--%>
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 : In long-run equilibrium earning of zero

    When, in a perfectly competitive industry, where the market price facing a firm is above its average total cost on the output here marginal revenue equivalents marginal cost, in that

    		•
  • Q : Determine the productively efficiency

    To be productively efficient, a country should: (w) maximize the satisfaction attainable from its budget. (x) be concerned only with macroeconomic analysis. (y) concentrate on removing scarcity. (z) maximize the value of output produced through specif

    		•
  • Q : Determine relative price when two

    When the prices for doughnuts and croissants are $.50 and $1 correspondingly: (w) the opportunity cost for one doughnut is two croissants. (x) this is better to buy two doughnuts than one croissant. (y) one croissant will make Pierre twice as happy as one doughnut. (z

    		•
  • Q : The supply curve when each of these

    What happens to the supply curve when each of these determinants changes?

    		•
  • Q : Determine opportunity cost of making an

    The opportunity cost of making an exact alternative is: (i) useful primarily as an indicator of relative prices. (ii) its nominal costs into terms of all other goods. (iii) the information which guides your decision. (iv) measured through the subjecti

    		•
  • Q : Major players in international trade

    Who are the major players in international trade today?  Besides Japan, what other Asian nations play significant roles in international trade?

    		•
  • Q : Production possibilities curve is a

    How a production possibilities curve is a graphical representation of choices?

    		•
  • Q : Elucidate the growth record of the

    Elucidate the growth record of the United States?

    		•
  • Q : Why is the problem of unemployment a

    Why is the problem of unemployment a part of the subject matter of economics?

    		•
  • Q : Marketing in action Which of the

    Which of the following are examples of public goods?

    		•