H11. Q5In a two-period model, suppose that a consumer's utility function is:U(c₁, c₂) = log(c₁) + log(c₂)where c₁, c₂ are the consumption of a good (orange) in the two periods.Let the endowment real income in the two periods be 2, 1 respectively.The real interest rate is unknown and is to be determined in the equilibrium. Assume that all consumers areidentical.** Part aSolve the demand for c₁ given any real interest rate r.** Part bFind the level of the real interest rate such that the market clears in Period 1.

Utility function : U(c1, c2 ) = log (c1) + log(c2) Period 1 Budget constraint - c1 + S = Y1…

Q5 In a two-period model, suppose that a consumer's utility function is: U(C₁, C₂) = log(c₁) + log(c₂) where c₁, c₂ are the consumption of a good (orange) in the two periods. Let the endowment real income in the two periods be 2, 1 respectively. determined in the equilibrium. Assume that all

Q5 In a two-period model, suppose that a consumer's utility function is: U(C₁, C₂) = log(c₁) + log(c₂) where c₁, c₂ are the consumption of a good (orange) in the two periods. Let the endowment real income in the two periods be 2, 1 respectively. determined in the equilibrium. Assume that all

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.2P

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Consider the two-period household-maximization model discussed in class. The model is modified in order to look at applications including credit constraints, interest-rate markups, and taxation. A representative household lives for two periods and maximizes utility of consumption in period 1 and in period 2. The utility is represented by log(c) where c denotes consumption. Assuming no discounting between period 1 and period 2. The maximization problem for the representative household can be written as a) Explain what is meant by a representative household. Briefly explain the budget constraints of the representative households and of the government. Explain the role played by the assumption that the representative households lives for only two periods and the assumption of “no discounting”.
Consider the two-period household-maximization model discussed in class. The model is modified in order to look at applications including credit constraints, interest-rate markups, and taxation. A representative household lives for two periods and maximizes utility of consumption in period 1 and in period 2. The utility is represented by log(c) where c denotes consumption. Assuming no discounting between period 1 and period 2. The maximization problem for the representative household can be written as below (see image): Question: Show consumption c1 and c2 (you can use algebraic or graphical methods). In theanswer, you should discuss whether a1 ≥ 0 or a1 < 0 and provide an economic interpretation.What determine(s) the sign of a1 and why?
According to Irving Fisher’s two period model, if the consumers face borrowing constraint, the first-period consumption cannot exceed first-period income True False
Consider an economy where individuals live for two periods only. Their utility function over consumption in periods 1 and 2 is given by U = 2 log(C1) + 2 log(C2), where C1 and C2 are period 1 and period 2 consumption levels respectively. They have labor income of $100 in period 1 and labor income of $50 in period 2. They can save as much of their income in period 1 as they like in bank accounts, earning interest rate of 5 percent per period. They have no bequest motive, so they spend all their income before the end of period 2. a. What is each individual’s lifetime budget constraint? If they choose consumption in each period so as to maximize their lifetime utility subject to their lifetime budget constraint, what is the optimal consumption in each period? How much do the consumers save in the first period? b. Suppose that the government introduces a social security system that will take $10 from each individual in period 1, put it in a bank account, and transfer it back to…
Consider the two-period household-maximization model discussed inclass. The model is modified in order to look at applications including credit constraints,interest-rate markups, and taxation. A representative household lives for two periods andmaximizes utility of consumption in period 1 and in period 2. The utility is represented bylog(c) where c denotes consumption. Assuming no discounting between period 1 and period 2. The maximization problem for the representative household can be written asmax{log c1 + log c2}c1 + a1 = y1 − τ1 + (1 + r)a0c2 = y2 − τ2 + (1 + r)a1where y1 and y2 denote income levels in period 1 and period 2, τ1 and τ2 are taxes in the twoperiods, and a0 and a1 denote the assets of the households in each period. a0 is exogenouslygiven. Assume the interest rate r = 0, and the government can borrow or save at the sameinterest rate so that its present-value budget constraint is given byg1 + g2 = τ1 + τ2where g1 and g2 are exogenous government expenditures in the two…
