--%>
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 : Describe World Trade Organization

    Describe World Trade Organization (WTO)?

    		•
  • 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 : Initial systematic and popular

    The initial systematic and popular description of capitalism was explained in: (1) Sir Thomas Mun’s England’s Treasure by Foreign Trade. (2) Joseph A. Schumpeter’s Capitalism, Socialism, and Democracy. (3) John Maynard Keynes’

    		•
  • 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 : Why private goods are produced through

    Why private goods are produced through the market?

    		•
  • Q : Describe the term-Only to be part with

    Describe the term: “Only to be part with it we want money”?

    		•
  • Q : Equal share criterion of distribution

    According to the equivalent share criterion of the distribution, individuals must: (1) Share income according to personal requirement. (b) All make equivalent shares of output. (3) Each consists of incomes equivalent to their productive output. (4) Re

    		•
  • Q : Explain the term leverages Briefly

    Briefly explain the term leverages?

    		•
  • Q : High-convexity portfolios outperform

    a) Whether the bond market moves up or down, high-convexity portfolios will for all time outperform low-convexity portfolios of equal duration and yield." Elucidate the argument supporting this statement and the connection to the classical immunization strategy. What

    		•
  • Q : Understates the economic cost of a

    Computing the cost of college education like the cost of books, tuition and materials, room as well as board, and spending money: (i) overstates the economic cost of a college education. (ii) accurately measures the economic cost of a college educatio

    		•