F.Derive the intratemporal optimality condition; that is, the consumption-leisuretrade-off in period 1. (Hint: What is the MRS = MU₁-1/MU?) Interpret.(a) Hint 1: A higher labor income tax rate 7 reduces consumption relative to leisure.(b) Hint 2: A higher consumption tax rate in period 1 Te, reduces consumption relativeto leisure. Let's incorporate the labor-leisure trade-off and capitalincome taxes in the two-period model. Let c₁, c₂ be consumption in two periods, I the numberof hours worked, Te Te the proportional taxes on consumption in 2 periods, s the savingrate, w the wage rate, b pension in the 2nd period, and 7, the tax on savings (capital incometax). The household's maximization problem in this case is: given by max₁,02,8,1-1 log(c₁) +log (1-1)+5log (c₂) such that (1+T₁₁) C₁+s=(1-7)wl and (1+T₂)C₂ = [1+r(1-T)]s+b,where measures how the household values leisure vis-a-vis consumption.

In the field of economics, the term intertemporal choice signifies a method of decision-making that…

F. Derive the intratemporal optimality condition; that is, the consumption-leisure trade-off in period 1. (Hint: What is the MRS = MU₁-1/MUC₁?) Interpret. (a) Hint 1: A higher labor income tax rate 7 reduces consumption relative to leisure. (b) Hint 2: A higher consumption tax rate in period 1 Te, reduces consumption relative to leisure.

F. Derive the intratemporal optimality condition; that is, the consumption-leisure trade-off in period 1. (Hint: What is the MRS = MU₁-1/MUC₁?) Interpret. (a) Hint 1: A higher labor income tax rate 7 reduces consumption relative to leisure. (b) Hint 2: A higher consumption tax rate in period 1 Te, reduces consumption relative to leisure.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1) In the IS equation why wasnt G in the calculations. 2)Suppose that with all exogenous variables, including T and M at their original values, households become less confident about the future and reduce their autonomous level of consumption from 200 to 150. Solve for the new values of e, Y and NX. With the help of graphs, explain very carefully the mechanisms by which a new equilibrium is reached. 3)Suppose that with all exogenous variables at their original values, the autonomous part of money demand increases to 70. Solve for the new values of e, Y and NX. With the help of graphs, explain very carefully the mechanisms by which a new equilibrium is reached.
Let's incorporate the labor-leisure trade-off and capital income taxes in the two-period model. Let c₁, c₂ be consumption in two periods, I the number of hours worked, Te Te the proportional taxes on consumption in 2 periods, s the saving rate, w the wage rate, b pension in the 2nd period, and 7, the tax on savings (capital income tax). The household's maximization problem in this case is: given by maxe₁,e2,8,1-1 log(c₁) + log (1-1)+5log (c₂) such that (1+T₂) C₁+8 = (1-7)wl and (1+T₂)C₂ = [1+r(1-Ts)]s+b, where measures how the household values leisure vis-a-vis consumption.
Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income. Derive and plot the feasible set, between daily values of consumption c, and “leisure”, l. Label the values at the intercepts (the points where the feasible frontier cuts the two axes).
11. A worker derives utility from consumption, C and leisure, L U = U(C, L) and initially faces the constraints p.C = N+w.H H = 24 - L where p is the nominal price of consumption, N> 0 is unearned income, w is the nominal wage and H is hours worked. (a) Derive the budget constraint in terms of C and L and show on a diagram an initial optimal choice of C and L, in which both are positive. (b) State this equilibrium algebraically, and briefly explain how it can be derived. (c) Show that, assuming normality of leisure, for some value N*, if N> N*, the individual will choose not to work. Is the initial level of N in your answers to parts a) and b) greater or less than N*?
Suppose that there are T periods to maximize over. Show that the intertemporal budget constraint is Ct+2 Yt+2 Yt+1 (1+r) (1+r)² (1 + r)² Ct + Ct+1 (1 + r) + 2+...+ Ct+T+1 (1+r)² \ T = Yt + + +...+ Yt+T+1 (1+r)
Q7: An individual lives for only two periods and has preferences given by the follow- ing intertemporal utility function: U = lng + aln(1-h₁) + B[lno₂+ a ln(1 — h₂)] (1) where, c₁, c₂ denotes consumption in period 1 and period 2 respectively h₁, h₂ denote the labour supply in period 1 and 2 respectively. Therefore 1-h is the amount of leisure time in period 1. The term 3 is the discount factor. The problem of the individual at period 1 is to choose consumption in both periods and labour supply in both periods subject to the following budget constraints: +8= why and 0₂= w₂h₂ + (1+r)s where s denote the saving, w denotes the wates and r denotes the real interest rate. (a) Provide an economic interpretation of the two budget constraints written above. (b) Combine the two budget constraints written above and prove the economic interpretation of of life time budget constraint. (c) Set the Lagrangean function and find the first order conditions with respect to C₁ C₂, hi and h₂. (d) Find the…
10. Suppose in our model, lifespans increased due to a productivity in- crease. What would likely happen to hours worked and leisure over the lifetime of a represent ative consumer. (a) Let's consider one of two common ways of implementing this change. Suppose the increase raised both lifespans and the amount of years consumers are healthy enough to work by the same amount, how would that likely affect the measured numbered of hours work by prime aged adults within a given year? What would likely hap- pen to the retirement age? (b) Let's consider the other way to implement it. Suppose the change in lifetimes came about changes in technology that delayed death but did not extend the amount of years consumers are healthy enough to work. What would likely happen to hours worked within a year? What would happen to the retirement age? (c) In the US, the generalized stylized fact is that the actual age of retirement is not increasing. Nor are hours worked per week. Why are both of the above…
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
Assume that Kelly is a life cycle consumer and receives incomes of 20, 30, 45 and 0 in her four period life. What is Kelly's marginal propensity to consume out of her new wealth (AC/AW) in the following situations: [Hint: Let AC be the the change in consumption compared to what she would have done before the inheritance changed her wealth AW]. 19. In period 2 following an unexpected inheritance of 10: (a) 0.25; (b) 0.33; (c) 0.75; (d) 1.0; 20. In period 3 following an expected lump sum payment from her trust fund of 15: (a) 0.33; (b) 0.75; (c) 0.45; (d) 0.50; 21. What is her desired optimal consumption in period 3 with the anticipated trust fund gift of 15: (a) 20; (b) 30; (c) 27.50; (d) 22.50; 22. In what period of her working life (Y > 0) would her marginal propensity to consume out of an unexpected inheritance of 10 be the highest: (a) 1; (b) 2; (c) 3; (d) 4;