--%>
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 : Strategic behaviour of decisionmaker If

    If one decisionmaker in interdependent circumstances calibrates its decisions to the anticipated reactions of the other party, in that case the decisionmaker is engaged within: (1) psychological forecasting. (2) profit maximization. (3) collusion. (4) strategic behavi

    		•
  • Q : Describe the duty of bondholders in a

    Describe the duty of bondholders in a bond?

    		•
  • Q : When productive resources are utilized

    While productive resources are utilized efficiently: (w) prices greatly exceed production costs for current outputs. (x) opportunity costs are at their minimums for all goods. (y) domestic production exceeds the value of foreign output. (z) the value

    		•
  • 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 : Eco Quantity TR TC 0 $0.00 $10.00 1

    Quantity TR TC 0 $0.00 $10.00 1 $150.00 $30.00 2 $290.00 $50.00 3 $420.00 $80.00 4 $540.00 $120.00 5 $650.00 $170.00 6 $750.00 $230.00 7 $840.00 $300.00 8 $920.00 $

    		•
  • Q : Inefficiencies and inequities by

    An employer that exaggerates the safety of a position or the prospects for advancement to job applicants makes inefficiencies as well as arguable inequities due to: (1) signaling. (2) credentialism. (3) screening. (4) adverse selection. (5) a moral hazard.

  • Q : Impact of dollar on aspects of

    Question Discuss the impact of dollar depreciation on the various aspects of American Economy. Devaluation of the DollarIntroduction:

    		•
  • Q : Example of public goods Drinking at a

    Drinking at a public water fountain is: (w) a public good because anyone may drink from it. (x) results in a negative externality because others can’t drink from this at similar time. (y) a positive externality because you are benefiting by other’s provisi

    		•
  • Q : What does high or low operating

    What does high or low operating leverage specify?

    		•
  • Q : Define the term Weak-form market

    Define the term Weak-form market efficiency. Explain briefly.

    		•