## Suppose that the utility function of a consumer is of the form U = Xa Yb., where a=1/3 and b=1/4 Determine the utility maximizing choice of X and Y when Px = $2, Py=$3 and income M = $360.

ECON 300

Assignment 1.1

- Suppose
that the utility function of a consumer is of the form U = X
^{a}Y^{b}., where a=1/3 and b=1/4- Determine the utility maximizing choice of X and Y when Px = $2, Py=$3 and income M = $360.
- Suppose Px increased to $4/unit. Determine the new utility maximizing quantities of X and Y.
- Are X and Y gross substitutes, independent, or complements?

- A
consumer has a budget of $500 to spend on two goods, X and Y. She likes to consumer a unit of X in
combination with a unit of Y. Any
unit of X she cannot consume in combination with Y is useless. Any good Y that she cannot consume in
combination with good X is useless.
If Px = $5 and Py = $10:
- How many units of each good will she purchase
- Show graphically the budget line and the consumer indifference curve.

- Roger’s
budget line relating good X and good Y has intercept of 50 units of good X
and 20 units of good Y. If the
price of good X is $12:
- What is the price of good Y?
- What is the slope of the budget line?
- How much money does Roger have?
- If Roger’s MRSxy = 2 at a certain bundle along the budget line, does this bundle maximize his happiness? If the answer is “no”, what do you suggest to change his bundle? ( more x or more y?) Explain it by using indifference curve analysis.

- With an excise tax of $.50 per six-pack of beer a student purchases 12 six-packs per month. If the government requires the students to pay $6.00 per month as lump sum tax instead of imposing excise tax, how will the student’s consumption pattern and welfare be affected? Explain by using the graph.

- Arej
is an impoverished graduate student who has only $200 a month to spend on
food. She limited herself to a diet
of peanut butter and carrots in the fixed ratio for 2 pounds of peanut
butter to one pound of carrots.
- If peanut butter costs $4 per pound and carrots cost $2 per pound, how much can she eat during the month?
- Suppose the cost of peanut butter rises to $5, by how much will Arej have to reduce her food purchases.
- How much in food stamp aid will the government have to give Arej to compensate for the increase in cost of peanut butter.
- How would you graph the indifference curve for Arej?