--%>
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 : Comparative Advantage-Mutual exchange

    Mutually beneficial exchange is probable whenever relative production costs vary previous to trade, is a manner to state the law of: (1) Positive profits from trade. (2) Comparative benefit. (3) Specialization and Division. (4) Purchasing power parity

    		•
  • Q : Illustrate other than price many factors

    Illustrate other than price many factors determine the outcome?

    		•
  • Q : Define the terms Plant Define the

    Define the following terms?

    		•
  • Q : Problem on Legislature budget XY School

    XY School District has a large number of students in need of remedial instruction. The superintendent of XY School System can allocated her budget between purchasing X units of remedial instruction at a price of $2,000/unit and spending an amount ($Y) on all other sch

    		•
  • 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 : Theory of Purchasing Power Parity

    Question: The Theory of Purchasing Power Parity says that, in the long run, nominal exchange rates change to offset changes in relative i. _________________________ so that the purchasing power of two currencies st

    		•
  • Q : Importance of rationally optimal

    Economic scarcity is pervasive, that makes choices essential. Therefore, rationally optimal decisions hinge upon tradeoffs which essentially reflect: (i) cooperation to minimize human greed. (ii) opportunity costs. (iii) competitive social behavior. (

    		•
  • Q : Why businesses are not really free to

    Why businesses are not really “free” to produce what they wish?

    		•
  • Q : Case of arbitrage while selling and

    Assume that melons sell for $5 in Brazil when moose pelts sell for $10, still into Canada melons sell for $10 as well as moose pelts sell for $5. A person who buys moose pelts within Canada to sell into Brazil would be doing: (1) speculation. (2) the “invisible

    		•
  • Q : Describe the term cost of capital

    Briefly describe the term cost of capital and also illustrate out its significance?

    		•