--%>
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 often exceeds supply and supply

    “In the corn market, demand often exceeds supply and supply sometimes exceeds demand.” “The price of corn rises and falls in response to changes in supply and demand.” Among these 2 statements used correctly which in the terms “supply&rdq

    		•
  • Q : Why do governments enact trade barriers

    Why do governments enact trade barriers?

    		•
  • Q : Wealth of Nations academic

    By the perspective of nowadays academic standards, Adam Smith must have more evidently acknowledged that several the analyses and insights for that he took credit within his Wealth of Nations had really been gleaned from the writings

    		•
  • Q : Roundabout production Describe the

    Describe the merits of “roundabout” production?  Describe the term “division of labor”?

    		•
  • Q : Comparative Advantage-Mutual exchange

    Mutually beneficial exchange is probable whenever relative production costs vary previous to trade, is a manner to state the law of: (1) Positive profits from trade. (2) Comparative benefit. (3) Specialization and Division. (4) Purchasing power parity

    		•
  • Q : Illustrate Economics for citizenship

    Illustrate Economics for citizenship?

    		•
  • Q : Problem on private resource ownership

    Relative to most of the other countries, the United States encompasses historically relied more greatly on: (1) Public resource ownership and private income distribution. (2) Decentralized decision making and private resource ownership. (3) Exports of textiles, automo

    		•
  • Q : Summary of what can cause a decrease in

    Illustrate a summary of what can cause a decrease in demand?

    		•
  • Q : Analysis of US GDP and GDP growth rate

    You may use a calculator and MINITAB to conduct the necessary calculations for all questions.  Analysis of US GDP and GDP growth rate (1959-2004). The following variables can be retrieved from MIN

    		•
  • Q : Meaning of Modigliani-Miller Briefly

    Briefly describe the meaning of Modigliani- Miller (M and M) approach?

    		•