James has a wage income of $50.000 in the present and $200.000 in the future. His utility is given as U = min (2Cp, Cr) - that is, his utility is the lesser of twice the dollars spent on present consumption or the dollars spent on future consumption. The interest rate is 30%. (A) What is the minimum amount of money James would be willing to accept today to have the interest rate at 40% rather than 30%? Explain and show work (B) What is the maximum amount of money James would pay today to have the interest rate at 30% rather than 40%? Explain and show wor

James has a wage income of $50.000 in the present and $200.000 in the future. His utility is given as U = min (2Cp, Cr) - that is, his utility is the lesser of twice the dollars spent on present consumption or the dollars spent on future consumption. The interest rate is 30%. (A) What is the minimum amount of money James would be willing to accept today to have the interest rate at 40% rather than 30%? Explain and show work (B) What is the maximum amount of money James would pay today to have the interest rate at 30% rather than 40%? Explain and show wor

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.3P

See similar textbooks

Related questions

Q: Find consumption if income is $660 and APC is 0.67

A: The data presented in the question above is:- Income = $660 Average propensity to consume = 0.67…

Q: EXERCISE 7 Aisha is considering how to allocate the next 6 hours of her free time. She could choose…

A: Budget Line: given the price of 2 goods and consumer’s income. The budget line shows different…

Q: Suppose apartments are in four locations: Location A, Location B, Location C, and Location D.…

A: The term "opportunity cost" refers to the value of missing out on the "next best option."It is…

Q: Barney sells fruits and vegetables at an outdoor market stand. He pays $20 in rent per day for the…

A: Total sales are x. The employee takes 8% of the sales, i.e., 0.08x. Barney pays rent of $20 and…

Q: Consider a representative consumer whose utility function is given by U(C.L) In(C) + 0.4xL. where C…

A: Given information Utility function U=lnC+0.4L Budget constraint C=-6L+450 W=6

Q: Consider a CES (constant elasticity of substitution) utility function u : R++ → R where el-y – 1…

A: Derivating both sides w.r.t c Therefore, the elasticity of marginal utility is

Q: just subparts d, e and f please

A: d)If the consumer wage rate increases to $50, the consumer budget line becomes: C = 50(80 - L) +…

Q: Tatum is a mother of Anny (1 year old). Tatum derives utility from income Y (i.e. a disposable…

A: Utility, in economics, refers to the satisfaction, well-being, or happiness that individuals derive…

Q: The utility of Amanda for leisure (L) and income (Y) is U = LY. The price of income is 1. If Amanda…

A: The literal meaning of utility is satisfaction. It means the satisfaction derived by the individual…

Q: Jerry's utility function is U(x,y) = (5x + y )18. Find Jerry's MRS (for good X in terms of good Y)…

A: The quantity of a good that a consumer is prepared to consume in comparison to another good,…

Question

James has a wage income of $50.000 in the present and $200.000 in the future. His

utility is given as U = min (2Cp, Cr) - that is, his utility is the lesser of twice the dollars spent on

present consumption or the dollars spent on future consumption. The interest rate is 30%.

(A) What is the minimum amount of money James would be willing to accept today to have the interest rate at 40% rather than 30%? Explain and show work

(B) What is the maximum amount of money James would pay today to have the interest rate at 30% rather than 40%? Explain and show work

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Part a

VIEW

Part b

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.

