--%>
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 : Production possibility frontier

    Question: Scenario: You have been hired as the economics adviser for the newly elected State Premier. On your first day, the Premier introduces you to the new Minister for Health

    		•
  • Q : Describe double coincidence of wants

    Double coincidence of wants: This means that one person's wishing to buy and sell should coincide with another person’s wish to buy and sell.

    		•
  • Q : Comparative Advantage of free trade

    According to the advocates of free trade and World Trade Organization, each and every country potentially advantages from trade liberalization and the lowering of tariffs since each and every country: (1) Has a comparative benefit in something. (2) Ga

    		•
  • Q : Problem on productive contribution

    Suppositions underpinning simple production possibilities frontier models don’t comprise a need that: (i) Net resources are fixed. (ii) All resources are efficiently employed. (iii) Technology is steady. (iv) Resource owners are paid according t

    		•
  • Q : What does financial leverage specify

    What does financial leverage specify? And also states its limitations?

    		•
  • Q : Theory of wages according to Adam Smith

    Least consistent along with Adam Smith’s theory of wages would be the suggestion that wages vary positively along with the: (w) effort required to learn skills necessary to accomplish particular types of work. (x) stability of employment and the

    		•
  • Q : Impact of dollar on aspects of

    Question Discuss the impact of dollar depreciation on the various aspects of American Economy. Devaluation of the DollarIntroduction:

    		•
  • Q : Production Possibility Curve Production

    Production Possibility Curve: Similar to the individuals, a society as entire has restricted resources. It has to decide what to manufacture with restricted resource

    		•
  • Q : Write short note on Demand Write short

    Write short note on Demand?

    		•
  • Q : Illustrate Freedom of enterprise and

    Illustrate Freedom of enterprise and choice exist?

    		•