--%>
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 : The economies of Japan and US Question:

    Question: What can we learn from the Japanese experience? Is the US headed for a 'lost decade? Answer: There was

    		•
  • Q : Elucidate how to maintain competition

    Elucidate how to maintain competition?

    		•
  • Q : Depreciation of the euro change the

    If the European euro declines in value (depreciates) in the foreign exchange market, would it be easier or harder for the French to sell their wine in the United States?  Suppose you were planning a trip to Paris.  How would the depreciation of the euro chan

    		•
  • 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 : Elucidate the overview of Business Cycle

    Elucidate the overview of Business Cycle?

    		•
  • Q : How is productivity of labor based

    In Wealth of Nations by Adam Smith, opined that the productivity of labor based primarily on: (w) workers’ education. (x) divisions of labor. (y) technologically advanced machines. (z) suitable wage rates.

    Q : Explain about the Payments for using

    Payments for the use of land, capital and labor are respectively termed as: (w) rent, wages and profits. (x) rent, interest and wages. (y) dues, profits and depreciation. (z) fruit, profits and money.

    Q : Freely Floating Currency Question: For

    Question: For a freely floating currency, currency i.____________________ occurs when the market value of a country's currency rises relative to the value of another country's currency, while currency ii.__________

    		•
  • Q : Why Trade barriers hurt American

    Why Trade barriers hurt American consumers?

    		•
  • Q : Which type of maximization required in

    Productive (technical) efficiency needs maximization of the: (i) opportunity cost of a specified value of output. (ii) resources used to produce a specified value of output. (iii) value of output produced for a given total cost. (iv) satisfaction atta

    		•