decimal places.) The firm should produce units in plant 1 and in plant 2. To maximize profits, it should charge a price of $ (per unit.

Answer 1

The marginal cost of first plant is irrelevant since it lies above the demand curve. The maximum price is $ 20 and the marginal cost of plant 1 is $ 20 and it lies above the demand curve. Therefore, the firm will not produce any output in plant 1.

Therefore, the marginal cost curve of plant 2 will be considered and the demand curve is

P = 20 - 3Q₂

TR₂ = 20Q₂ - 3Q₂²

^{​​​​​}MR₂ = 20 - 6Q₂

Equate it to MC

20 - 6Q₂ = 10 + 4Q₂

10Q₂ = 10

Q₂ = 1

Price, P = 20 - 3(0 + 1) = $ 17

The firm should produce 0 units in plant 1 and 1 unit in plant 2. To maximize profits, it should charge a price of $ 17 per unit.

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