Question

Please help me understand how to solve this.

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+502 The firm's estimate of demand for the product is P 20-3(1+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.) units in plant 1 andin plant 2. To maximize profits, it should charge The firm should produce a price of $1-1 per unit.

Answer 1

The drug company has a monopoly. A monopolist produces at the point where its Marginal Revenue (MR) is equal to the Marginal Cost (MC).

MC from the two plants are given in the question.

Also, the demand function is given which is equal to the Average Revenue (AR). Multiply the AR with the quantity to get Total Revenue (TR), as follows:

$AR=P=20-3(Q_{1}+Q_{2})$

$TR=P\times Q =[20-3Q]\times Q =20Q-3Q^{2} =20Q_{1}+20Q_{2}-3Q_{1}^{2}-3Q_{2}^{2}$

Marginal Revenue (MR) can be calculated by differentiating the TR with respect to different quantities.

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For plant 1, MR is:

$MR=20-6Q_{1}$

Equate MR and MC,

$20-6Q_{1}=20+2Q_{1}$

$\boldsymbol{Q_{1}=0}$

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For plant 2, MR is:

$MR=20-6Q_{2}$

Equate MR and MC,

$20-6Q_{2}=10+5Q_{2}$

$\boldsymbol{Q_{1}=0.91}$

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Price charged will be:

$P=20-3(Q_{1}+Q_{2})=20-3(0.91)=17.3$

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Thus, firm should produce 0 units in plant 1 and 0.91 units in plant 2. To maximize profits, it should charge a price of $17.3 per unit.