3) Joint Ownership and Contracts A firm is jointly owned by Juan and Roda. The firm's production function requires two input: effort by Juan, denoted by x and effort by Roda denoted by y. Effort is only observable by the person who exerts it. The cost to Juan of a unit of his effort is c; = 2 and the cost a unit of her effort is c, = 2. The price received for the goods is p = 2. The production of the firm is given by Q = 10[ln(x +1) + In(y+1)]. Assume that both Juan and Roda are risk neutral rational agents. Roda of a) What are the socially optimal amount of effort r* and y*? What is the total surplus in that case? (Hint: Solve the problem of a social planner that cares equally for Juan and Roda) b) Suppose that Juan and Roda have a contract that specifies that Juan pays a fixed amount w=15 to Roda and that Juan gets to keep and sell all the output. What is the total surplus now? How much of that surplus goes to Juan? To Roda?

3) Joint Ownership and Contracts A firm is jointly owned by Juan and Roda. The firm's production function requires two input: effort by Juan, denoted by x and effort by Roda denoted by y. Effort is only observable by the person who exerts it. The cost to Juan of a unit of his effort is c; = 2 and the cost a unit of her effort is c, = 2. The price received for the goods is p = 2. The production of the firm is given by Q = 10[ln(x +1) + In(y+1)]. Assume that both Juan and Roda are risk neutral rational agents. Roda of a) What are the socially optimal amount of effort r* and y*? What is the total surplus in that case? (Hint: Solve the problem of a social planner that cares equally for Juan and Roda) b) Suppose that Juan and Roda have a contract that specifies that Juan pays a fixed amount w=15 to Roda and that Juan gets to keep and sell all the output. What is the total surplus now? How much of that surplus goes to Juan? To Roda?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.1P

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