Reference no: EM13853244
A consumer has preferences u(x) = 2x 1 2 1 + x2. The price of good 1 is p1 > 0 and the price of good 2 is 1. You may restrict your attention to interior solutions throughout.
(a) Explain whether these preferences are i) monotonic, ii) quasilinear, iii) essential and/or iv) convex.
(b) Find the consumer’s (Marshallian) demand functions and indirect utility function. For full credit, use a Lagrangian and show your work.
(c) Suppose that there were a a tax of t per unit on good 1. How much revenue would be raised (in terms of the exogenous variables)? How much worse off does the consumer become, in dollars, from such a tax (in terms of exogenous variables)?
(d) Suppose that p1 = 1 2 and the tax is also t = 1 2 . What was the original amount of good 1 purchased? What would be the values of revenue and consumer welfare loss from the formulas that you calculated in part (c). Which is larger? Briefly explain why.
(e) Suppose that later, with the tax still in place, you give back to the consumer the amount of money that was raised by the tax. With the rebate and the tax in place, what would be the new optimal consumption bundle? What would be the consumer’s utility? By how much does the consumer’s utility change relative to the pre-rebate level? Explain the economic intuition for the change in welfare you found from the rebate relative to the original (pre-tax) level of utility.
|
What is price and quantity equilibrium in this market
: Graph the supply and demand curves in this market. Be sure to put the quantity (Q) on the horizontal axis and the price (P) on the vertical axis. You may use quantities two (Q = 2) through eighteen (Q = 18) by units of one (1) for your graph. What is..
|
|
What is the equivalent value of series at beginning
: Consider a series of end-of-period CFs spanning 2046-2053, which increase at a 1% rate each period. The amount of the first CF in the series is $92. The interest rate is 3%. What is the equivalent value of this series at the beginning of 2046?
|
|
Indifference curve for this consumer and indicate its slope
: Suppose a consumer’s preferences over goods 1 and 2 are represented by the utility function u(x, y) = (x+ y)^3. Draw an indifference curve for this consumer and indicate its slope.
|
|
Is the demand for iphones price inelastic or elastic
: What would happen to unit sales and total revenue for this textbook if the bookstore reduced it's price? Is the demand for iPhones price inelastic or elastic? Why? Is income elasticity high or low?
|
|
Explain whether preferences-monotonic-convex-quasilinear
: A consumer has preferences u(x) = 2x 1 2 1 + x2. The price of good 1 is p1 > 0 and the price of good 2 is 1. You may restrict your attention to interior solutions throughout. Explain whether these preferences are i) monotonic, ii) quasilinear, iii) e..
|
|
Determine whether amelia and bernard have identical tastes
: Amelia buys coffee for $1 per cup and tea for 50¢ per cup; every day she drinks 1 cup of coffee and 2 cups of tea. Bernard buys coffee for 50¢ per cup and tea for $1 per cup; every day he drinks 2 cups of coffee and 1 cup of tea. Can you determine wh..
|
|
Bell curve be inappropriate tool for looking at market risk
: This will be a real challenge, but it should be an interesting challenge. Much of the way we measure risk relies on probability distribution (the bell curve as shown on page 425). For many things in life, and business, this is perfectly valid, but fo..
|
|
What impact did that job loss have on the us economy
: Reflect on the changes in U.S. manufacturing over the last half century. Why did the United States lose so many jobs? What impact did that job loss have on the U.S. economy and on the economies of countries like China and Mexico that have been the re..
|
|
What is the real interest rate
: If the nominal interest rate is 4 percent and expected inflation is 1 percent, what is the real interest rate? Suppose instead that the nominal interest rate is 80 percent and the expected inflation rate is 40 percent.
|