In the two-period Fisher model of consumption, suppose that the first period income is $5,000 and the second period income is $5,000 for both Matt and Paola. The interest rate is 10 percent. Matt’s lifetime utility function is C1 + C2 while Paola’s lifetime utility function is C1 + 0.8C2. If there is a borrowing constraint, whose consumption is affected by that?
Consider an individual who lives for two periods and has utility of lifetime consumption U = log(C1) + 1/1+δ log(C2), where C1 and C2 are the consumption levels in the first and second period respectively, and δ, 0 1 > 0 in the first period and no income in the second period, so Y2 = 0. He can transfer some income to the second period at a before-tax rate of return of r, so saving $S in the first period gives $[1 + r]S in the second period. The government levies a capital tax at rate τ on capital income received in the second period. The tax proceeds are paid as a lump-sum transfer to the following generation. The present generation does not care about the next one. a. What is the lifetime consumption profile of this individual? What is his lifetime indirect utility function expressed as a function of Y1 and b. Evaluate the change in initial income Y1 that is required to compensate the individual for the welfare loss due to the capital income tax τ. c. What is…
Calua is an economy in which people live for three periods. They receive an endowment in only one period as follows: 80 goods when young, or 90 goods when middle-aged or 115 goods when old. The real interest rate in Calua is 10%. Given this information, what endowment should a typical person choose? Assume the interest rate increases to 15%. Which endowment should a typical person now choose?
Consider the two-period endowment economy we discussed in class. In this economy, a household lives for two periods and can save s. The return on saving is the real interest rate,r. Income is exogenous and given as y and y'. Households have utility overconsumption,c, in each period by U(c)=In(c)+B In(c') where future utility is discounted with rate B. Households choose consumption in both periods,c and c'. 1-Write down the current period and future period budget constraints. Derive the lifetime budget constraints. 2-What is the slope of the lifetime budget constraint? What are the intercepts? What is the significance of the endowment point? 3-Write down the expression for the consumer's optimization problem. What is the tangency condition? Provide an intuitive explanation for this condition. 4-Solve for c,c', and s. Given that B=1 and r=0, how would you modify the answers for c,c; and s? Explain.
Consider the two-period household-maximization model discussed in class. The model is modified in order to look at applications including credit constraints, interest-rate markups, and taxation. A representative household lives for two periods and maximizes utility of consumption in period 1 and in period 2. The utility is represented by log(c) where c denotes consumption. Assuming no discounting between period 1 and period 2. The maximization problem for the representative household can be written as Max{logc1+logc2} c1+a1=y1-τ1+(1+r)a0 c2=y2-τ2+(1+r)a1 where y1 and y2 denote income levels in period 1 and period 2, τ1 and τ2 are taxes in the two periods, and a0 and a1 denote the assets of the households in each period. a0 is exogenously given. Assume the interest rate r = 0, and the government can borrow or save at the same interest rate so that its present-value budget constraint is given by where g1 and g2 are exogenous government expenditures in the two periods. (b). Show…
In a two-period model, an individual earns and consumes C1 in period 1 and only consumes C2 in period 2. Suppose the saving interest rate is 3.3% and the income in period 1 is $4,500. Assuming consumption smoothing, the consumption (C1 or C2) for period 1 and period 2 should be $ A . Compute A.In a two-period model, an individual earns and consumes C1 in period 1 and only consumes C2 in period 2. Suppose the saving interest rate is 3.3% and the income in period 1 is $4,500. Assuming consumption smoothing, the consumption (C1 or C2) for period 1 and period 2 should be $ A . Compute A.
Consider the two-period Real Business Cycle (RBC) model without uncertainty presented in the lecture slides, but with one modification. Now assume that the instantaneous utility function for households takes the form: where Ct is consumption at time t and (1- lt) is leisure time at time t. Given that the time endowment is normalized to 1, it follows that lt is hours worked at time t. Finally, Ɵ > 0, b > 0 and gamma > 0 are parameters. All households in the economy are assumed to be identical. We can therefore consider a 'representative household' (henceforth 'the household'). Set t = 1 for the present period and set t = 2 for the next period. For example, C1 is consumption in the present period and C2 is consumption in the next period. Remember, this is a two-period model so there are no time periods prior to t = 1 and there are no time periods after t = 2 Assume that the household begins and ends life with no accumulated wealth and that the real interest rate is r (where…