Reference no: EM13886533
Assume that a consumer has the utility function U(x,y) = (3x+1)y, where x and y represent the quantities of two goods, X and Y. For parts (a)-(h), assume that good X costs pX=$3 per unit and good Y costs pY=$4 per unit. “Wealth” and “income” have the same meaning in this problem.
(a) With good X on the horizontal axis and good Y on the vertical axis, draw the consumer’s budget line if she has W=$31 to spend, Show the exact coordinates of the intercepts.
(b) On your budget line, show the optimal point (which you calculated in Homework #6). How much utility does that point produce? Draw the indifference curve that passes through that optimal point, showing the exact coordinates of at least three points on the curve.
(c) On the same diagram, draw three new budget lines, representing the consumer’s budget constraint for other possible values of her wealth: W=$7, W=$55, and W=$79. For each budget line, show the exact coordinates of its intercepts.
(d) If the consumer’s wealth is W=$7, then calculate the optimal point and show it on the appropriate budget line. Do the same for W=$55 and W=$79. Your diagram should now show four possible budget lines and four optimal points.
(e) Calculate the marginal rate of substitution of X for Y, at each of the four optimal points. Explain the pattern that emerges.
(f) Connect the four optimal points to show the income expansion path. Are X and Y normal or inferior goods?
|
Auto repair facility in a remote area of the nevada desert
: Jimbob’s Garage is the only auto repair facility in a remote area of the Nevada desert. The proprietor, Jimbob, does not post his prices for services. Knowing his customers are travelers who are desperate to get their vehicles repaired, he sizes each..
|
|
Monopolist that owns two mines
: Boron Industries is a monopolist that owns two mines. Mine B is smaller and has less capacity, thus its marginal costs rise more steeply than Mine A’s. Mine A has TCa = 5000 + 50*qa + 2 qa2 Mine B has TCb = 8000 + 50*qb + 3qb2 a. Before knowing deman..
|
|
Operates as a price-discriminating monopolist
: Cinemax is the only movie theater in Dannyburg. As such, it operates as a price-discriminating monopolist. Two types of customers view movies there: adults (A) and high school students (S) . Their respective demand functions are: Qa = 6400 Pa-2 Qs = ..
|
|
Utility function-number of units of good
: Sam’s utility function is U(x1, x2) = 2x1 + x2, where x1 is the number of units of good 1 he consumes per week and x2 is the number of units of good 2 he consumes per week. Sam has $200 a week to spend. If he belonged to the club, he could buy good 2..
|
|
Assume that consumer has the utility function
: Assume that a consumer has the utility function U(x,y) = (3x+1)y, where x and y represent the quantities of two goods, X and Y. For parts (a)-(h), assume that good X costs pX=$3 per unit and good Y costs pY=$4 per unit. “Wealth” and “income” have the..
|
|
Utility functions and prices
: Determine the optimal bundle of x1 and x2 given the stated prices and income using one of the methods we went over in class.
|
|
The federal minimum wage was last increased
: The federal minimum wage was last increased from $6.55 to $7.25 per hour. Suppose that the elasticity of labor supply of teenagers is 0.12. Using this estimate, by what percent would you expect teenagers’ quantity of labor supplied to change in respo..
|
|
The targeted jobs tax credit existed
: The Targeted Jobs Tax Credit existed from 1979 through 1994 and offered employers a tax credit for each less-skilled worker they employed. Assume that the tax credit was fixed at $3 per hour worked by a less-skilled worker. How would this tax credit ..
|
|
Make up a value for the exchange rate
: Suppose that a Starbuck’s venti latte currently sells for US$4.00 in the United States and C$5.00 in Canada. Make up a value for the exchange rate between the U.S. dollar and the Canadian dollar (expressed as Canadian dollars per U.S. dollar) that le..
|