--%>
Assignment Help - homework help

Calculating fat-tax

Question:

Max has a utility function U =√ x1x2 where x1 is litres of ice-cream and x2 is boxes of strawberries. The marginal utility of a litre if ice-cream is MU1 =0.5 √x2/ x1 and the marginal utility of a box of strawberries is MU2 =0.5 √x1 /x2. The prices of x1 and x2 are both $2 and Max has a budget of $80.

(a) How much of each good will Max demand?

(b) A fat-tax of $2 per litre is placed on ice-cream so that it now costs Max $4 per litre. Everything else remains the same. How much of each good does Max now consume? How much tax does he pay?

(c) Now suppose that, instead of imposing a $2 tax on ice-cream, the government imposes a $20 income tax, reducing Max's budget to $60. Would Max prefer the $2 tax on ice-cream or the $20 reduction is his budget?

Solution:

U = (x1x2)0.5, P1 = 2, P2 = 2, m = 80

Therefore, the budget equation is:

2x1 + 2x2 = 80

MU1 = 0.5(x2/x1)0.5, MU2 = 0.5(x1/x2)0.5

Therefore, MRS = MU1/MU2 = x2/x1

Setting MRS = P1/P2 = 1, we get,

x2/x1 = 1 => x2 = x1

a) Using the budget equation:

2x1 + 2x2 = 80

  1.   x1 + x2 = 40
  2.   2x1 = 40
  3.   x1 = 20 = x2

Therefore, he will demand 20 units each of both the goods.

b) Now, P1 = 4

MRS = P1/P2

  1.   x2/x1 = 4/2
  2.   x2/x1= 2
  3.   x2 =2x1

Putting it into the budget equation:

x1 + x2 = 40

  1.   x1 + 2x1 = 40
  2.   x1 = 40/3
  3.   x2 = 80/3

Therefore, tax paid = 40/3 x 2 = 80/3

c) The new budget equation:

x1 + x2 = 60/2 = 30

Putting, x1 = x2 in the budget equation, we get,

  1. 2x1 = 30
  2.   x1 = 15
  3.   x2 = 15

Utility with fat-tax = (40 x 80/9)0.5 = [40Ö2]/3= 18.86

Utility with income tax = 15

Therefore, Max will prefer the fat-tax on ice cream.

   Related Questions in Business Economics

  • Q : Demand supply Newspaper item: “Due to

    Newspaper item: “Due to lower grain prices, consumers can expect retail prices of choice beef to begin dropping slightly this spring with pork becoming cheaper after midsummer,” the Agriculture Department predicted. “This reflects increasing supply,” the department said. Does the statement use th

    		•
  • Q : Introduction of the term Operating

    Give a brief introduction of the term Operating Leverage?

    		•
  • Q : International trade to the U.S. economy

    How important is international trade to the U.S. economy?  In terms of volume, does the United States trade more with industrially advanced economies or with developing economies? What country is the United States’ most important trading partner, quantitati

    		•
  • Q : Examples and Applications of

    What are the Examples and Applications of International Trade?

    		•
  • Q : Determine the lowest average wages

    Consider a huge group of identically smart and strong industrious workers. All else identical, Adam Smith would predict such that the lowest average wages would be earned through the workers who were in the work that: (1) had the leas

    		•
  • Q : Illustrate the complex cases when both

    Illustrate the complex cases when both supply and demand shift?

    		•
  • Q : Explain the term Earnings per share

    Briefly explain the term Earnings per share (or EPS)?

    		•
  • Q : Write short note on Markets Write short

    Write short note on Markets?

    		•
  • Q : Formally adopt inflation targeting

    Question: Why might it be difficult for the Fed to formally adopt inflation targeting?  Would inflation targeting be a good policy for the Fed in the present economic environment? Answer:

  • Q : Limitations of activities to generate

    Illustrations of activities which generate negative externalities would not comprise: (w) burning coal that results in acid rain. (x) smoking a cigar at the opera. (y) killing fish by dumping sewage into a river. (z) being inoculated against a contagi

    		•