This question is about private consumption. Consider a household that lives for two periods. In periodj, the price level is P; and the real labour income is given by w; for j = {1,2}. The initial real wealth is2 - 1. The household hasgiven by A. The nominal interest rate is i and the inflation rate (CPI) is 7 =a constant relative risk aversion (CRRA) utility function which readsP111--u (С1,С2) %3D и(С1) + Bu(C2) —u(С1) + Вu(С2)+B1 – 01 – 0where 0 > 0, BE (0,1) is the subjective discount factor of the household and C; is consumption inperiod j for j = {1,2}.' Now consider the consumption choice of the household.(1.1) Firstly, demonstrate how we can obtain the lifetime budget constraint of the household consist-ing of nominal interest rate, price levels, real labour income, initial real wealth, and consump-tion. Secondly, transform the budget constraint you have just obtained into another budget con-straint consisting of the real interest rate, real labour income, initial real wealth, and consumption.Lastly, interpret.

Private consumption refers to the spending by individuals and households on goods and services for…

This question is about private consumption. Consider a household that lives for two periods. In period j, the price level is P; and the real labour income is given by w; for j = {1,2}. The initial real wealth is given by A. The nominal interest rate is i and the inflation rate (CPI) is = ₁-1. The household has a constant relative risk aversion (CRRA) utility function which reads C₁-0-1 1-0 U (C₁, C₂) = u(C₁) + Bu(C₂) = where > 0, ß € (0,1) is the subjective discount factor of the household and C; is consumption in period j for j = {1,2}.¹ Now consider the consumption choice of the household. +B. 1 1-0 (1.1) Firstly, demonstrate how we can obtain the lifetime budget constraint of the household consist- ing of nominal interest rate, price levels, real labour income, initial real wealth, and consump- tion. Secondly, transform the budget constraint you have just obtained into another budget con- straint consisting of the real interest rate, real labour income, initial real wealth, and consumption. Lastly, interpret.

This question is about private consumption. Consider a household that lives for two periods. In period j, the price level is P; and the real labour income is given by w; for j = {1,2}. The initial real wealth is given by A. The nominal interest rate is i and the inflation rate (CPI) is = ₁-1. The household has a constant relative risk aversion (CRRA) utility function which reads C₁-0-1 1-0 U (C₁, C₂) = u(C₁) + Bu(C₂) = where > 0, ß € (0,1) is the subjective discount factor of the household and C; is consumption in period j for j = {1,2}.¹ Now consider the consumption choice of the household. +B. 1 1-0 (1.1) Firstly, demonstrate how we can obtain the lifetime budget constraint of the household consist- ing of nominal interest rate, price levels, real labour income, initial real wealth, and consump- tion. Secondly, transform the budget constraint you have just obtained into another budget con- straint consisting of the real interest rate, real labour income, initial real wealth, and consumption. Lastly, interpret.

