--%>
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 : Labour economic Can someone help me in

    Can someone help me in finding out the right answer from the given options. The Taft Hartley Act of 1946 made it illegal to encompass a: (1) Right-to-work law passed by the state legislature. (2) Conviction for the misdemeanor and serve as union officer. (3) Union for the agricultural migrants or go

    		•
  • Q : Internal factors which influencing the

    Write down the internal factors which influencing the capital structure?

    		•
  • Q : Reciprocal Trade Agreements Act had

    How Reciprocal Trade Agreements Act had goal of reducing tariffs?

    		•
  • Q : What is the opportunity cost of your

    Suppose you arrive at a store expecting to pay $100 for an item, but learn that a store two miles away is charging $50 for it.  Would you drive there and buy it?  How does your decision benefit you?  What is the opportunity cost of your decision?  Now suppose you arrive at a s

    		•
  • Q : Elucidate the gains that have occurred

    Elucidate the gains that have occurred using the resources as before specialization?

    		•
  • 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 : Difference between normal and inferior

    Difference between normal goods and inferior goods. Give illustration.

    		•
  • Q : Why producers not be able to find

    Why producers not be able to find enough paying buyers for “public goods”?

    		•
  • Q : Surpluses in the balance of trade The

    The advocates of laissez-faire policies favor: (i) Govt. control of economy. (ii) Public ownership of all the resources. (iii) Income to be distributed according to requirement. (iv) Surpluses in the balance of trade. (v) Minimal govt. intervention in economy.

  • Q : Perfectly competitive market and its

    Which of the given is not a characteristic of a perfectly competitive market structure: w) there are a very huge number of firms which are small compared to the market. x) All firms sell the same products. y) There are no restrictions to entry through

    		•