Let the consumer have the utility function a. Show that the utility maximizing demands are and b. Letting p1 = p2 = 1, use the inverse elasticity rule to show that the optimal tax rates are related by c. Setting w = 100, r1 = 0:75, and r2 = 0:5, find the tax rates required to achieve revenue of R = 0:5 and R = 10. d. Calculate the proportional reduction in demand for the two goods comparing the no-tax position with the position after imposition of the optimal taxes for both revenue levels. Comment on the results.
Let the consumer have the utility function a. Show that the utility maximizing demands are and b. Letting p1 = p2 = 1, use the inverse elasticity rule to show that the optimal tax rates are related by c. Setting w = 100, r1 = 0:75, and r2 = 0:5, find the tax rates required to achieve revenue of R = 0:5 and R = 10. d. Calculate the proportional reduction in demand for the two goods comparing the no-tax position with the position after imposition of the optimal taxes for both revenue levels. Comment on the results.
Microeconomics A Contemporary Intro
10th Edition
ISBN:9781285635101
Author:MCEACHERN
Publisher:MCEACHERN
Chapter5: Elasticity Of Demand And Supply
Section5.A: Appendix: Price Elasticity And Tax Incidence
Problem 1AQ
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Let the consumer have the utility function
a. Show that the utility maximizing demands are
and
b. Letting p1 = p2 = 1, use the inverse elasticity rule to show that the optimal tax rates are related by
c. Setting w = 100, r1 = 0:75, and r2 = 0:5, find the tax rates required to achieve revenue of R = 0:5 and R = 10.
d. Calculate the proportional reduction in demand for the two goods comparing the no-tax position with the position after imposition of the optimal taxes for both revenue levels. Comment on the results.
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Step 1: State the given information
VIEWStep 2: prove that the utility maximizing demands x1 and x2
VIEWStep 3: Use the inverse elasticity rule to show that the optimal tax rates
VIEWStep 4: Find the tax rates required to achieve the following revenue
VIEWStep 5: Calculate the proportional reduction in demand before and after tax
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