Consider the plight of Bonget, a middle-aged professor facing retirement soon. Suppose that the present value of Bonget's consumption is equal to financial wealth plus the present value of income (a.k.a. human wealth). Suppose, too, that Bonget derives utility from consumption using the log utility from where ß= 1. Suppose that the real interest rate is 5%; initial financial assets f = P 50,000, y = P 100, 000 (working age) and y'= P10,000 (retirement age). Assume that taxes are zero. A. B. C. D. What is this person's human wealth and total wealth? According to the neoclassical consumption model, how much does this person consume today and in the future? How much does she save today? If her current labor income y were to increase by P20,000, how much will saving change? If her future labor income were to increase by P10,000, how much will con- sumption today (c) rise? E. Using initial conditions, what if the interest rate rises to 10%? By how much will total wealth and today's consumption change compared to before and why (give a brief explanation)? How much will saving change?

Consider the plight of Bonget, a middle-aged professor facing retirement soon. Suppose that the present value of Bonget's consumption is equal to financial wealth plus the present value of income (a.k.a. human wealth). Suppose, too, that Bonget derives utility from consumption using the log utility from where ß= 1. Suppose that the real interest rate is 5%; initial financial assets f = P 50,000, y = P 100, 000 (working age) and y'= P10,000 (retirement age). Assume that taxes are zero. A. B. C. D. What is this person's human wealth and total wealth? According to the neoclassical consumption model, how much does this person consume today and in the future? How much does she save today? If her current labor income y were to increase by P20,000, how much will saving change? If her future labor income were to increase by P10,000, how much will con- sumption today (c) rise? E. Using initial conditions, what if the interest rate rises to 10%? By how much will total wealth and today's consumption change compared to before and why (give a brief explanation)? How much will saving change?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.8P

See similar textbooks

Similar questions

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)
Problem 1. Consider the plight of Bonget, a middle-aged professor facing retirement soon. Suppose that the present value of Bonget's consumption is equal to financial wealth plus the present value of income (a.k.a. human wealth). Suppose, too, that Bonget derives utility from consumption using the log utility from where 3 = 1. Suppose that the real interest rate is 5%; initial financial assets f = P50,000, y = P100, 000 (working age) and y'= P10,000 (retirement age). Assume that taxes are zero. A. B. C. D. E. What is this person's human wealth and total wealth? According to the neoclassical consumption model, how much does this person consume today and in the future? How much does she save today? If her current labor income y were to increase by P20,000, how much will saving change? If her future labor income were to increase by P10,000, how much will con- sumption today (c) rise? Using initial conditions, what if the interest rate rises to 10%? By how much will total wealth and…
Consider the plight of Bonget, a middle-aged professor facing retirement soon. Suppose that the present value of Bonget's consumption is equal to financial wealth plus the present value of income (a.k.a. human wealth). Suppose, too, that Bonget derives utility from consumption using the log utility from where = 1. Suppose that the real interest rate is 5%; initial financial assets f = P50,000, y = P100,000 (working age) and y'= P10,000 (retirement age). Assume that taxes are zero. A. B. C. D. What is this person's human wealth and total wealth? According to the neoclassical consumption model, how much does this person consume today and in the future? How much does she save today? If her current labor income y were to increase by P20,000, how much will saving change? If her future labor income were to increase by P10,000, how much will con- sumption today (c) rise? E. Using initial conditions, what if the interest rate rises to 10%? By how much will total wealth and today's consumption…
2. Mr. A has the following utility function and budget constraints: Max 0.1Ln(C1) + 0.7Ln(C2) Subject to S1 + C1 = 100 C2 + S2 = (1 + r)S1 where C1 and C2 are consumption level at young and that at old respectively. Likewise, S1 and S2 are saving at young and saving at old respectively. a) Find out Mr. A’s optimal consumption levels (i.e. C1*, C2*) and optimal savings (i.e. S1*, S2*) in terms of interest rate r. b) Show clearly the results in part a) in a suitable diagram (with C1 as x-axis and C2 as y-axis). c) Is Mr. A a saver ? or a borrower ? d) If r is equal to 0 (i.e. saving gives no returns), will Mr. A still choose to save when he is young (i.e. is S1 still bigger than 0) ? Why ? e) Suppose that Mr. A is not allowed to save (i.e. S1 = 0). What are his optimal consumption levels ? Show his optimal consumption levels in the same diagram you prepare for part a) (with a suitable indifference curve). f) If r increases,…
Dr Issac Parish will live for two periods only. His utility function is U(c1, c2) = c1c2, where c1 is consumption in period 1 and c2 is consumption in period 2. He will have no income in period 2. His income in period 1 is £40,000. If the interest rate rises from 10 to 14%: Select one: O a. his savings will not change but his consumption in period 2 will increase by £800. b. his consumption in both periods will decrease. c. his savings will increase by 4% and his consumption in period 2 will increase. O d. his consumption in period 1 will decrease by 14% and his consumption in period 2 will increase. e. his consumption in both periods will increase.
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.
Patience has a utility function 1/2 1/2 U(cl, c2) = c? + 0.80c/? where c is her consumption in period 1 and c is her consumption in period 2. Her income in period 1 is 3 times as large as her income in period 2. At what interest rate will she choose to consume the same amount in period 1 as in period 2? a. 2 b. 0.13 c. 0.25 d. 0 е. О.38 20% 13% 25% 0%
Rodrigo is taking a year between high school and college to work and save up. His utility from consumption each year is U(c) = discounts future utility by B. Rodrigo is going to make $I his year of working, and whatever he doesn't consume from that income will a savings account which will earn return r before he consumes next year. He has to pay for school expenses E in year two, before he consumes (but after return has been realized). 1-o and he go into
A consumer whowill consume c1 in period 1 and c2 in period 2 exhibits pure time discounting if they evaluate their consumption using the utility functionU(c1; c2) = u(c1) + βu(c2)where 0 < β < 1, and β < 1 captures the idea that consumption inthe future is not worth as much as current consumption. Note thatU(·; ·) depends on two arguments, while u(·) depends on only oneargument. We assume that u0(·) > 0, u00(·) < 0, and suppose thatthe consumer can split their current wealth, W, between the twoperiods as they please. In this problem, you are supposed to findproperties of the the optimal savings, s, as the solution tomax0≤s≤W U(W - s; s) = u(W - s) + βu(s):1. Using the FOCs, show that W - s∗ is larger than s∗ for anyβ < 1.2. Show that s∗ is a weakly increasing function of W (this can bedone without FOCs).3. Show that s∗ is a weakly increasing function of β (this too canbe done without FOCs).4. If u(x) = log(x), give the optimal savings as a function of β andW.
Suppose a person lives for 4 periods. His salary during each period of his life is $30, $60, $90 and $0. He was born without any financial wealth. 1. If the interest rate is 8% per period, what is the present value of the income of this agent? 2. If the individual wishes to have a constant consumption during his life, what will it be? Deduct his level of savings during each of the 4 periods of his life. 3. Suppose our individual cannot borrow (but can save). Determine the consumption and savings profile of the individual. 4. Suppose our individual receives an inheritance at birth of $10. How your answer in c) be affected?
A decision maker allocates an endowment of W > 0 dollars across two periodst = 1, 2. He discounts the future by β ∈ (0, 1) while facing a gross interest rateof R > 1. His utility is the same as studied in class. Solve for the intertemporalchoice problem. Show that the optimal consumption is decreasing over time ifβR < 1, constant over time if βR = 1, and increasing over time if βR > 1.
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…