--%>
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 : Public policies for low-income Fuel

    Fuel stamp programs which subsidize heating oil purchases through low-income households encourage those families to: (w) create more income by working. (x) particularly conserve on their use of fuel. (y) live along with less purchasing power. (z) subs

    		•
  • Q : Business Strategies Cingular and Alltel

    Cingular and Alltel involve in aggressive and expensive advertising for cell-phones. A reason for this advertising may be: (1) attempts to increase market share. (2) predatorily drive other firms by the market. (3) to increase the use of cell phones.

    		•
  • Q : Perfect competition and efficiency

    Which of the given describes a condition in which a good or service is produced at the lowest probable cost: w) productive efficiency. x) allocative efficiency. y) marginal efficiency. z) profit maximization Please

    		•
  • 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 : What is the basic principle of

    What is the basic principle of comparative advantage?

    		•
  • Q : Meaning of invisible hand according to

    Adam Smith’s opinion of an “invisible hand” powerfully implies the meaning that: (w) pursuit of individual self interest must be controlled. (x) most people lose sight of what’s good for society. (y) most peopl

    		•
  • Q : Transfer income in national income Is

    Is transfer income involved in national income? Explain Why? Answer: No, since transfer income does not effect in the production of services and goods.

    		•
  • Q : Introduction of the term Risk Principle

    Give a brief introduction of the term Risk Principle?

    		•
  • Q : Help How is a shift in demand reflected

    How is a shift in demand reflected in a demand equation? How is a shift in supply reflected in a supply equation? How is a movement along a demand (supply) curve reflected in a demand (supply) equation?

    		•
  • Q : Describe the types of multiplant firms

    Describe the types of multiplant firms?

    		•