question archive A monopolist faces a demand curve given by P = 40 - Q, where P is the price of the good and Q is the quantity demanded
A monopolist faces a demand curve given by P = 40 - Q, where P is the price of the good and Q is the quantity demanded
Subject:MarketingPrice:2.88 Bought18
A monopolist faces a demand curve given by P = 40 - Q, where P is the price of the good and Q is the quantity demanded. The marginal cost of production is constant and is equal to $2. There are no fixed costs of production. How much output should the monopolist produce in order to maximize profit?
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A profit maximizing monopolist will choose to produce at the quantity level where marginal revenue is equal to marginal cost: MR=MC.
We derive the marginal revenue from the total revenue function:
- TR(Q)=P∗Q=(40−Q)Q=40Q−Q2MR=TR(Q)′=40−2QTR(Q)=P∗Q=(40−Q)Q=40Q−Q2MR=TR(Q)′=40−2Q
Equate MR and MC we get:
- 40−2Q=22Q=38Q=1940−2Q=22Q=38Q=19
Therefore, the monopolist should produce the quantity of 19 in order to maximize its profit.
