--%>
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 : What are the facts of inflation What

    What are the facts of inflation?

    		•
  • Q : Exchange and Specialization I have a

    I have a problem in economics on Exchange and Specialization. Please help me in getting the right answer from the following question. Sarah the wheat farmer would be most probable to trade for fruit from the Kathy's orchard if: (i) Sarah's opportunity

    		•
  • Q : Distribution of income and wealth in a

    Of the given options, the economist whose theories pivoted least upon the distribution of income and wealth (class conflict) in a capitalist system would have been: (1) Adam Smith. (2) David Ricardo. (3) Karl Marx. (4

    		•
  • Q : Independent queue vs. pooled queue

    Instruction: McDonald's vs. Burger King - these two fast food chains use different waiting line design: Independent queue vs. pooled queue. To compare the two different queue systems on equal footing, let's assume that we pick a McDonald's sto

    		•
  • Q : Meaning of Modigliani-Miller Briefly

    Briefly describe the meaning of Modigliani- Miller (M and M) approach?

    		•
  • Q : Symptoms of governmental interference-

    Adam Smith and the “typical liberal” economists who followed within his footsteps viewed persistent monopolization and market power as: (1) ineffective and best regulated through government. (2) crucial in finding the rate of technological

    		•
  • Q : Writ short note on the income of

    Writ short note on the income of functional distribution?

    		•
  • Q : Subjective aspects of pricing- economic

    Adam Smith must have emphasized more strongly how his Wealth of Nations drew concepts and inspiration by Richard Cantillon’s Essai. Now today’s perspective that the Wealth of Nations would considered even

    		•
  • 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 : Define the for whom query in market

    The market system responses the “for whom?” query with: (i) distributing goods on the basis of require. (ii) using central planning to coordinate production decisions. (iii) catering to consumers with adequate resources to demand goods. (i

    		•