4 Excess burden [25 marks] Consider an economy with two goods, consumption c and

Question

4 Excess burden [25 marks] Consider an economy with two goods, consumption c and leisure l, and a representative consumer. Since there are 24 hours in a day a consumer's daily leisure hours are equal to l-24-h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad-valorem tax on their earnings of r percent. The consumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance) The consumer's preferences over consumption and hours of work can be represented by the utility function U(c, h) ac_ßA H. (a) What is this consumer's budget constraint? (b) Solve for the consumer's utility maximizing hours T, , , Y) and consumption c*(w, 1-7, , , Y). of work h'(w,1 (c) Suppose that w $10, Y = $1, 3 and -1. The government is debating whether to increase the labor income tax from 0.3 to T2 0.5. Using Excel (or another program) or pen-and-paper, draw a graph with hours of work on the r-axis and after-tax income (consumption) on the y-axis that indicates the additional excess burden (EB) from such a tax increase (d) Suppose that w = $10, Y-$1, -3 and -1. Also, suppose that we know that the consumer's compensated elasticity of hours worked with respect to the net-of-tax rate, Eh = derived in lecture (i) calculate the EB/R when -03, (ii) calculate the EB/R ratio when 0.5. aa,T= 0.1. Using the EB formula (e) Is knowing the compensated elasticity of hour's worked with respect to the net-of-tax rate sufficient (i.e. appropriate) for calculating EB? Explain why or why not Bonus: Suppose instead that the consumer's utility function was U(c, h)- min(ac, Bh). Would the EB from a unit excise tax be larger or smaller com- pared with the utility function considered earlier. Explain your answer in 3-4 sentences.

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macroeconomics. Both of us have researched and taught both microeconomic and

macroeconomic topics, and we have worked together on all aspects of the book. This means

that students who study both microeconomics and macroeconomics from our book will

benefit from a completely integrated and consistent approach to economics.

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