--%>
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 might government correct this

    What divergences arise between equilibrium and an efficient output spillover benefits are present?  How might government correct this divergence?

    		•
  • Q : Comparative Advantage of free trade

    According to the advocates of free trade and World Trade Organization, each and every country potentially advantages from trade liberalization and the lowering of tariffs since each and every country: (1) Has a comparative benefit in something. (2) Ga

    		•
  • Q : Micro economics and macro economics

    Micro economics and macro economics:Economic theory can be widely divided into micro and macroeconomics. The word micro means small and macro means big.In microeconomics, we deal

    		•
  • Q : Illustrate major economic flows that

    Illustrate major economic flows that link U.S. with nations.  Provide an example to illustrate each flow.  Explain the relationship between the top and bottom flows.

    		•
  • Q : Describe unanticipated inflation

    Describe unanticipated inflation?

    		•
  • Q : Public policies for low-income Fuel

    Fuel stamp programs which subsidize heating oil purchases through low-income households encourage those families to: (w) create more income by working. (x) particularly conserve on their use of fuel. (y) live along with less purchasing power. (z) subs

    		•
  • Q : The Federal corporate income tax Use

    Use the circular flow model to confirm this assertion for a 2% reduction in the Federal corporate income tax.

    		•
  • Q : Major implication of invisible hand of

    The major implication of Adam Smith’s conception of an “invisible hand” was such that: (w) pursuit of individual self interest must be controlled. (x) most people lose sight of what’s good for society. (y) most

    		•
  • Q : Regulate prices to ensure against

    Not between exact activities for government to undertake, according to Adam Smith, would be for the government to: (1) maintain public institutions and public works. (2) protect society by invasion. (3) serves as a medium for law and justice. (4) regu

    		•
  • 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

    		•