--%>
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 : How government might manipulate its

    Explain how government might manipulate its expenditures and tax revenues to reduce unemployment?

    		•
  • Q : Heterodox perspective of business

    I am facing difficulty in this question. Help me in find out correct answer of this economy based question. From heterodox perspective, why do business enterprises choose administered prices as opposed to highly flexible prices?

    		•
  • 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 : 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 : Technological advances in producing

    When given resources can now produce additional goods than was previously probable, then there have been a: (1) Stock market boom. (2) Competitive spurt which shrinks entrepreneurial gain. (3) Concavity reversal in the production possibilities frontier. (4) Bigger rel

    		•
  • Q : Illustrate how Macroeconomics examines

    Illustrate how Macroeconomics examines the economy as a whole?

    		•
  • Q : Wealth of Nations academic

    By the perspective of nowadays academic standards, Adam Smith must have more evidently acknowledged that several the analyses and insights for that he took credit within his Wealth of Nations had really been gleaned from the writings

    		•
  • Q : Introduction of the term net present

    Give a brief introduction of the term net present value? Write down its admittable rules, their merits and demerits?

    		•
  • Q : Calculate Equilibrium Quantity and Price

    1. The owner of a firm calculates that next year's profit will be $1,000. Each successive year profit will increase by 10% (i.e. year 2: $1100; year 3: $1210 and so on.) At the end of the 5th year the firm could be sold for $20,000. A) if the appropriate di

    		•
  • Q : Illustrate Qualification in

    Illustrate Qualification in International Trade?

    		•