--%>
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 : Eco Quantity TR TC 0 $0.00 $10.00 1

    Quantity TR TC 0 $0.00 $10.00 1 $150.00 $30.00 2 $290.00 $50.00 3 $420.00 $80.00 4 $540.00 $120.00 5 $650.00 $170.00 6 $750.00 $230.00 7 $840.00 $300.00 8 $920.00 $

    		•
  • Q : Calculating fat-tax Question: Max has a

    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

  • Q : Gains from the Exchange Even people who

    Even people who are extremely good at everything couldn’t encompass: (i) absolute benefits in approximately everything. (ii) Much higher incomes than average. (iii) Comparative benefits in everything. (iv) Superior natural endowments of talent.

    Q : Show that students who study more hours

    Suppose studies show that students who study more hours receive higher grades.  Is there any relationship which guarantees that any particular student who studies longer will get higher grades?

    		•
  • Q : Problem on Legislature budget XY School

    XY School District has a large number of students in need of remedial instruction. The superintendent of XY School System can allocated her budget between purchasing X units of remedial instruction at a price of $2,000/unit and spending an amount ($Y) on all other sch

    		•
  • Q : Define Benefit Cost Ratio or

    Briefly describe the term Benefit Cost Ratio (or B/C Ratio) or Profitability Index (or PI)?

    		•
  • Q : Best society according to Utilitarianism

    Utilitarianism proposes such that the finest society is one which gives the: (w) fundamental goods to meet people’s requirements. (x) greatest happiness for the maximum number of people. (y) exact measurement of utility and disutility. (d) highe

    		•
  • Q : International Trade & Globalization

    Question: 1.   Long-term Growth, International Trade & Globalization a.   In terms of understanding the importance of trade to an economy, the most impor

    		•
  • Q : Discuss the economic aspects of ticket

    Discuss the economic aspects of ticket scalping also identifying the gainers and losers?

    		•
  • Q : Describe the equation of a linear

    Describe the equation of a linear relationship?

    		•