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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 max{log c1 + log c2} 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 g1 + g2 = τ1 + τ2 where g1 and g2 are exogenous government expenditures…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. Solve for first order conditions of the representative agent. B. Write down the market clearing condition (resource constraint) for the aggregate economy. C. Solve for equilibrium consumption and labour choices.Question 2-Labor Supply (5,000 character limit on all answers combined) Consider individuals who have the following form for their utility function from leisure and consumption: U (c, 1) = A₁c110₂, where A, is an individual specific parameter. That is, each individual in the population is born with a different A₁. Let V be the non-labor income for the individual, let w and p be the hourly rate and the price of the consumption good respectively. Assume that an individual must sleep at least 7 hours a day, so the number of hours available for him/her is 24 - 7 = 17. Please complete the following questions: A. Derive the optimal number of leisure hours and the corresponding hours of labor supply. B. Discuss the impact that the non-labor income has on the labor supply of individuals. C. Suppose that there are two individuals, i and j, with the same 0₁, but with different 02, namely 0,2 and 02, with 02 > 2. How would the optimal behavior of the two individuals differ, if at all? D. Suppose…
- Now,suppose N=3 with a market clearing interest rate. The first two agents are the same as earlier. The third agent has an endowment of 20 in the first period and consumes 15 in the second period. If the first two agents each consumed 21 units in the first period, how much did the third agent consume in the first period? Plz do fastQ7: 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…Answer please with added diagrams b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves. c) Use indifference curves and the feasible set to show why, given the properties of the optimal choice in part b it is not optimal to work, say, 10, or 6 hours per day.
- Solve all this question......you will not solve all questions then I will give you down?? upvote...A decision maker allocates an endowment of W > 0 dollars across two periodst = 1, 2. He discounts the future by β ∈ (0, 1) while facing a gross interest rateof R > 1. His utility is the same as studied in class. Solve for the intertemporalchoice problem. Show that the optimal consumption is decreasing over time ifβR < 1, constant over time if βR = 1, and increasing over time if βR > 1.Use the following parameters to sketch two budget constraints, one with no (or $0) basic personal amount (BPA) and one with $1000 BPA, in a diagram:i. Assume there is only one tax bracket with income tax rate 50%ii. Time endowment = 24, wage rate per hour = $100iii. No other deductions and tax credits. Based on your diagram, discuss how the increase in BPA from $0 to $1000 would affect the labor supply due to the substitution and income effects.
- b) have a Cobb-Douglas production function where a = 0.2, L = 400, and labor income + capital income = $2,000, what is the price of the output given the neoclassical theory of distribution holds? Using the model for a closed economy, if the nominal wage is $40 and we %3DConsider 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”.A decision maker allocates an endowment of W > 0 dollars across two periodst = 1, 2. He discounts the future by β ∈ (0, 1) while facing a gross interest rateof R > 1. His utility is the same as studied in class. Solve for the intertemporalchoice problem. Show that the optimal consumption is decreasing over time ifβR < 1, constant over time if βR = 1, and increasing over time if βR > 1.