Kate has endowment E = (2775, 3000), i.e. she receives E1 = 2, 775 in the first period and E2 = 3,000 in the second period. Kate has access to a perfect capital market with interest rate r = 0.2 (i.e. 20%) per period. She also has access to a private investment opportunity. If she invests z in the private investment opportunity in the first period, it will return 180 - Vz – 100 if z > 100 R(z) = if z< 100 in the second period. Kate's preferences can be represented by the utility function u(x,y) = x · Y, where x is the number of dollars available to purchase goods in the first period and y is the number of dollars available to purchase goods in the second period. 1. What is the net present value, NPV (z), of the private investment opportunity? 2. What is Kate's budget constraint (including the investment opportunity)? 3. What is Kate's optimal consumption bundle (x*, y*)?

Kate has endowment E = (2775, 3000), i.e. she receives E1 = 2, 775 in the first period and E2 = 3,000 in the second period. Kate has access to a perfect capital market with interest rate r = 0.2 (i.e. 20%) per period. She also has access to a private investment opportunity. If she invests z in the private investment opportunity in the first period, it will return 180 - Vz – 100 if z > 100 R(z) = if z< 100 in the second period. Kate's preferences can be represented by the utility function u(x,y) = x · Y, where x is the number of dollars available to purchase goods in the first period and y is the number of dollars available to purchase goods in the second period. 1. What is the net present value, NPV (z), of the private investment opportunity? 2. What is Kate's budget constraint (including the investment opportunity)? 3. What is Kate's optimal consumption bundle (x, y)?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.10P

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