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, Tez 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)+6log(c₂) such that (1+₁)C₁+8 = (1-7)wl and (1+T₂)₂ = [1+r(1-T₁)]s+b, where measures how the household values leisure vis-a-vis consumption. A. Explain in English the meaning of the objective function and the 2 constraints.
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- 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 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 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…There are some simplifying assumptions in order to generate simple expressions. One of these assumptions is that r (interest rate) = ρ (rate at which household discounts future). Suppose we relaxed this assumption (i.e. allowed r to differ from ρ). Two results of the model are: i) The household keeps the expected value of consumption constant over time. ii) The household responds differently to permanent versus temporary income changes. Discuss the implications of allowing r to differ from ρ on each of these resultsAs a hypothetical case, suppose the typical individual has a utility function expressed as U = (C – 50)*(L – 10), where C is consumption and L is leisure time. The current wage, w, is $5 and she has a weekly return on assets of V = $100. She only has 60 hours per week to divide between work hours, h, and Leisure. A number of countries and communities are considering implementing a “Guaranteed Basic Income” as policy. A “Guaranteed Basic Income” is a government payment of a fixed a amount of money for each person Suppose the country of interest sets the weekly payment at $100. i) Using the Neo-classical labor supply with reference to specific numerical values discuss the consequences of the above “Guaranteed Basic Income”. ii) Using the basic Supply and Demand for labor approach discuss the consequences of the “Guaranteed Basic Income” policy on the overall labor market. iii) Using a feedback approach, from the Neo-classical labor supply to market equilibrium and back to labor…
- 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 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 the Two-Period Endowment Model of the Household studied in class. Suppose that optimal consumption period is given by: where ωe is the household's lifetime wealth (after taxes). Is the optimal consumption behaviour implied by (1) consistent with the Permanent Income Hypothesis? Why?
- True or False: It is possible, in a basic hours towards leisure and income towards consumption model, that the Earned Income Tax Credit can encourage more hours towards leisure, less hours towards work and more money towards consumption.According to Irving Fisher’s two period model, if the consumers face borrowing constraint, the first-period consumption cannot exceed first-period income True FalseConsider 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…