--%>
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 : Comparative advantage in production I

    I have a problem in economics on Comparative advantage in production. Please help me in the following question. The oranges are grown in Florida and potatoes are grown in Maine mainly since: (i) orange-grower’s in Maine have not lobbied effectiv

    		•
  • Q : Illustrate Scarcity and choice of

    Illustrate Scarcity and choice of Economic Perspective?

    		•
  • Q : Writ short note on the income of

    Writ short note on the income of functional distribution?

    		•
  • Q : Argument on quantity theory of money by

    David Hume, who said about money such as “Tis none of the wheels of operate. Tis the oil’,” exposed a main error within mercantilism through explaining what is currently considered to as the: (w) quantity theory of money. (x) price l

    		•
  • Q : Explain the behavior of the workers Use

    Use the economic perspective to explain the behavior of the workers?  Why do they work so diligently?

  • Q : Best alternatives while choices are made

    Opportunity costs, which are the values of the: (i) monetary costs of goods and services. (ii) best alternatives sacrificed while choices are made. (iii) minimal budgets of families upon welfare. (iv) hidden charges passed upon to consumers. (v) exorb

    		•
  • Q : What are the main sources of growth

    What are the main sources of growth?

    		•
  • Q : Elucidate facilitating factors that

    Elucidate facilitating factors that explain the growth of trade?

    		•
  • Q : Generalization and abstraction are

    Explain the statement: “Generalization and abstraction are nearly synonymous.”?

    		•
  • 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

    		•