--%>
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 : Introduction of the term Risk factor

    Give a brief introduction of the term Risk factor?

    		•
  • Q : Limitations of activities to generate

    Illustrations of activities which generate negative externalities would not comprise: (w) burning coal that results in acid rain. (x) smoking a cigar at the opera. (y) killing fish by dumping sewage into a river. (z) being inoculated against a contagi

    		•
  • Q : Variation of wages in inverse proportion

    This wages vary within inverse proportion to the agreeableness and constancy of the employment was a perception first explicitly stated through: (i) Adam Smith. (ii) Karl Marx. (iii) Thomas Malthus. (iv) John Stuart Mill. (v) David Ricardo.

  • Q : Problem on prisoners dilemma game Lets

    Lets assume an infinitely repeated prisoner’s dilemma game by two players. The resulting payoffs at each phase by the actions of two players are illustrated below in the table (payoffs are symbolized like (payoff for player 1, payoff for player 2)). Two players

    		•
  • 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 : 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 : Illustration of Absolute and Relative

    The price of KnickKnacks is $1 and the price of WigWags has increased with $2 to $3. Therefore:  (w) absolute price of KnickKnacks has decreased and the relative price of WigWags has increased. (x) relative and absolute prices of KnickKnacks have

    		•
  • Q : What are economic resources What are

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

    		•
  • Q : What is the basic principle of

    What is the basic principle of comparative advantage?

    		•
  • Q : Important source of revenue and major

    What is the most important source of revenue and the major type of expenditure at the Federal level?