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- 4. A consumer’s utility function over leisure and consumption is given by u(L, Y) =LY. Wage rate is w and the price of the composite consumption good is p = 1. (a) Suppose w = 10. Find the optimal leisure - consumption combination. (b) Suppose the overtime wage law is passed so that the firm must pay 1.5 times the normal wage for hours worked beyond the first 8 hours. Find the effect on the hours worked. Decompose the effect into substitution effect and income effectQ1: Suppose Labor and Capital are substitutes and the price of capital falls. All else equal, we should expect the labor select (supply, demand) Curve shift select ( up to the right, down to the left ) and for equilibrium wages to select (rise, fall) Q2: An individual has a utility function over Leisure and Income such that ?=?1/2?1/2 This individual has a budget constraint ?=?⋅(24−?)+? The best possible wage this individual can earn in the labor market is $2 per hour. This individual is $30 in debt (they have negative non-labor income). If this individual is earning a utility level of 4, which of the following are true? Group of answer choices The worker could be supplying 1 unit of Labor The worker could be earning $10 The worker could be supplying 8 units of labor The worker is maximizing their utility given their budget The worker's Marginal Rate of Substitution at the point where the budget constraint intersects the indifference curve is equal to -221. Let U=x 2 +y 2 is the utility function of a worker who has 10 hours that to be allocatedbetween labour supply (L) and leisure (x). Let y is a consumption good whose price is 1.Wage rate (w) is Rs 1 and non-wage income is 20. Find out L.a) 10 b) 0 c) 5 d) 8 e) none 22. On the basis of the above question, hen w=0 and non-wage income is 40, find out L.a) 10 b) 0 c) 5 d) 8 e) none
- This question will analyze the impact on a person's labour supply from a shock to their partner's job. Assume leisure is a normal good. Let's assume Vanessa has a wage rate of $20 per hour. Recently her partner, Bill, had to take a wage cut at work, with his wage falling from $45 per hour to $30 per hour, but allowed them to continue working 40 hours per week. Analyze the decision of the household over choice consumption and Vanessa's leisure, taking Bill's hours as given (constant).(i) Keith’s marginal utility of leisure is C – 20 and his marginal utility of consumption is L – 50. There are 110 hours in the week available to split between work and leisure. Keith receives £250 of welfare payments each week regardless of how much he works (assume he spends all of his welfare payments on consumption). What is Keith’s reservation wage? (ii) Suppose Danny receives the same welfare payments each week as Keith and has the same number of available hours (110). However, Danny’s indifference curve is flatter than Keith’s. How would his reservation wage compare to Keith’s? Why?2. Let an individual’s utility function be given by where C and L are consumption and leisure respectively, and g, a and b are positive constants with a + b = 1. Derive the individual’s Marshallian labor supply function and comment on the magnitudes of the income and substitution effects of wage change. Derive the general form of Slutsky equation of labor supply.
- The weekly preferences over consumption (C) and leisure(L) are defined by u(C, L) = √C + 3√L. The person receives a weekly allowance of m from The hourly wage is $18 per hour, and the person can work up to50 hours each week (T = z + L = 50), where z is the number of hours spent working). a)How many hours will the person work if her allowance is m= $450 per week b) What is the smallest allowance m for which the person will stopworking altogether (z∗ = 0) for a wage of w = 18?Q2: Let a consumer’s daily hours of work is denoted by H, and hours of leisure by L. Consumer has no other source of income except wages for hours worked. She consumes what she earns each day. Her utility function is U(C, N) = ln(C) + 3 ln(N) Where C stands for the dollar amount of her consumption. Now answer following questions (a) Suppose the wage rate is 50Rs. per hour. Write down the consumer’s utility function and budget constraint with C and H as the choice variables. (b) How many hours will she choose to work, and what will be the resulting utility?d. Based on both the consumption-leisure optimality condition obtained in previous part (Based on both of the two first-order conditions, construct the consumption-leisure optimality condition) and on the budget constraint, qualitatively sketch two things in a diagram with the real wage on the vertical axis and labor on the horizontal axis. First, the general shape of the relationship between w and n (perfectly vertical, perfectly horizontal, upward-sloping, downward-sloping, or impossible to tell). Second, how changes. in / affect the relationship (shift it outward, shift it inward, or impossible to deter mine). Briefly describe the economics of how you obtained your conclusions.
- Consider 5 workers who care about their consumption and continuous job satisfaction J.Their preferences are described by the utility function U(C,J) = 2C + J. There are 5 firms thatare producing the output using the production function Q(J,L) = L√20 − J1. What are the marginal rate of substitution between consumption and job satisfaction andthe marginal rate of transformation between wages and job satisfaction?2. What are the equilibrium levels of wage and job satisfaction?3. What is the slope of the wage-job satisfaction locus?q7- When leisure is a normal good, the income effect from an increase in wages is manifest in a(n): Select one: a. desire to consume less leisure b. a change in preferences c. desire to consume more leisure d. a shift inwards of the budget constraintSuppose a worker is offered a wage of $5 per hour, plus a fixed payment of $40. What is the equation for the worker’s opportunity set in a given 24-hour day? What are the maximum total earnings the worker can earn in a day? The minimum? What is the price to the worker of consuming an additional hour of leisure?