Similar questions

Suppose Neha is a sports fan and buys only baseball caps. Neha 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. Fill in the chart: 0% 5% 8% Number of Caps Neha Can Purchase after One Year Choices: 291, 305, 315, 582 Choices: 291, 300, 305, 582 Choices: 291, 305, 315, 582 Real Interest Rate When the rate of inflation is less than the interest rate on Neha's deposit, the purchasing power of her deposit __________ (options: falls, rises, remains the same) over the course of the year.
Assume a consumer has current-period income y = 200, future-period income y′ = 150, current and future taxes t = 40 and t′ = 50, respectively, and faces a market real interest rate of r = 0.05, or 5% per period. The consumer would like to consume according to the following utility function: U (c, c′ ) = ln(c) + ln(c′ ). Show mathematically the lifetime budget constraint for this consumer. Find the optimal consumption in the current and future periods and optimal saving. Suppose that instead of r = 0.05 the interest rate is r = 0.1. Repeat parts (a) and (b). Does the substitution effect or the income effect dominate?
Suppose Dariya is a fan of young-adult fiction and buys only young-adult books. Dariya deposits $4,000 into a savings account that pays an annual nominal interest rate of 5%. Assume this interest rate is fixed, and so it will not change over time. On the day she makes her deposit, suppose that a young-adult book has a price of $10.00. Initially, Dariya's $4,000 deposit has a purchasing power of young-adult books. For each of the annual inflation rates given in the following table, first determine the new price of a young-adult book, assuming it rises at the rate of inflation. Then enter the corresponding purchasing power of Dariya'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 young-adult book. For example, if you find that the deposit will cover 20.7 young-adult books, you would round the purchasing…
The Fly-by-Night finance company advertises a "bargain 6% plan" for financing the purchase of automobiles. To the amount of the loan being financed, 6% is added for each year money is owed. This total is then divided by the number of months over which the payments are to be made, and the result is the amount of the monthly payments. For example, a woman purchases a $10,000 automobile under this plan and makes an initial cash payment of $2,500. She wishes to pay the $7,500 balance in 24 monthly payments: Find the IRR and Effective Annual Interest rate. Purchase price -Initial payment = Balance due, (Po) +6% finance charge = 0.06 × 2 years × $7,500 = Total to be paid .. Monthly payments (A) = $8,400/24 = $10,000 2,500 7,500 900 8,400 $350
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
Suppose your utility function for money is a square-root function of its value in US dollars. So, for instance, $400 is worth 20 utils for you, $961 is worth 31 utils for you, and $62.5K is worth 250 utils for you. Now, let’s say your annual salary is $90K, although there is a small risk (p = 0.05) that something catastrophic will happen and reduce your income for the year to $14.4K. An insurance company comes along and offers to insure you against the loss of your salary. The cost of the insurance is $4,736. If you buy the policy and catastrophe strikes, the insurance company will pay out the $75,600 that you would otherwise have lost. From the standpoint of maximizing expected utility, would buying this insurance be a good deal for you? What would be the insurance company’s expected monetary value of selling you the policy?
10
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…
Suppose you have the option of spending $[x] now or saving it until next year. If you save it, the bank will pay you an interest rate of 9.8%. Your utility function is u(w) = w. What does your discount factor & need to be for you to be indifferent between spending the money now and saving it? Round your answer to 3 decimal places (so an answer might be, for example, 0.476).
Clare is contemplating her possible consumption patter for this year and next. She know that she will have income of $50,000 this year and $55,000 next yea. Her plan is to consume $40,000 this year (t=0). She is also going to invest 30,000. This investment has a positive NPV of $450. She decides to take the investment; in addition, the return on the investment is 9.62%. What consumption she can expect at t=1? (show a detailed procedure)
As is true for all of us, Lisa has many weekly expenses. What might be less common is the fact that Lisa likes to buy broccoli (qB) and carrots (qc) for all the money left after her required expenses. Lisa's utility function is standard Cobb-Douglas, U(qB¹9c) =q³qc7. 0.3 1. Before we specify what Lisa's "disposable" income is and what the price of a head of broccoli and a small bag of carrots are, please derive expressions for the demand for broccoli and carrots (that is, derive demand for the two goods as functions of Y, PB, and pc). In other words, find the following demand functions: qB = f(Y,PB, Pc) and qc = f(Y,PB, Pc). Use the substitution method for one good and the short-cut for the other good. 2. Using the demand functions that you derived in question 1, please find Lisa's optimal consumption of broccoli and carrots (the quantity demanded, if you will) if Y = 10, PB = 0.60, and Pc = 1.00. 3. Draw the (inverse) demand curve for broccoli and indicate Lisa's consumption of…
Every week I spend a total of £400 buying two goods, luxuries (L) and necessities (N). I obtain utility (U) from these goods according to the rule U(L, N) = 10 + L + 20N−2N2. Suppose that I pay £10 for each unit of L and £20 for each unit of N and that I am a utility-maximiser. MUL=1 and MUN=20-4N. Define the Marginal Rate of Substitution (MRS) as MRS ≡ MUL/MUN). Calculate its value at the bundle (L = 0 and N = 4) and at (L = 1 and N = 4). By referring to a graphic illustration of the above calculations or otherwise, argue that an increase in my budget will have no effect on my consumption of N if I am already consuming 2.5 units of N. Calculate my optimum choice of L and N if instead I have £40 to spend. Fully explain your answer.