--%>
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 : Show that students who study more hours

    Suppose studies show that students who study more hours receive higher grades.  Is there any relationship which guarantees that any particular student who studies longer will get higher grades?

    		•
  • Q : Consumer and producer surplus in the

    In perfectly competitive market, the market demand and market supply curves are provided by Qd = 1000 −10Pd and Qd = 30Ps. Assume that the government gives a subsidy of $20 per unit to each and every seller in the mark

    		•
  • Q : Argument by Adam Smith for a true

    Within the Wealth of Nations, argument by Adam Smith such that a nation’s true wealth is its capability to: (1) obtain stocks of financial capital. (2) inspire its people’s courage and diligence. (c) give

    		•
  • Q : Main advantage of EVA The main

    The main advantage of using EVA is that it is simple to calculate and understand. It uses simple measures like operating profits and cost of capital terms which are widely known and accepted in the financial arena. It helps the managers to assess thei

    		•
  • Q : What are the major legal forms of

    What are the major legal forms of business organization?

    		•
  • Q : Opportunity Cost Opportunity Cost :

    Opportunity Cost:Whenever you select a particular alternative, the next best alternative should be given up. For illustration, when you desire to watch cricket highlights in T.V., you should

    		•
  • Q : Type of expenditure at the local level

    What is the most important source of revenue and the major type of expenditure at the local level?

    		•
  • Q : Importance of Economics Importance of

    Importance of Economics:Economics has become one of the major branches of social sciences. This is of enormous practical value in our day by day life. In pure sciences, we study the subject

    		•
  • Q : Illustrate the Goals of Mixed Economy

    Illustrate the Goals of Mixed Economy?

    		•
  • Q : Write short note on Demand Write short

    Write short note on Demand, Supply and Equilibrium?

    		•