4. Consider an individual with utility function U(C₁, C₂) = (c₁) 3/4 (c₂)¹/4 who is alive for two periods and has an income stream (m₁, m₂). At some point the government decides to intervene in the economy: in the first period the individual has to pay a fraction 0 ≤ ≤ 1 of its income as taxes, and in the second period he receives a transfer equal to q as pension. (b) Use the value of q obtained in the previous question and find the effect of the gov- ernment intervention on the savings of the individual. Differentiate the case when the individual is initially a saver and the case when the individual is initially a borrower.

4. Consider an individual with utility function U(C₁, C₂) = (c₁) 3/4 (c₂)¹/4 who is alive for two periods and has an income stream (m₁, m₂). At some point the government decides to intervene in the economy: in the first period the individual has to pay a fraction 0 ≤ ≤ 1 of its income as taxes, and in the second period he receives a transfer equal to q as pension. (b) Use the value of q obtained in the previous question and find the effect of the gov- ernment intervention on the savings of the individual. Differentiate the case when the individual is initially a saver and the case when the individual is initially a borrower.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Suppose the initial budget constraint is: p₁x₁ + P2x2 = m. Then, a new government imposes an ad valorem sales tax on all goods, at a rate of 5%. What is the new budget constraint? 1.5 p1x1 + 1.5 p2x2 = m 105 p1x1 + 105 p2x2 = m P1x1 + P2X2 = 1.05 m 1.05 p₁x₁ +1.05 p2x2 = m O P1X1 + P2X2 = m
Assume that an economy is characterized by the following equations: C = 100 + 0.5(Y – T) T = 100 G = 200 I = 50 – 2r (M/P) = (M/P) = Y – 6r (a) Solve for the equilibrium values of Y and r, assuming P = 10 and M = 4,000. (6 pointa) (b) Assume the federal government reduces spending to balance the budget. Calculate the effective IS-LM multiplier and explain why the equilibrium reduction in output was less than the value implied by the Keynesian-cross multiplier. (6 pointa)
2. Use the budget constraint to replace c in the first-order condition to obtain a single equation that relates the household's choice of I to w and T. 3. Suppose that the government uses all the tax revenue to hire emergency front-line health workers to help during the COVID-19 pandemic. The government pays these workers the prevailing wage rate. How much time (in units) can the government afford to purchase from the workers? Denote this number by m.
1. For what kind of preferences will the consumer be just as well off facing a quantity tax as an income tax? 2. Someone is willing to maximize his/her utility. Assume he/she knows his/her u(x,y) = %3D x0.Sy0$ (Cobb-Douglas) (a) Find his/her optimal consumption given the income = 20, Px=2, Py=4! %3D (b) Depict his/her optimal consumption graph! 3. Suppose that x and y (from your answer in number 2) are now perfect complement with u(x,y) = min(x,y). (a) Find his/her optimal consumption (given the same income and prices)! (b) Depict his/her optimal consumption graph! Best of Luck!
Consider the consumption function: C 120+ 0.8Yd where Yd is disposable income. a) Write down expressions for C, in terms of national income Y, when there is: i. No tax ii. A lump sum tax of £100 iii. A proportional tax in which the proportion is 0.25. b) Sketch all three functions on the same diagram, over the range 0≤Y≤800, and briefly describe any differences or similarities between them.
Suppose the households in a hypothetical economy has the following consumption function C = 1200+ 0.85Y, d Where Y is the disposable income. The government in this economy imposes a tax d rate of 0 < t < 1 to households' income (ex. A t = 0.10 means that 10% of households' income goes to tax payments).
An agent lives for 2 periods and gains utility only by consuming. Future consumption is discounted at rate θ where 0<θ<1. Agent consumes c, saves s at interest rate r in first period of life from income y. In second period agent consumes from savings plus interest earned but must pay a flat fixed tax. Find the Euler equation for this agent and what it shows.
Consider a utility function defined over hours of leisure and consumption expenditure: U(c, h) ch. The after- tax wage rate is given by w and the amount of nonwage income, by N. Assume the number of hours of leisure in a year is 8000. Potential annual income, I, is given by 1-8000wN. It is allocated over hours of leisure, which cost wh, and consumption expenditure, c. The budget constraint is thus 8000wN-cwh 0. 1. Find the demand functions for leisure and consumption. a. Write the Lagrangean function for this problem. b. Find the first order conditions. c. Solve the first order conditions to obtain the condition that the MRS wage rate. Show your steps in the solution. d. Use the results from c to obtain the expansion path
Consider a model in which an individual lives only two periods. The individual has diminishing marginal utility of consumption and receives an income of RM100,000 in the first period and an income RM6,000 in the second period. The private interest rate is 10 percent for each period, in which the individual can borrow or lend money at this rate. Assume also that the individual intends to consume all of her income overs his lifetime. i) ii) If there is no Social Security program, what is the individual's optimal consumption in each period? Assume that there is a Social Security program that takes RM6,000 from the individual in the first period and pays her this amount with interest in the second period. What is the impact of this system on the individual's saving?
= 4. Consider an individual with utility function U(C₁, C₂) (c₁) 3/4 (c2)¹/4 who is alive for two periods and has an income stream (m1, m2). At some point the government decides to intervene in the economy: in the first period the individual has to pay a fraction 0 ≤ T ≤ 1 of its income as taxes, and in the second period he receives a transfer equal to q as pension. (a) What is the value of q that makes the present value of income the same before and after the government intervention? (b) Use the value of q obtained in the previous question and find the effect of the gov- ernment intervention on the savings of the individual. Differentiate the case when the individual is initially a saver and the case when the individual is initially a borrower.
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?
Exercise 5 (Borrowing Constraints and Consumption Taxes). Consider a two-period economy in which households face the borrowing constraint S p 1 ≥ 0. Suppose that the constraint is binding. In period 1, the household receives an exogenous endowment of goods Y1 = 50, and the government levies a proportional tax on consumption at the rate τ1 = 0.25 and has expenditures in goods and services in the amount G1 = 2. Firms borrow in period 1 at the interest rate r and use the funds to invest in physical capital, denoted I1. Investment becomes productive in period 2. The investment schedule is I1 = 12.5 (1 + r) ^2 1. Calculate private consumption in period 1 (C1), government saving in period 1 (S g 1 ), and national saving in period 1 (S1). 2. Calculate the equilibrium real interest rate (r).