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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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- Suppose there are two identical job offers in the same competitive labor market for a software developer position. Both offers have the same salary of $80,000 per year. However, Job A allows the employee to work from home, while Job B requires the employee to commute to the office daily. The average monthly commuting cost for Job B is estimated to be $400. Calculate the compensating differential in this scenario, and determine if it makes economic sense for the employee to choose Job B over Job A. Assume a working year consists of 12 months.Suppose that following represents the utility function of the individual U(c,l)=log(c)+log(l) c = consumption level of the individual and l = leisure, while the market wage is 10 and available time is 20. 1) Find and draw the labor supply function. 2) Suppose that the government introduces a cash grant for the labor (who is in the labor force) in the amount of R. Find and draw the labor supply function? Compare it to the labor supply function you have found in a). 3) Discuss the existence of reservation wage in the settings described in a and b? If your answer is : “there are no reservation wages under those settings”, please introduce a change in the policy described in b) to make sure that the reservation wage would exist.Anna and Bob are the only residents of a small town. The town currently funds its fire department solely from the individual contributions of these two residents. Each of the two residents has a utility function over private goods ? and total number of firemen ?, of the form: ?(?,?)=2ln?+ln?. The total provision of firemen hired, ?, is the sum of the number hired by each of the two persons: ?=??+??. Ann and Bob both have income of 200 each, and the price of both the private good and a fireman is 1. They are limited to providing between 0 and 200 firemen. For the purposes of this problem, you can treat the number of firemen as a continuous variable (it could be man-years). Consider the setup from Question 2. Suppose that the government recruits additional ?N firemen and taxes Ann and Bob equally to cover the cost. Therefore, the total number of firemen is ??+??+?MA+MB+N, where ??,??MA,MB are appropriate individually-optimal contributions of ?A and ?B(i.e., the agents behave optimally,…
- Consider the Two-Period Endowment Model of the Household studied in class. Suppose that optimal consumption period is given by: where ωe is the household's lifetime wealth (after taxes). Is the optimal consumption behaviour implied by (1) consistent with the Permanent Income Hypothesis? Why?Consider a society consisting of two people. Edison earns an income of $85,000 per year and Hilary earns an income of $25,000 per year. The government is considering a redistribution plan that would impose a 25% tax on Edison's income and give the revenue to Hilary. Without any incentive distortion, Edison would retain $63,750 and Hilary would end up with $46,250. However, let us assume that since Edison will not receive all the income he earns, he decides to work less and earn an income of only $75,000, of which 25%×$75,000=$18,75025%×$75,000=$18,750 will be owed in taxes. With the redistribution plan, Edison will take home an income of_________. . The $18,750 that Edison pays in taxes will be transferred by the government to Hilary. Let us assume that since Hilary now receives payment from the government, she will not work as many hours and will earn an income from work of only $24,000 instead of her initial $25,000. With the redistribution plan, Hilary's total…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 Give 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 Derive worker’s income elasticity. Is leisure a normal or inferior good for this worker?All individuals have the same utility function over consumption, C, and leisure, L, given by U = C1/3L2/3, Denote the wage rate by w. The total time available for labour and leisure is equal to 12. The price of consumption is PC=1. Denote the amount of labour supplied as N. 1)Find the Labour supply function. 2)The government introduces a tax t=0.2 on wage, such that the after-tax wage is (1-t)w. How much tax revenue does the government collect on everyone? What is the effect on labour supply? 3)The government chooses instead to collect a fixed lump-sum T from everyone. What is the effect on labour supply?How does path dependency provide an explanation for differentiation in earnings between men & women?
- Suppose the bottom 50 percent of a population (in terms of earnings) all receive an equal share of p percent of the nation’s income, where 0 ≤ p ≤ 50. The top 50 percent of the population all receive an equal share of 1 − p percent of the nations income. Calculate the Gini coefficient as an expression of pSolve step by step in digital format If the slope of the total income curve is given by 12-13q and if p=6 when q=4. Find:a) The function of total income as a function of q.b) The equation of the inverse demand curve.Assume that utility is given by u(x, y) = x0.3y0.7 1. Derive the Walrasian demand function. Then use the derived Walrasian de- mand functions to compute the indirect utility function. 2. Derive the expenditure function and the Hicksian (compensated) demand functions for this case. Hint: Use Propositions 5 and 4.
