Consider a monopolist who sells its product in two distinct markets (and therefore can charge different prices in these different markets). By the way, charging observably different group different prices is called 3rd-degree price discrimination. The cost function is C(Q1 + Q2) = 0.25[Q1 + Q2]^2 The inverse demand curves for these markets are p1(Q1) = 200 – Q1 for market 1 and p2(Q2) = 300 – Q2 for market 2, where Q1 is the quantity sold in market 1 and Q2 is the quantity sold in market 2. At some point below, you may wish to use the marginal cost function, which is MC(Q1 + Q2) = 0.5[Q1 + Q2]. a) State this 3rd-degree price discriminating monopolist’s maximization problem, using the particulars of this problem. Think carefully about what this monopolist is choosing and what it is trying to maximize. b) State two equations that an (interior) solution will satisfy. c) Solve for the optimal quantity to sell in each market. d) Solve for the price to charge in each market. e) Compute the monopolist’s profit. On your own, you might want to check the monopolist’s profit if it charges slightly different prices in each market
Consider a monopolist who sells its product in two distinct markets (and therefore can charge different
prices in these different markets). By the way, charging observably different group different prices is called
3rd-degree
C(Q1 + Q2) = 0.25[Q1 + Q2]^2
The inverse demand
market 2, where Q1 is the quantity sold in market 1 and Q2 is the quantity sold in market 2. At some point
below, you may wish to use the marginal cost function, which is MC(Q1 + Q2) = 0.5[Q1 + Q2].
a) State this 3rd-degree price discriminating monopolist’s maximization problem, using the particulars of
this problem. Think carefully about what this monopolist is choosing and what it is trying to maximize.
b) State two equations that an (interior) solution will satisfy.
c) Solve for the optimal quantity to sell in each market.
d) Solve for the price to charge in each market.
e) Compute the monopolist’s profit. On your own, you might want to check the monopolist’s profit if it
charges slightly different prices in each market.
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