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- 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.Consider the representative consumer who decides consumption and leisure. Theenvironment is the same as in Lecture 5. Keep the same notation. The preference is givenby U (C,L) = αln C + (1 −α) ln L. Assume h = 1, i.e., the time endowment is one day.(a) Write down the utility maximization problem.(b) Derive the demand for consumption and the supply for labour.(c) Suppose the non-wage income π −T increases while the wage rate w falls at the sametime. The size of the changes can be different. Determine the effects on consumptiondemand and labour supply (i.e., leisure demand). Use the indifference map to explainyour results in terms of income and substitution effects for the following cases:(i) The increase in π −T exactly cancels out the drop in w, i.e., |∆ (π −T)|= |∆w|.(ii) The increase in π −T is greater than the drop in w, i.e., |∆ (π −T)|> |∆w|.(iii) The increase in π −T is smaller than the drop in w, i.e., |∆ (π −T)|< |∆w|.(d) Suppose the utility function is Cobb-Douglas: U…Consider a representative agent with the utility function U = ln(Ct)+ Nt The budget constraint is Ct = wtNt +Dt where wt is the wage and Dt is non-wage income (i.e. a dividend from ownership in the firm). The agent lives for only one period (period t), and hence its problem is static. (a) Derive an optimality condition characterizing optimal household behav- ior. (b) Solve for the optimal quantities of consumption and labor. Plz do fast asap, urgent.
- Consider worker 1 with non-labour income Y facing a wage offer w and a utility function defined over consumption and leisure. U(c,l) = lnC + 4lnl a) Compare worker 1 with worker 2 whose utility function is described by U(c,l) = cl. Which worker places a higher value on labour market work? b) Suppose the worker participates in the labour market. Derive worker’s compensated labor supply function and the compensated labour supply elasticity with respect to wage as a function of utility level and wage. c) Derive worker’s uncompensated labour supply function (for labour market participants and non-participants) and the uncompensated labour supply elasticity (for labor market participants) with respect to wage as a function of non-labour income and wage.Consider worker 1 with non-labour income Y facing a wage offer w and a utility function defined over consumption and leisure. U(c,l) = lnC + 4lnl Give that the Slutsky equation holds for this worker.Explain the similarities and differences between the assumptions of Specific Factor Theory and the Model Trading Heckscher – Ohlin
- discuss the key concepts of the Heckscher-Ohlin Model in factor abundenceSuppose there are two identical job offers in the same competitive labor market for a software developer position. Both offers have the same salary of $80,000 per year. However, Job A allows the employee to work from home, while Job B requires the employee to commute to the office daily. The average monthly commuting cost for Job B is estimated to be $400. Calculate the compensating differential in this scenario, and determine if it makes economic sense for the employee to choose Job B over Job A. Assume a working year consists of 12 months.One proposal includes increasing the EITC for childless workers to provide additional assistance for many poor workers. While an increase in the EITC would increase resources to qualifying childless workers, what impact will it have on their working decision? Assume a basic hours towards leisure and income towards consumption model. a. If qualifying childless workers already have a strong preference to work so they are already choosing to work (ex: 10 hours), an increase in the EITC could lead to a new choice involving fewer hours spent working, more hours spent towards leisure and more income towards consumption. Thus, the EITC expansion could discourage work. b.If qualifying childless workers already have a strong preference to not work so they are already choosing to work very littleand mostly enjoy leisure, an increase in the EITC could lead to a new choice involving more hours spent working, fewer hours spent towards leisure and more income towards consumption. Thus, the…
- Consider a worker who is endowed with T hours of time and investment income V per week, faces a wage rate w per hour, and whose preferences over the consumption of goods, the price of a unit of which is p, and leisure can be represented by the utility function U(C,L) = C1/2L1/2. Find the worker’s labour supply. When is it positive? Will the worker ever work more than half their time endowment? (25%)In a standard consumer optimization problem in microeconomics, a consumer purchases any pair of goods untilU1U2=p1p2(?), at an interior solution, where Ux is the marginal utility of good x for the consumer and px is the price of good x, where x={1,2}. What is the corresponding optimality condition for a worker-consumer in his labour-leisure optimization problem and why is it just a variation on the standard optimality condition (?)?The HO model is based on four key relationships: between factor prices andcommodity prices, between goods prices and outputs, between goods prices and factor returns, and lastly between factor endowments and outputs.Clearly Explain.