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Cosuption function
................. (1)
where a>0 and 0<b<1
The marginal function of consumption function:
differentiating eq 1 w r t Y
Average function:
Dividing eq 1 by Y
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- Assume 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 a three-commodity consumer setting with the expenditure function: e(p, u) = up1α p2βp3γ Find the indirect utility function Find the Walrasian demand function Verify Roy's identity Recover consumer's direct utility functionConsider 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.
- Prove that if the Walrasian demand function is generated by a rational preference relation, then it must satisfy the weak axiom. Is the converse true? If yes, prove it, or else give a counterexample?The representative consumer has the following utility function: U(c, I) = In c + In I where c is the consumption good, and I is the leisure hours. She has h hours of time available which she can allocate between work and leisure. For each hour of work, she earns w units of consumption good. She also earns t as dividend (profit) income which is measured in consumption goods. The government collects revenues using a consumption tax; in particular, the representative consumer pays t units of goods to the government for each unit of consumption good she buys. Note that there is no lump-sum tax. (a) Determine the consumer's budget constraint. (b) Solve for the c and I that maximize the utility of the consumer. (c) Suppose that the tax ratet increases. What is the impact of this increase in the tax rate, t, on the consumer's choice for c and l? What is the impact of this on the labour hours of the consumer?An individual’s utility function is given by where is the amount of leisure measured in hours per week and is income earned measured in cedis per week. Determine the value of the marginal utilities, when = 138 and = 500. Hence estimate the change in utility if the individual works for an extra hour, which increases earned income by GH¢15 per week. Does the law of diminishing utility hold for this function?
- e(p, u) = up1αp2βp3γ Find the indirect utility function Find the Walrasian demand function Verify Roy's identity Recover consumer's direct utility functionConsider a single mother with the utility function U = 2/3 log(x) + 1/3 log(), where x is consumption and is leisure. The mother can work up to 100 hours per month. Any of the 100 hours that are not worked are leisure hours. She earns a wage of $10 per hour and pays no taxes. The consumption price is normalized to $1. To be able to work, she has to incur a child care cost of $5 for every hour worked. a. Suppose that there is no tax and welfare benefits. How many hours will she work and what will be her consumption level? Draw the graph depicting her budget set with consumption on the vertical axis and leisure on the horizontal axis. b. Suppose that the government introduces a negative income tax (NIT) that guarantees an income of $200 per month. The benefit is taken away one for one as earnings increase. Draw the new budget set. Compute the new number of hours worked and consumption level. Has consumption increased and is the mother better off? Why or why not? c. Now…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?
- 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.The utility of Amanda for leisure (L) and income (Y) is U = LY. The price of income is 1. If Amanda uses her spare L hours a day, (24 - L) hours will be labored. Since wages are w, the daily income is (24 - L). If the wages are positive, show that the optimal number of leisure hours that Amanda will use will always be the same. How much leisure time does Amanda demand and how much work time do she want to provide?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.