Exercise 2: Investment and Optimal Consumption Choice 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 pref ences can be represented by the utility function u(x, y) = x · y, where r 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*)? 4. How will Kate finance this consumption plan (i.e. how much does she borrow/save/invest in the first period and payback/receive in the second period)? 5. What is the effect of the private investment opportunity on Kate's consumption choice? That is, compare Kate's optimal choice with and without the private investment opportunity.
Exercise 2: Investment and Optimal Consumption Choice 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 pref ences can be represented by the utility function u(x, y) = x · y, where r 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*)? 4. How will Kate finance this consumption plan (i.e. how much does she borrow/save/invest in the first period and payback/receive in the second period)? 5. What is the effect of the private investment opportunity on Kate's consumption choice? That is, compare Kate's optimal choice with and without the private investment opportunity.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Exercise 2: Investment and Optimal Consumption Choice
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 r 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, N PV (2), 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*)?
4. How will Kate finance this consumption plan (i.e. how much does she borrow/save/invest in the first
period and payback/receive in the second period)?
5. What is the effect of the private investment opportunity on Kate's consumption choice? That is,
compare Kate's optimal choice with and without the private investment opportunity.
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