--%>
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 : Explain about Market Structures briefly

    Explain about Market Structures briefly.

    		•
  • Q : Describe cost of equity shares Briefly

    Briefly describe cost of equity shares? And also write down way to evaluate the cost of equity shares?

    		•
  • Q : Government policies with respect to the

    Can you explain how different government policies with respect to the recycling of aluminum and paper might account for these different market outcomes?

    		•
  • Q : Perfect competition and efficiency

    Which of the given describes a condition in which a good or service is produced at the lowest probable cost: w) productive efficiency. x) allocative efficiency. y) marginal efficiency. z) profit maximization Please

    		•
  • Q : An Inquiry in the Nature and Causes The

    The first comprehensive work upon economics written within English was authored through Adam Smith in 1776 year and entitled that “An Inquiry within the Nature and Causes of: (1) Laws of Supply and Demand.” (2) Wealth of Nations.” (3

    		•
  • Q : Write short note on Demand Write short

    Write short note on Demand, Supply and Equilibrium?

    		•
  • Q : Our junior high school serves a

    Comment on the following statement from a newspaper article:  “Our junior high school serves a splendid hot meal for $1 without costing the taxpayers anything, thanks in part to a government subsidy.”

    		•
  • Q : Labour economic Can someone help me in

    Can someone help me in finding out the right answer from the given options. The Taft Hartley Act of 1946 made it illegal to encompass a: (1) Right-to-work law passed by the state legislature. (2) Conviction for the misdemeanor and serve as union officer. (3) Union for the agricultural migrants or go

    		•
  • Q : Technical change and vintage technology

    In heterodox economics, what implications does technical change and vintage technology contain for the cost structure of the business enterprise?

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

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

    		•