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HW4_s - HOMEWORK 4 Exercise 10A.6 How would Graph 10.4b...

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HOMEWORK 4 Exercise 10A.6 How would Graph 10.4b change if X 1 were an inferior rather than a normal good? (Hint:Your answer should be that marginal willingness to pay curves corresponding to higher utility levels will lie to the left of those corresponding to lower utility levels.) Exercise 10A.9 Can you think of a scenario under which a consumer does not change her consumption of a good when it is taxed but there still exists an inefficiency from taxation? If an inferior good is taxed, substitution and income effects might exactly offset one another. This would result in no change in consumption of the good, but the presence of a substitution effect still implies there exists an inefficiency from the tax. End-of-Chapter Exercise 10.1 Suppose I care only about consumption this year and consumption next year, and suppose I earn an income this year but do not expect to earn an income next year. X Other goods $ A Slope = - P 1 X P x P 1 X 1 B X 1 A B D I B D I A Demand Curves Solution to Q10A.4 X Other goods $ A Slope = - MRS X P x MRS X 1 B X 1 A B MWTP(U 1 B ) MWTP Curves Solution to Q10A.5 MWTP(U 1 A )
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A : The government announces a new tax on interest income (assume that interest income was previously untaxed). Call this year’s income Y. Call the interest rate r %. Call the new tax rate t %. Illustrate my before and after tax intertemporal budget constraint. (a) Suppose I save 50% of my income after the new tax is imposed. Illustrate the amount of the tax the government will collect from me next year. Call this T. T is vertical distance from a to b (b) Illustrate the most I would be willing to pay next year to keep the government from imposing this tax on interest income. Call this amount L. Amount L is vertical distance from a to c. I am indifferent between points F (where my interest income is taxed at rate t) and G (where I pay a lump sum tax). If I pay a lump sum tax rather than a tax on interest income, my budget constraint shifts from the original (black) line to the new (green) line. Thus the amount of the lump sum that I would be willing to pay is the vertical distance from a to c (i.e., the vertical distance between the black and green parallel lines). (c) Is L larger or smaller than T? What does your answer depend on? L is bigger than T. The only circumstance under which L would not be bigger is if this year’s consumption and next year’s consumption are perfect complements, in which case L = T. This Year Next Year Y a = Y(1+ r) b = Y[1+r(1-t)] Y = this year’s income r = interest rate (%) t = tax rate (%) on interest income Slope = -(1+r) Slope = -[1+r(1-t)] This Year Next Year Y a b Y/2 Y(1+r) T = (Y/2) x r x t This Year Next Year Y a b c Y/2 Y(1+r) F G T L
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(d) If consumption is always a normal good, will I consume more or less next year than I would have had the tax not been imposed?
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