--%>
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 : 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 : Maximizes profits in a perfectly

    Which of the given is not true for a firm within perfect competition: w) Profit equivalents total revenue minus total cost. x) Price equivalents average revenue. y) Average revenue is greater than marginal revenue. z) Marginal revenue equivalents the

    		•
  • 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 : Construct a 2-D graph which comprises

    How to construct a 2-D graph which comprises drawing a horizontal and a vertical axis?

    		•
  • 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 : Explain Self-interest of the Market

    Explain Self-interest of the Market System?

    		•
  • Q : The federal fiscal stimulus Question:

    Question: Was the stimulus package passed in 2009 as success?  In answering this question the focus should be the articles on the syllabus, but you should also include opinions of other commentators.   Your answer should also describe w

    		•
  • 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 : Circular flow model to confirm this

    Use the circular flow model to confirm this assertion for the construction of a new high school in Blackhawk county?

    		•
  • Q : Describe the Slope of a nonlinear curve

    Describe the Slope of a nonlinear curve?

    		•