Industrial Organization

Suppose we have two types of consumers (for simplicity we’ll assume that there is one person of each type). They have inverse demand curves given by:

p1 =110−2q1 and p2 =70−4q2.

Initially, we will assume that the monopolist can tell them apart and that consumers cannot change or fake their type. Let the marginal cost of production be equal to 10. Label group 1 as the “high type” and group 2 as the “low type.”

(g) Explain why the profit function of the monopolist under block pricing can be written as:

π(V1, q1, V2, q2) = V1(q1, q2) + V2(q2) − 10(q1 + q2).

(h) Derive general forms for V1 and V2 in terms of the primitives of the model.

(i) Take the partial derivative of the profit function with respect to q2. At the margin, explain the tradeoffs the monopolist faces for decreasing q2.

(j) Next draw two graphs of the demand functions for the two consumer types, with the optimal block pricing schemes illustrated. Explain graphically what happens when the monopolist reduces q2.

(k) At what point will the monopolist want to stop decreasing q2?

(l) Solve for the optimal (V1, q1) and (V2, q2) that satisfies the incentive compatibility constraints.

(m) What rents do the low-type consumers earn in any equilibrium? What about the high-type consumers?

(n) How does welfare compare to the case when the monopolist can tell the two groups apart? What drives the difference?