Homework 6

# Homework 6 - b Assume that the government imposes a \$1.50...

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Economics 1480 Homework #6 1) Rosen Chapter 14: problem 5 2) Under legislation passed in 2001, the marginal tax rate on the wages of workers in the highest income category decreased from 39.9 percent to 34.0 percent. Use equation 15.4 in the textbook to approximate the proportion by which this change reduced the excess burden for individuals in this tax bracket. 3) This problem investigates (in more detail) the example of perfect substitutes that I covered in class. Joel has \$50 to spend on Coke and Pepsi, which are perfect substitutes. In the special case of perfect substitutes, Joel maximizes his utility by consuming only the cheaper good. a) Initially, the price of Coke is \$1 and the price of Pepsi is \$0.50. Using a graphical analysis of indifference curves and budget constraints, show that Joel will purchase only Pepsi. (Hint: indifference curves are linear with a slope of 1 in this special case of perfect substitutes).

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Unformatted text preview: b) Assume that the government imposes a \$1.50 tax on Pepsi. Again, using indifference curve analysis, show that Joel will now purchase only Coke. c) How much revenue does this tax raise? In dollars, what is the excess burden associated with this tax? Demonstrate this excess burden using graphical analysis. 4) Ramsey Rule Janet has income m and receives Cobb-Douglas utility from consumption of two goods (X and Y): U = α log(X) + (1-α ) log(Y) Pre-tax prices are given by P X and P Y and ad-valerom tax rates are given by T X and T Y . a) Show that, with Cobb-Douglas utility, demand functions are given as follows: X = α m / (P X (1+ T X )) Y = (1-α )m / (P Y (1+ T Y )) b) Show that the Ramsey rule requires T X = T Y . Hint: Δ X = dX/dT X . c) Relate your answer in part b) to the inverse elasticity rule. Hint: First calculate the price elasticity of demand for good X [(dX / dP X ) / ( X / P X )] and good Y....
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Homework 6 - b Assume that the government imposes a \$1.50...

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