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 consumer's current income (y) is 200 and the future income ( t.') is 240. A current lump sum tax (t) of 10 is paid and the tax in the next period (t') is 15. The real interest rate is 20% for each period. Please assume that current and future consumption are complements. and the consumer always prefers to have one unit of current consumption and two units of consumption in the future.Calculate the consumer's lifetime wealth.Calculate the optimal current and future consumption and the optimal current and future savings. Is the consumer a lender or a borrower? How does he she. as a lender or a borrower. affect the future consumption?
A consumer's current income (y) is 200 and the future income ( t.') is 240. A current lump sum tax (t) of 10 is paid and the tax in the next period (t) is 15. The real interest rate is 20% for each period. Please assume that current and future consumption are complements. and the consumer always prefers to have one unit of current consumption and two units of consumption in the future. Calculate the optimal current and future consumption and the optimal current and future savings. Is the consumer a lender or a borrower? How does he she. as a lender or a borrower. affect the future consumption?
Wherein:TU = Total Utilityf= is a function ofMU = Marginal UtilityO = units of consumptionA= infinitesimal change EMV= Expected Monetary Value
Assume a set of well-behaved (i.e. strictly monotone and strictly convex) intertemporal indifference curvesbetween period 1 and 2. Then suppose that the nominal interest rate r decreases. Explain what happens to thenew interior solution if current and future consumption are normal and inferior goods, respectively.
There are some simplifying assumptions in order to generate simple expressions. One of these assumptions is that r (interest rate) = ρ (rate at which household discounts future). Suppose we relaxed this assumption (i.e. allowed r to differ from ρ). Two results of the model are: i) The household keeps the expected value of consumption constant over time. ii) The household responds differently to permanent versus temporary income changes. Discuss the implications of allowing r to differ from ρ on each of these results
Suppose that Annie's real income this year is $150 and next year it will be $100. Assume that the real interest rate is 10%. How much can Annie consume this year if she borrows against all of her income next year? Round to the nearest whole dollar, type without units (e.g. 10).
Suppose that a person can borrow and lend at an interest rate of 10 percent. But there is a 5% rate of inflation and one has to pay an income tax of 30 % on all interest income. If you borrow money, you can deduct interest as an expense. Where current consumption is on the horizontal axis and future consumption is on the vertical axis: (a) the budget line will have a kink at the point of no saving or lending. (b) the budget line will be a straight line with a slope of about 1: 02. (c) the budget line will be a straight line with a slope of about 1:05. (d) the budget line will be a straight line with a slope of about 1:35.
Consider a two-period consumption saving model and let f1 and f2 denote the first and secondperiod consumption, respectively. Assume that the interest rate at which the consumer may lend or borrowis 10%. Suppose that a consumer’s utility function is x (f1> f2) = f1 + 20√f2= The consumer first periodincome is L1 = $100 and the present value of her income stream is $330=(a) What is the optimal consumption stream (consumption bundle) of this consumer?(b) Is this consumer borrower or lender? How much does she borrow or lend?(c) What is the effect of a reduction of the interest rate to 5% on the consumer’s optimal first-periodsaving? (Make sure to take into account the effect of the decline in the interest rate on the present value ofthe consumer’s income stream.)
5. Consider a two-period consumption model in which an individual's life time- utility is u(c1,c2) = ee. The individual earns I1 = 1000 in period 1 and re- ceives a government pension I2 = 800 in period 2. Suppose the individual can save or borrow at the net interest rate 10% (r = 0.1). Assume that the price levels in both periods are one (p1 = p2 = 1). (a) Find the individual's optimal consumption level in each period. How much does she save or borrow in period 1?. (b) Suppose the interest rate goes up to 40%. Find the total, substitution, and income effects on period 2 consumption. Based on your answer, would you classify period 2 consumption as normal or inferior? Is it Giffen? (c) Suppose the government wants to adjust the pension to I', so that the individual is equally well off as before the interest rate change. Find I. Is I', larger or smaller than I2? Give a brief, intuitive explanation of this result.
3. A consumer maximises the following two-period utility function 1 V = max 1 ule,) + Fu(c) (1+p)? subject to the following 2-period budget constraint, C2 Ao + 1+r" (1+r)² Y2 1+r*(1+r)²' By choosing consumption at each period, c, and c2. r denotes the real interest rate, p is the time preference rate, Ao is initial wealth and y, and y2 represents incomes in period 1 and period 2 respectively. (a) Use the Lagrangian method to obtain the first order conditions for the utility maximisation problem and obtain the Euler equation. (b) Assume utility function has the form of u(c,) = 5 0.2 and r = 0.3. Obtain the equations/solutions for maximal c, and c2 by substituting the Euler equation back into the two-period budget constraint for the situations of either A, = -50 or Ao = 50. Explain the results. , Y1 = 200, y2 = 300, p = 0.6
Discuss the lifecycle income hypothesis theory of consumption and explain its applicability in the Kenyan context.
Bora's income in the current period is y=200, and income in the future period is y'=250. He pays lump-sum taxes t=30 in the current period and t'=10 in the future period. The real interest rate is 5%, per period.Suppose that Bora will always choose current consumption, c and the future consumption, c′ in a constant proportion:c=32c′ a) Determine the optimal current-period and future-period consumption for Bora. b) Determine the optimal saving for Bora, and show this in a diagram with his budget constraint and indifference curves, and also determine if Bora is a lender or a borrower?