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 8,2 and 02, with 0,2 0,2. How would the optimal behavior of the two individuals differ, if at all?
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- Problem 4 Consider the leisure demand/labor supply model studied in class, and let the consumer have a spccific utility function U(N, Y) = N2/3y!/3. As in lecture, let the price of consumption be normalized to 1, and let w denote the wage. (a) Say that w = 10. What are the optimal N* and Y*? How many hours does the agent work? Draw a sketch to illustrate this situation. (b) Solve for the general demand functions N(w) and Y(w) as a function of the wage, as well as the labor supply function H(w). Calculate the elasticity of labor supply with respect to the wage, w. Do you notice anything special about this particular example? (c) Say the wage rises to some w' > w. What is the change in leisure demand N(w)? Carefully draw a sketch that decomposes this into an income effect and a substitution effect. (d) Sketch the labor supply function. (e) Let H(w) be the labor supply as a function of the (take-home) wage w. Say now that the government imposes an income tax of a. Let T(a) denote the…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) Derive worker’s income elasticity. Is leisure a normal or inferior good for this worker? b) Provide the functional form of the income effect from a marginal decrease in income. c) Provide the functional form of the substitution and total income effects of a marginal increase in wage.
- Consider the standard labor-leisure choice model. Consumer gets utility from consumption (C) and leisure (L). She has H total hours. She works NS hours and receives the hourly wage, w. She has some non-labor income T and pays lump-sum tax T. Further suppose (n-T)>0. The shape of utility function is downward-sloping and bowed-in towards the origin (the standard U-shaped case just like a cobb-douglas function) If this consumer decides to NOT WORK AT ALL, then it must be the case that O A. MUL = MUC O B. MRSL,CI 2 w OC. IMRSL,CIs w O D. MRSL,C = w O E. None of aboveAssume Lorena derives utility from consumption and leisure. Through the following utility function. U=VC-R where C is consumption and R is hours of leisure consumed per day (there are 24 hours in her day). Let w be the wage rate and H be the hours of work chosen. The price of consumption goods, C, is $1. In addition, assume Lorena has $M amount of non- wage income each day. Set up the utility maximizing Lagrangian needed to maximize utility subject to the budget constraint but do not solve for the demand for C and R. a b. Draw the consumer choice model for this situation (fully label the graph). Use it to graphically derive/describe/explain her labor supply function and explain what would be true for her labor supply to rise or fall when the wage rises (you may want to draw the graph twice. Measure and explain the loss in consumer surplus using the concept of compensating variation. g. h. What is the expenditure-price elasticity equation for y? That is, the elasticity for the % change…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.Provide the functional form of the income effect from a marginal decrease in income and provide the functional form of the substitution and total income effects of a marginal increase in wage.
- Consider a consumer who could earn $400 per week and has 50 weeks available each year to allocate between work (H) and nonmarket time (L). They have no non-labour income. Their utility function is U = C2L , where C is the value of consumption goods. What is their optimal choice for the number of weeks in nonmarket time and consumption? Show this in a diagram. Suppose the government introduces a policy that (i) offers no benefits to people who do not work, (ii) offers a wage subsidy on earnings at a rate of 25%, with a maximum benefit of $5000, and (iii) the benefit is subject to reduction at a rate of 25% for every dollar earned above $20,000 in the year. Show the person’s new budget constraint in a new diagram, and discuss how the person’s optimal choice might change (you do not have to calculate this, but point to where it is likely on the new budget constraint). Discuss how income and substitution effects play a role.A worker , who satisfies our normal assumptions , is indifferent between consuming 4 units of leisure while earning 100 dollars and consuming 12 units of leisure while earning 40 dollars . If both bundles are feasible , is this worker maximizing utility ? Why or why not ?Let the demand and supply function for a commodity be Qa= D(p,Y) Dp 0 Qs = S(p, w) Sp>0, Sw<0 where p is the price, Y in exogenous income, and w is the exogenous wage rate. a. Find dp and dp using the implicit-function theorem. dw dp dy b. Find and dp by totally differentiating the equilibrium condition. dw
- Construction workers in the town of Cortland, NY have Cobb-Douglas utility for labor and consumption, UL=(20-L)C, MRS=C20-L where L is the number of hours of labor supplied in a day and C is the dollar amount of consumption goods purchased with wage income (pc=$1 ). R=20-L is the number of hours of leisure that the worker has during the day. Derive the labor supply function for workers in Cortland. Draw the labor supply curve on a graph with L on the horizontal axis and w on the vertical axis.3. The value of a worker's marginal product is $40 per hour for high-ability workers and $10 per hour for low-ability workers. Each worker cares about the wage (w) and amount of education (e) he or she obtains. Preferences over education- wage pairs (e, w) of high-ability workers are representable by utility function un(e, w) = w - 5e, and low-ability workers by utility function u(e, w) = w – 10e. By law, everyone is required to attend at least 10 years of school. One-third of the population has low ability and two-thirds has high ability. Reservation wage for each type is zero. What can you say about the educational attainment of each type of the worker in a separating equilibrium? Show your work. a) b) What can you say about the educational attainment of each type of the worker in a pooling equilibrium? Show your work.Susan obtains utility by consuming carrots C and enjoying leisure L. Suppose that she has a daily non-wage income Y of £100 and is paid a fixed hourly wage rate of £10 for every hour she works in a local coffee shop. Assume that Susan is a utility maximiser and is free to choose x hours of work per day where 0 ≤ x ≤ 10. Assume also that the unit price of C is £1. a) Suppose that L is measured on the horizontal axis and C on the vertical axis. Use these axes to draw the set of all C and L combinations that Susan can choose from. Write down Susan’s budget equation. b) Suppose that Susan’s preferences over carrots and leisure are expressed by the following utility function: U(C,L) = min{C, 10L}. Calculate Susan’s optimal consumption bundle, both algebraically and graphically. Calculate the value of MRS at the optimal choice. c) Suppose instead that Susan’s preferences are such that indifference curves in the L-C space are strictly convex to the origin, and that she chooses to work 5…