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 Derive worker’s income elasticity. Is leisure a normal or inferior good for this worker?
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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
Derive worker’s income elasticity. Is leisure a normal or inferior good for this worker?
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- 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.A consumer has preferences over bundles of leisure (L) and consumption (z) respresented by the utility function u(L, r) = La and has 24 hours in the day to divide between work and lesiure. This consumer has sorme positive amount of nonwork income per day (m > 0) and is able to select how many hours they wish to work at some positive wage per hour (w > 0). Find the consumer's reservation wage as a function of m: this is the lowest wage at which the consumer will work positive hours. Equivalently, it is the highest wage at which the consumer will work zero hours. (Hint: this is all about the MRS when working zero hours.)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 1) Provide the functional form of the income effect from a marginal decrease in income. 2) Provide the functional form of the substitution and total income effects of a marginal increase in wage. 3) Show that the Slutsky equation holds for this worker.
- 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.Winona has 80 hours to divide between leisure and labor. Her utility function is u(r,c) = f(r) + c, when r represents hours of leisure,c represents dollars of consumption, and f is strictly concave. Winona’s wage is w0= $15/hr. initially, then it rises to w1= $20/hr. (i) Explain what happens to Winona’s labor supply when the wage rises,and why. (ii) Explain how the answer to (i) would change if Winona were to win a lottery.Consider an individual who lives in an economy without a welfare program. They initially work T-L0hours per week, where (T-L0)>0. They earn an hourly wage (W) and no non-labour income. a) Draw a graph that reflects this individual’s income-leisure constraint, utility-maximizing indifference curve (U0), choice of leisure hours (L0) and income (Y0). b) Now, assume that a welfare program has been implemented in this economy. The welfare benefit is smaller than the individual's initial income level (Y0) and there is a 50% clawback on any labour income earned. The individual now maximizes their utility by working and collecting a partial welfare benefit. On the same graph as part a, draw this individual’s new income-leisure constraint, utility-maximizing indifference curve (U1), choice of leisure hours (L1) and income (Y1).
- 21. 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) noneA worker has 110 hours available in a week that can be used for leisure (L) or work (h). The utility function is U = (1 - α)ln(C) + α ln(L), where C is consumption. a) The price per unit of consumption is 1, the hourly wage is w, and the worker has a non-labor income of V. Show that the labor supply is: h* = (110(1-a)- (av)/w). Also, find the demand for consumption and leisure. b) What is the effect on labor supply of i) an increase in the hourly wage and ii) an increase in non-labor income? c) Set α = ½. What are C, L, and h when w = 200 and V = 10000? What is the reservation wage? d) What is the effect on labor supply of i) a 30% income tax and ii) a 10% wealth tax (on V)? e) What is the labor supply if V increases to 11600? f) An increase in V to 11600 gives the worker the same utility as w = 250 and V = 10000 (you do not need to show it). What are the income, substitution, and total effects on labor supply of an increase in wage from 200 to 250 while V remains at 10000?…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 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 functiondefined over consumption and leisureU(c,l) = lnC + 4lnl1) Compare worker 1 with worker 2 whose utility function is described by U(c,l) = cl. Whichworker places a higher value on labour market work?12) Suppose the worker participates in the labour market. Derive worker’s compensated laborsupply function and the compensated labour supply elasticity with respect to wage as a functionof utility level and wage.3) Derive worker’s uncompensated labour supply function (for labour market participants andnon-participants) and the uncompensated labour supply elasticity (for labor market participants)with respect to wage as a function of non-labour income and wage.4) Derive worker’s income elasticity. Is leisure a normal or inferior good for this worker?5) Provide the functional form of the income effect from a marginal decrease in income.6) Provide the functional form of the substitution and total income…(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?Cindy gains utility from consumption C and leisure L. The most leisure she can consume in any given week is 168 hours. Her utility function is U ( C, L) = C x L. This functional form implies that Cindy’s marginal rate of substitution is C/L. Cindy receives $630 each week from her great-grandmother—regardless of how much Cindy works. What is Cindy’s reservation wage?
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