do only qu 2 u();1. Consider a deterministic DGE model where time lasts for two periods.The representative consumer has the utility function U₁ =faces the budget constraint c, +a, -y, +(1+r), for t=0,1; and has aninitial assets position given by a., <0.a) Specify the maximization problem of the representative consumerand provide its economic interpretation.b) Assume (1)= and (ii) y, for t=0,1, with y>0. Derive1+ranalytically the optimal consumption and assets holding plan andprovide an economic interpretation.c) Explain how your result in part (b) changes if the initial assetposition is positive.2. Consider a stochastic DGE model with uncertainty about future income.The representative consumer has the utility function U,E,'(c.).faces the budget constraint c, +a, = y, +(1+r),.,. for 120, and has aninitial assets position given by a...a) Derive analytically the consumption function under the permanentincome hypothesis.b) Use your result to illustrate analytically how income shocks affectconsumption and provide an economic interpretation.c) Show analytically how increase in income volatility affects currentconsumption and provide an economic interpretation.

Dynamic stochastic general equilibrium (DGE model) is a macroeconomic method of explaining…

1. Consider a deterministic DGE model where time lasts for two periods. The representative consumer has the utility function U, - Σ(₂): faces the budget constraint c, +a, -y, +(1+r),, for t=0,1; and has an initial assets position given by a., <0. a) Specify the maximization problem of the representative consumer and provide its economic interpretation. b) Assume () and (i) y, for t=0,1, with 90. Derive 1+r analytically the optimal consumption and assets holding plan and provide an economic interpretation. c) Explain how your result in part (b) changes if the initial asset position is positive. stochastic DGE 2. Consider a stochastic model with uncertainty about future income DGE model

1. Consider a deterministic DGE model where time lasts for two periods. The representative consumer has the utility function U, - Σ(₂): faces the budget constraint c, +a, -y, +(1+r),, for t=0,1; and has an initial assets position given by a., <0. a) Specify the maximization problem of the representative consumer and provide its economic interpretation. b) Assume () and (i) y, for t=0,1, with 90. Derive 1+r analytically the optimal consumption and assets holding plan and provide an economic interpretation. c) Explain how your result in part (b) changes if the initial asset position is positive. stochastic DGE 2. Consider a stochastic model with uncertainty about future income DGE model

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.14P

See similar textbooks

Similar questions

Consider a one period model in which a representative agent maximises the utility function: u(c,l) = lnc + 5lnl subject to the budget constraints: c = (1-t)w(1-l) + v where c is consumption and l is the amount of leisure, they enjoy out of a total of one unit of time available, t is the tax on wage earnings which pays for v in government transfer payments. A. Derive the equation that determines how much revenue the government will receive for a given rate of tax t. What is this relationship called? B. Solve for the maximum amount of revenue the government can raise from this tax. Hint: the tax rate will be a fraction between 0 and 1. C. In this particular example, what are the contributions of the income and substitution effects?
Indicate whether the statement is true or false, and justify your answer.If a person discounts utility from future periods, her preferences are time-inconsistent because she does not value utility in all periods equally.
Present the classical model of choice under uncertainty. What are the five assump- tions which characterize the Von-Neumann-Morgenstern expected utility repre- sentation?
Based on the model in the image answer the following questions: a. Write down agent period 2 and period 3 budget constraint separately. b. Set up the agent's utility maximization problem showing her choice of variables clearly. Write down the first order conditions for agent's utility maximization. c. Derive the ratio of consumption in period 2 and period 3 i.e. c2/c3 in terms of the parameter of the model. d. Explain how investment on the parameter,e, depends on value of B
Which axiom of the exponential discounted utility model is violated by the quasi-hyperbolic ( β,δ) model? Explain.
Emma has a utility function U(x1, x2, x3) = log x1 + 0.8 log x2 + 0.72 log x3 over her incomes x1, x2, x3 in the next three years. This is an example of (A) expected value; (B) quasi-hyperbolic utility function; (C) standard discounted utility; (D) none of the above. Emma’s preferences can exhibit which of the following behavioral patterns? (A) preference for flflexibility; (B) context effffects; (C) time inconsistency; (D) intransitivity.
A consumer who starts (i.e. has an endowment) at point B, and has preferences shown by IC1, will want to borrow. Question 13Select one: True False Question text Assuming a mix of present and future consumption is preferred, ANY consumer who starts (i.e. has an endowment) at point A will gain utility from a rise in interest rates. Question 14Select one: True False Question text A consumer who starts at point B will want to borrow, but as little as possible in order to minimise the cost of interest. Question 15Select one: True False Question text If a consumer starts at point A, and then receives extra income in the present, this would appear as an outward shift of the budget constraint. Question 16Select one: True False
In the Two Period Consumer model, the Effect from a decrease in current income is: Group of answer choices C1↑; C2↑; Savings ↑ C1↓; C2↓; Savings ↓ C1↑; C2↑; Savings ↓ C1↓; C2↓; Savings ↑ C1↑; C2↓; Savings ↑
Indicate whether the statement is true or false, and justify your answer.Expected utility theory offers one possible valuation function that satisfies the properties of completeness, transitivity, and independence of preferences under uncertainty.
The one-period model with quasi-linear utility predicts that a decrease in marginal income tax rates could increase tax collection if:Group of answer choices Substitution effects dominate income effects so that the percent change in taxes is greater than the percent change in GDP Substitution effects dominate income effects so that the percent change in taxes is less than the percent change in GDP Income effect dominate substitution effects so that the percent change in taxes is less than the percent change in GDP Income effects dominate substitution effects so that the percent change in taxes is greater than the percent change in GDP
Suppose we wanted to investigate the saving and borrowing behavior of consumers. It’s not that difficult to extend our basic model. We can use the same framework as before, but define our two goods as “consumption in period 1” (horizontal axis) and “consumption in period 2” (vertical axis). a. Construct a budget constraint for a consumer who earns $100 in income in period 1 and $300 of income in period 2. Label this point E for the “Endowment” point. Assume that he can choose to save some income in period 1 to be used in period 2, or to borrow some income from period 2 to use in period 1. (Let’s imagine the consumer saves the money by putting it in a piggy bank and can borrow money from his parents, who don’t charge interest.)
Consider the following function describing the utility of a consumer: U(x1, x2, x3) = a1*ln(x1) + a2*ln(x2) + a3*ln(x3), where ln = natural logarithm and a1, a2, a3 constants a. Pose the primal problem (using Langrange's method), obtaining the Marshallian demands for each good and the individual's indirect utility function. b. From the results obtained from question a., find the minimum expenditure function and the Hicksian demands.