A university student was bequeathed $2,000 upon graduation at age 20 years. This person was hired by one of the largest global tech companies soon after graduation with an expected annual income of $250. Assume that the retirement age is 65 years and life expectancy is 85 years in the country in which the student resides. Given that this country has zero real interest rate and consumption smoothing is optimal for all individuals: Derive an expression for the person’s lifetime resources clearly describing each term. Calculate the value of the person’s lifetime resources. Derive an expression for the person’s consumption function clearly describing any new terms included. Derive an expression for the person’s average propensity to consuming. State the theory on which you based the calculations in parts i., ii. and iii. above.

A university student was bequeathed $2,000 upon graduation at age 20 years. This person was hired by one of the largest global tech companies soon after graduation with an expected annual income of $250. Assume that the retirement age is 65 years and life expectancy is 85 years in the country in which the student resides. Given that this country has zero real interest rate and consumption smoothing is optimal for all individuals: Derive an expression for the person’s lifetime resources clearly describing each term. Calculate the value of the person’s lifetime resources. Derive an expression for the person’s consumption function clearly describing any new terms included. Derive an expression for the person’s average propensity to consuming. State the theory on which you based the calculations in parts i., ii. and iii. above.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.2P

See similar textbooks

Similar questions

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…
Consider a two-period living consumer with a utility function, u(c)=sqrt(c). Suppose the real interest rate, R=10% and the utility discount factor, beta=0.95. If the consumer wants to maximize lifetime utility, what will be the growth rate of her consumption from the current to the future period? *
Consider a person who will live for two years (1 and 2). The real interest rate between the two periods is r. In period 1 any income they have to use, Y1, must be earned by working at wage w, denoted in period 1 dollars, for hours H1, which they can choose. In period 2 they cannot work, but they will be paid a stipend of Y2. Their intertemporal utility is defined over consumption of a composite in each period, q1 and q2, and leisure in each period, L1 and L2. You can assume that the price of consumption in each period is $1, denoted in that period's dollars. Given this information, state the person's utility maximization problem in full, and derive the first order conditions for an optimal solution. Give an economic interpretation of the conditions you derive (i.e., carefully describe the nature of the optimal choice).
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…
Consider an individual who lives for two periods and has utility of lifetime consumption U = log(C1) + 1/1+δ log(C2), where C1 and C2 are the consumption levels in the first and second period respectively, and δ, 0 1 > 0 in the first period and no income in the second period, so Y2 = 0. He can transfer some income to the second period at a before-tax rate of return of r, so saving $S in the first period gives $[1 + r]S in the second period. The government levies a capital tax at rate τ on capital income received in the second period. The tax proceeds are paid as a lump-sum transfer to the following generation. The present generation does not care about the next one. a. What is the lifetime consumption profile of this individual? What is his lifetime indirect utility function expressed as a function of Y1 and b. Evaluate the change in initial income Y1 that is required to compensate the individual for the welfare loss due to the capital income tax τ. c. What is…
I always thought my good friend Rado Coetzee was quite original given his choices. He then once told me his utility function was U(c1,c2) = min {c1,C2} where c1 and c2 are his consumption in period 1 and 2 respectively. I know in the first period he earns $105 thousand and $168 thousand in period 2. Rado can borrow or lend at an interest rate of 10%. Inflation is negligible. What will he do? a) Rado will borrow 30 thousand dollars b) Rado will save 133 thousand dollars c) Rado will save 30 thousand dollars d) Rado will save all his money, buy a BMW X5 in Luxembourg, tax free, and never let his wife Inga drive it. e) None of the above
When analyzing how borrowing and lending affect the consumer's budget constraint, we measure spending in the current time period on the horizontal axis and spending in the future time period on the vertical axis. Assume that the interest rate at which the consumer can lend and borrow is 10%, income in period 1 is $1000 and income in period 2 is $1200. The point of maximum current consumption can be expressed as 1000+ 1200/1.1. 1000(1.1) + 1200. 1000+ 1200 + .1 1000/1.1 + 1200/1.1 + 1.
if Age dependency ratio (% of working-age population) increase what will happen to fixed capital consumption?
Consider a training program that will result in a worker receiving a one time bonus of $2,900 two years from now. The cost of the training program is $2,000. What is the rate of return on this investment?
Susie Lee won a lottery. She will have a choice of receiving $25,000 at the end of each year for the next 30 years, or a lump sum today. If she can earn an annual return of 10 percent on any investment she makes, what is the least she should be willing to accept today as a lump-sum payment? (Round to the nearest hundred dollars.) Use the NPV as you have equal cash flows of $25,000 for the next 30 years.
Suppose Poornima is an avid reader and buys only comic books. Poornima deposits $3,000 in a bank account that pays an annual nominal interest rate of 10%. Assume this interest rate is fixed-that is, it won't change over time. At the time of her deposit, a comic book is priced at $15.00. Initially, the purchasing power of Poornima's $3,000 deposit is comic books. For each of the annual inflation rates given in the following table, first determine the new price of a comic book, assuming it rises at the rate of inflation. Then enter the corresponding purchasing power of Poornima's deposit after one year in the first row of the table for each inflation rate. Finally, enter the value for the real interest rate at each of the given inflation rates. Hint: Round your answers in the first row down to the nearest comic book. For example, if you find that the deposit will cover 20.7 comic books, you would round the purchasing power down to 20 comic books under the assumption that Poornima will…
Suppose Latasha is a sports fan and buys only baseball caps. Latasha deposits $3,000 in a bank account that pays an annual nominal interest rate of 5%. Assume this interest rate is fixed-that is, it won't change over time. At the time of her deposit, a baseball cap is priced at $10.00. Initially, the purchasing power of Latasha's $3,000 deposit is baseball caps. For each of the annual inflation rates given in the following table, first determine the new price of a baseball cap, assuming it rises at the rate of inflation. Then enter the corresponding purchasing power of Latasha's deposit after one year in the first row of the table for each inflation rate. Finally, enter the value for the real interest rate at each of the given inflation rates. Hint: Round your answers in the first row down to the nearest baseball cap. For example, if you find that the deposit will cover 20.7 baseball caps, you would round the purchasing power down to 20 baseball caps under the assumption that Latasha…