--%>
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 : Who define Theory of Moral Sentiments

    The argument which slicing off one’s pinkie would be extra bothersome to which person than the loss of millions of his brethren was made within A Theory of Moral Sentiments (1755) through: (1) Adam Smith. (2) David Ricardo. (3) Theophrastus Phil

    		•
  • Q : Elucidate how Personal income tax is a

    Elucidate how Personal income tax is a major source?

    		•
  • Q : Illustrate the 4th role is the

    Illustrate the 4th role is the reallocation of resources?

    		•
  • Q : Production possibility frontier

    Question: Scenario: You have been hired as the economics adviser for the newly elected State Premier. On your first day, the Premier introduces you to the new Minister for Health

    		•
  • Q : Speculators activities over the long-run

    Over the long-run the speculators activities are tend to: (1) decrease the volatility of prices. (2) attract legal attention and result in imprisonment. (3) increase the level and volatility of prices both. (4) yield tremendous profits and raise costs

    		•
  • Q : Comparison between EVA and Ratio

    Comparison between EVA and Ratio Analysis: EVA helps in measuring the economic performance of the company. It is the profit earned by the firm less the cost of financing the firm’s capital. It shows that the shareholders gain when the return fro

    		•
  • Q : Surpluses in the balance of trade The

    The advocates of laissez-faire policies favor: (i) Govt. control of economy. (ii) Public ownership of all the resources. (iii) Income to be distributed according to requirement. (iv) Surpluses in the balance of trade. (v) Minimal govt. intervention in economy.

  • Q : Define Benefit Cost Ratio or

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

    		•
  • 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 : Market structure and pricing decision

    Just need help to see if I am in the right direction if there any think wrong need help with it.

    		•