a b. 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. 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.
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- The consumer's utility function for Consumption (C) and Leisure (L) is given as U(C,L) = √CLHis hourly wage is $10, non-labor income is $20; and he has a total of 16 hours to allocate between labor and leisureBased on this information, the consumer's total utility at the optimal level (or optimal C,L combination) is:a. 57.0 utilsb. 28.5 utilsc. 99.75 utilsd. 114.5 utilse. Cannot be determined with the information given I prefer typed answers.Suppose that a person has 2000 hours to allocate each year between leisure and work. a. Derive the equation of his budget constraint given an hourly wage of $(15)/hour. b) Graph his budget constraint line based on the equation you derived in part a. (Consumption (C) on the vertical axis and leisure (L) on the horizontal axis). Please make sure to include the value for the vertical and horizontal intercepts. c) Now suppose that the local government introduces an income guarantee program for single parents in which the income transfer is $10,000 per year if an individual does not work during that year (this dollar amount represents the benefit guarantee). If the individual decides to work, this transfer program imposes a 100% benefit reduction rate (e. g.. each additional hourly wage earned is reduced by 100%). Derive the new budget constraint equation that corresponds to this scenario. d) Draw the budget line that corresponds to the new scenario on a new graph. (Consumption (C) on the…Income $240 $192 0 15 16 17 a) Using the above diagram, decompose the effect of a wage decrease for this individual into Income Effect (IE) and Substitution Effect (SE). Leisure 24 b) How many hours of work is effected because of the IE? c) How many hours of work is effected because of the SE? d) What is the net effect of this wage decrease on hours of work for this individual?
- 5. Cindy gains utility from consumption C and Leisure L. Then most leisure she can consume in any given week is 110 hours. Her utility function is U (C, L) = C × L. Cindy receives $660 each week from her great-grandmother. (a) Find her marginal rate of substitution |M RS|. (b) Find her reservation wage. (c) Interpret the reservation wage.Sharon spends her time (16h) between leisure (L) and work and he consume Y product from his working income (P=1). Assume that she gets W$ per hour of working (W>0) and has the following utility function: U (L, Y) =LY 4Y. a.Calculate the demand function for L. and show it on a graph (L. vs W). b. Calculate the labor supply (H) and show it on a graph (H vs W). c.What will happen to L. Y and H if the wage per hour (W) will decrease?a) If Kyeiwaa has GhC 50 of non-labor income per week, and she faces a market wage rate of GhC 5 per hour; and has 110 hours of nonsleeping hours to allocate between work and leisure activities (assuming she sleeps roughly 8hours per day) b) Write down the budget equation for Kyeiwaa c) Graph Kyeiwaa 's budget line. d) Assuming leisure is a normal good (with the aid of a graph), describe what will happen to Kyeiwaa 's hours of work if her non-labour income increases. e) If Kyeiwaa 's substitution effect dominates her income effect, with the aid of a diagram describe what will happen to her hours of work when her wage increases.
- Discuss the possible substitution effect and the income effect of an increase in income on leisure time.Suppose that the owner of Boyer Construction is feeling the pinch of incrs associated with worker’s compensation and has decided to cut the wages of its two employees (Albert and Sid) from $25 per hour to $22 per hour. Assume that Albert and Sid view income and leisure as “goods,” that both experience a diminishing rate of marginal substitution between income and leisure, and that the workers have the same before- and after-tax budget constraints at each wage. Draw each worker’s opportunity set for each hourly wage. At the wage of $25 per hour, both Albert and Sid are observed to consume 12 hours of leisure (and, equivalently, supply 12 hours of labor). After wages were cut to $22, Albert consumes 10 hours of leisure and Sid consumes 14 hours of leisure. Determine the number of hours of labor each worker supplies at a wage of $22 per hour. How can you explain the seemingly contradictory result that the workers supply a different number of labor hours? (LO2, LO3, LO7)What is the budget line for consumption (C) and leisure (L) if a person faces a constant wage of $12 per hour, there are 110 hours in the week to work, and she receives nonlabor income of $300 per week?
- An individual values both consumption and leisure. Suppose the individual has 1600 hours per week they can allocate between leisure and work. IF the individual works, they make a wage of $25 per hour. The individual's utility function is given as a function of leisure time, L and consumption, c: U(L, c) = L^(1/2)c ^ (1/2) a) Draw the individual's budget constraint for leisure and consumption. b) How much leisure time will the individual have when utility maximizing? c) Consider a Universal Basic Income policy like the one proposed by Andrew Yang that would give all individuals a lump -sum, unconditional cash transfer of $1,000 each month. How much leisure time will the individual have when utility maximizing with the cash transfer? d) Now suppose, instead of a cash transfer, a minimum wage of $40 per hour is implemented. How much leisure time will the individual have when utility maximizing with the cash transfer? e) What change in leisure time can be attributed to the substitution…1) Sharon spends her time (20h) between leisure (L) and work and he consume Y product from his working income (Py=1). Assume that she gets W$ per hour of working and has the following utility function: U (L, Y)=LY+2L a. b. C. Calculate the demand function for L and show it on a graph (L vs W). Calculate the labor supply (H) and show it on a graph (H vs W). What will happen to L, Y and H if the wage per hour (W) will decrease? =A worker views leisure and income as “goods” and has an opportunity to work at an hourly wage of $15 per hour. a. Illustrate the worker’s opportunity set in a given 24-hour period. b. Suppose the worker is always willing to give up $11 of income for each hour of leisure. Do her preferences exhibit a diminishing marginal rate of substitution? How many hours per day will she choose to work?