All 500 consumers in a market have identical demand for a product that is descri

Question

All 500 consumers in a market have identical demand for a product that is described by individual demand curves P=40-2q. A monopolist produces the product and has a cost function of TC(Q)=10000+8Q. What is the monopolist's maximum profit if it cannot price discriminate or use a two-part tariff? All 500 consumers in a market have identical demand for a product that is described by individual demand curves P=40-2q. A monopolist produces the product and has a cost function of TC(Q)=10000+8Q. What is the monopolist's maximum profit if it cannot price discriminate or use a two-part tariff?

Explanation / Answer

P=40-2q

TR = Pq x 500 => 20,000q - 1000q2

MR = dTR /dq => 20,000 - 2000q

TC(Q)=10000+8Q.

MC = dTC /dq => 8

At equilibrium, MR = MC

20,000 - 2000q = 8

q = 9.996

P = 40 - 2 x  9.996 => 20

TR = 20 x 9.99 x 500 => 99940

TC = 10000 + 8 x  9.996 => 10080

Profit = TR - TC => 89860

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