1. A food stamp is a voucher that can be used only to purchase food. Suppose that the government provides the poor with food stamps worth 40 units of food, and that the market value of one unit of food is €3. (a) Suppose that a poor individual has an income of €900. Normalize the price of “all other goods” to €1. Draw the poor individual’s budget constraint before and after receiving the food stamps. (b) Can we conclude that an individual would be worse off if provided with a cash grant of €100 instead of the food stamps? Explain with a graph. (c) Explain why governments may provide transfers-in-kind rather than give cash transfers. 2. Suppose there are only two people in society, Claire and Jimmy, who must split a fixed income of €200. For Claire, the marginal utility of income is MUC = 1000 – 4YC . For Jimmy, the marginal utility of income is MUJ = 800 – 6YJ , where YC , YJ are the amounts of income to Claire and Jimmy. (a) What is the optimal distribution of income if the social welfare function is additive and non-weighted? (b) What is the optimal distribution of income if the marginal utility of income is constant for both Claire and Jimmy: MUC = 1000 and MUJ = 800? Comment on your answer. (c) What is the optimal distribution of income if their utility functions are the same? Comment on your answer. 3. Suppose that when Megan has an income of YM , her utility is UM = p YM . Suppose also that when Sam has an income of YS , his utility is US = p YS + 0.8UM . (a) Define Pareto efficient redistribution, and explain why it is relevant here. (b) Suppose that initially Megan and Sam each have incomes of €100. Assuming Utilitarian social welfare function (additive and non-weighted), what happens to social welfare if €25 is taken from Sam and given to Megan? (c) Repeat (b), but with a redistribution of 25 from Megan to Sam. (d) Explain how you would determine the income distribution that maximizes the Utilitarian social welfare function. 4. Suppose that the government imposes an income tax on its citizens according to the following tax schedule: Ti = a + tYi , where Ti is the tax payment of an individual with income Yi for the given parameters a, t. 1 of 2 Homework 3 Economics 376, AUP (a) Write down a formula for the average tax rate of individual i as a function of i’s income. (b) Using your formula, explain the difference between a progressive and regressive income tax system. (c) Prove that the tax system is progressive if a is negative, and regressive if a is positive. 5. Assume that supply and demand are given by the equations: Q s = 5P and Q d = 36 – 10P A $0.60 per unit tax imposed on sellers in this market alters the supply equation to: Q s = 5P + 3 (a) Sketch a graph showing values for equilibrium price and quantity before the tax. (b) Show the effect of the tax on the price paid by consumers, the price retained by sellers, and the quantity bought and sold. Show all of these values in your graph. (c) How much tax revenue does the government collect? (d) What percentage of the tax is borne by consumers? 6. Suppose that the inverse demand curve for a commodity is p(Q d ) = a – bQd and the inverse supply curve for a commodity is p(Q s ) = c + dQs . (a) Find the equilibrium price and quantity when an ad valorem tax rate of t is imposed on the buyers of the commodity. (b) Under what conditions on the parameters will the entire incidence fall upon suppliers of the commodities? Explain your answer.
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