--%>
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 : Heterodox pricing process Compare the

    Compare the costing and pricing process of heterodox pricing process to the procedures utilized in neoclassical microeconomics to set prices.  In what ways are heterodox prices altered from neoclassical prices?

    		•
  • Q : Initial systematic and popular

    The initial systematic and popular description of capitalism was explained in: (1) Sir Thomas Mun’s England’s Treasure by Foreign Trade. (2) Joseph A. Schumpeter’s Capitalism, Socialism, and Democracy. (3) John Maynard Keynes’

    		•
  • Q : Cooperative and non-cooperative outcome

    Question: Cineplex and AMC are two rival movie theatre chains. They must each decide whether to set an admission price of $10 or set an admission price of $12; of course, the number of movie goers (and thus their r

    		•
  • Q : Competitive market economy will make

    Briefly explain how the competitive market economy will make the needed adjustments to reestablish an efficient allocation of society’s scarce resources?

    		•
  • Q : Why Trade barriers hurt American

    Why Trade barriers hurt American consumers?

    		•
  • Q : Illustrates inverse relationship

    Illustrates the inverse relationship between price and quantity?

    		•
  • Q : Independent queue vs. pooled queue

    Instruction: McDonald's vs. Burger King - these two fast food chains use different waiting line design: Independent queue vs. pooled queue. To compare the two different queue systems on equal footing, let's assume that we pick a McDonald's sto

    		•
  • Q : Increase in the American dollar price

    “An increase in the American dollar price of the South Korean won implies that the South Korean won has depreciated in value.”  Explain.

    		•
  • Q : Resource payments correspond to

    Explain the foundation of economics where society’s material wants are Resource payments correspond to resource categories?

    		•
  • Q : Define Average cost and Marginal cost

    Briefly explain the term Average cost and Marginal cost?

    		•