Question

The following game is taken from Problem Set 5. A firm sells two substitute goods–Good A and Good B–to two types of consumers–workers and students. Workers comprise a fraction b of all customers. The firm cannot identify the consumer type. However, depending on its pricing strategy, consumers with different willingness to pay might sort themselves into purchasing different products. The firm earns 140b + 70 from selling Good A to students and Good B to workers. The firm is a profit-maximizer. Good A Good B Unit Production Cost 80 120 Unit Price x y Willingness to Pay Workers 300 480 Students 150 200 Scenario I: Suppose the firm wants to sell Good B to both workers and students. 1. List only relevant constraints for each consumer type. If irrelevant, say so and briefly explain your rationale. If applicable, please explicitly indicate a binding constraint. a. (10 pts) Participation Constraints b. (10 pts) Incentive Compatibility Constraints 2. (15 pts) Derive the firm’s profit equation in the simplest form. Use the term b if needed. Your final expression should not contain x and y. Show all work. 3. Evaluate the following statement: The firm is better off selling Good B to all consumers than selling Good A to students and Good B to workers. a. (5 pts) Is this statement true or false? b. (10 pts) Show your work. If false, derive a condition under which the statement is false.

          The following game is taken from Problem Set 5. A firm sells two substitute goods–Good A and Good B–to two types of consumers–workers and students. Workers comprise a fraction b of all customers. The firm cannot identify the consumer type. However, depending on its pricing strategy, consumers with different willingness to pay might sort themselves into purchasing different products. The firm earns 140b + 70 from selling Good A to students and Good B to workers. The firm is a profit-maximizer.
Good A
Good B
Unit Production Cost
80
120
Unit Price
x
y
Willingness to Pay
Workers
300
480
Students
150
200
Scenario I: Suppose the firm wants to sell Good B to both workers and students.
1.   List only relevant constraints for each consumer type. If irrelevant, say so and briefly explain your rationale. If applicable, please explicitly indicate a binding constraint.
a.    (10 pts) Participation Constraints
b.   (10 pts) Incentive Compatibility Constraints
2.   (15 pts) Derive the firm’s profit equation in the simplest form. Use the term b if needed. Your final expression should not contain x and y. Show all work.
3.   Evaluate the following statement: The firm is better off selling Good B to all consumers than selling Good A to students and Good B to workers.
a.    (5 pts) Is this statement true or false?
b.   (10 pts) Show your work. If false, derive a condition under which the statement is false.

Added by Victoria I.

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