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

  1. Suppose that the utility function of a consumer is of the form U = Xa Yb., where a=1/3 and b=1/4 
    1. Determine the utility maximizing choice of X and Y when Px = $2, Py=$3 and income M = $360.
    2. Suppose Px increased to $4/unit.  Determine the new utility maximizing quantities of X and Y.
    3. Are X and Y gross substitutes, independent, or complements?
  1. 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:
    1. How many units of each good will she purchase
    2. Show graphically the budget line and the consumer indifference curve.
  1. 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:
    1. What is the price of good Y?
    2. What is the slope of the budget line?
    3.  How much money does Roger have?
    4. 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.
  1. 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.
  1. 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.
    1. If peanut butter costs $4 per pound and carrots cost $2 per pound, how much can she eat during the month?
    2. Suppose the cost of peanut butter rises to $5, by how much will Arej have to reduce her food purchases.
    3. How much in food stamp aid will the government have to give Arej to compensate for the increase in cost of peanut butter.
    4. How would you graph the indifference curve for Arej?
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