A price discriminating monopolist sells to two individuals, 1 and 2. Individual 1 has demand function...

 

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A price discriminating monopolist sells to two individuals, 1 and 2. Individual 1 has demand function p1(q1) and individual 2 has demand function p2(q2). The monopolist's cost function is c(q1 + q2). Assume the revenue function is concave and the cost function is convex. The monopolist's profit is π = p1(q1) q1 + p2(q2) q2 - c(q1 +q2). The monopolist maximises profit subject to q1 ≥ 0 and q2 ≥ 0. (1) Write down the first order conditions. (ii) Consider all four cases (both constraints bind, no constraints bind, one constraint binds and the other does not). What are the conditions for profit maximising in each case? (iii) Represent each case on a diagram. A price discriminating monopolist sells to two individuals, 1 and 2. Individual 1 has demand function p1(q1) and individual 2 has demand function p2(q2). The monopolist's cost function is c(q1 + q2). Assume the revenue function is concave and the cost function is convex. The monopolist's profit is π = p1(q1) q1 + p2(q2) q2 - c(q1 +q2). The monopolist maximises profit subject to q1 ≥ 0 and q2 ≥ 0. (1) Write down the first order conditions. (ii) Consider all four cases (both constraints bind, no constraints bind, one constraint binds and the other does not). What are the conditions for profit maximising in each case? (iii) Represent each case on a diagram.

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i First Order Conditions IT q1 p1q1 cq1 q2 0 IT q2 p2q2 cq1 q2 0 ii Conditions for Profit Maximis... View the full answer