--%>
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 : Economic efficiency enhancement as

    Transaction costs are decreased and economic efficiency is enhanced by: (1) long-term wage and price controls. (2) monopolies which cooperate with central planners. (3) blacklists and yellow dog contracts. (4) bureaucratic tendencies

    		•
  • Q : Perfect competition leads the economic

    The perfectly competitive market structure benefits consumers since: w) firms do not generate goods at the lowest possible price within the long run. x) firms are forced through competitive pressure to be as efficient as possible. y) firms add a much

    		•
  • Q : Elucidate reallocation of Government

    Elucidate reallocation of Government resources?

    		•
  • Q : Help How is a shift in demand reflected

    How is a shift in demand reflected in a demand equation? How is a shift in supply reflected in a supply equation? How is a movement along a demand (supply) curve reflected in a demand (supply) equation?

    		•
  • Q : Example of simultaneous changes in both

    Elucidate an example of simultaneous changes in both supply and demand?

    		•
  • Q : How can we evaluate cost of capital How

    How can we evaluate cost of capital?

    		•
  • Q : Distribution of income and wealth in a

    Of the given options, the economist whose theories pivoted least upon the distribution of income and wealth (class conflict) in a capitalist system would have been: (1) Adam Smith. (2) David Ricardo. (3) Karl Marx. (4

    		•
  • Q : Organization identify the reasons for

    identify the reasons for the formation of organizations

    		•
  • Q : Understates the economic cost of a

    Computing the cost of college education like the cost of books, tuition and materials, room as well as board, and spending money: (i) overstates the economic cost of a college education. (ii) accurately measures the economic cost of a college educatio

    		•
  • Q : What are economic resources What are

    What are economic resources? What are the major functions of the entrepreneur?

    		•