A college professor is planning for his retirement years. His utility function is ?(?t , ?r ) = 3c t 0.5+2cr0.5 where ct represents his consumption today (period 1), his active years of teaching, and cr represents his consumption in his retirement years (period 2). During his active years of teaching, he makes a total of ₺3 million, while in his retirement years his total income is ₺1 million. He can borrow or lend at an interest rate of 25% between the two periods. Write an equation that describes the professor’s budget assuming he will spend all his income during his lifetime. If the professor chooses neither to borrow nor to lend during his active years, what will be his marginal rate of substitution between his consumption today and his retirement years? If the professor aims at maximizing his utility, how much does he consume in each period (use the Lagrangian method)? Does he save for his retirement years? If so, how much? At what interest rate would the professor choose to consume the same amount in his working years as in his retirement years? What would be his consumption in each period?

A college professor is planning for his retirement years. His utility function is ?(?t , ?r ) = 3c t 0.5+2cr0.5 where ct represents his consumption today (period 1), his active years of teaching, and cr represents his consumption in his retirement years (period 2). During his active years of teaching, he makes a total of ₺3 million, while in his retirement years his total income is ₺1 million. He can borrow or lend at an interest rate of 25% between the two periods. Write an equation that describes the professor’s budget assuming he will spend all his income during his lifetime. If the professor chooses neither to borrow nor to lend during his active years, what will be his marginal rate of substitution between his consumption today and his retirement years? If the professor aims at maximizing his utility, how much does he consume in each period (use the Lagrangian method)? Does he save for his retirement years? If so, how much? At what interest rate would the professor choose to consume the same amount in his working years as in his retirement years? What would be his consumption in each period?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.3P

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A college professor is planning for his retirement years. His utility function is u(c¿, C7) = 3cº5 + 2c5, where c; represents his consumption today (period 1), his active years of teaching, and c, represents his consumption in his retirement years (period 2). During his active years of teaching, he makes a total of Ł3 million, while in his retirement years his total income is Ł1 million. He can borrow or lend at an interest rate of 25% between the two periods. .0.5 a. Write an equation that describes the professor's budget assuming he will spend all his income during his lifetime. b. If the professor chooses neither to borrow nor to lend during his active years, what will be his marginal rate of substitution between his consumption today and his retirement years? c. If the professor aims at maximizing his utility, how much does he consume in each period (use the Lagrangian method)? Does he save for his retirement years? If so, how much? d. At what interest rate would the professor…
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