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[See Solution] A monopolist produces at total cost TC(y), where y=y_1+y_2, and sells this output in two separated markets, producing a total revenue of

Question: A monopolist produces at total cost \(TC\left( y \right)\), where \(y={{y}_{1}}+{{y}_{2}}\), and sells this output in two separated markets, producing a total revenue of \(TR\left( {{y}_{1}},{{y}_{2}} \right)=T{{R}_{1}}\left( {{y}_{1}} \right)+T{{R}_{2}}\left( {{y}_{2}} \right)\). Throughout the problem, assume interior solutions

  1. Show that the profit maximizing monopolist will equate the marginal cost of production to marginal revenues in each market
  2. Assume that second order sufficient conditions for the problem are satisfied. What do they imply about the slopes of MR and MC curves?
  3. Use the equation
\[MR=p\left( 1+\frac{1}{\varepsilon } \right)\]

and your results in (a) to show that a price discriminating monopolist will charge a higher price in the market whose demand curve is less elastic.

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