--%>
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 : Importance of Price Earnings Ratio

    Write down the importance of Price Earnings Ratio?

    		•
  • Q : Elucidate the gains that have occurred

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

    		•
  • Q : Nation’s production possibilities curve

    Suppose that, based on a nation’s production possibilities curve, for 10,000 pizzas domestically an economy must sacrifice to get the one additional industrial robot it desires, but can get that robot from another country in exchange for 9,000 pizzas. To the fol

    		•
  • Q : Changing rates of Appreciation and

    Elucidate the changing rates of Appreciation and Depreciation?

    		•
  • Q : Specialization in division of labor I

    I have a problem in economics on Specialization in division of labor. Please help me in the following question. Jennifer writing computer code whereas Melissa handles the business features of Econo-Software would be an illustration of specialization i

    		•
  • Q : Introduction of the term Cost Principle

    Give a brief introduction of the term Cost Principle ?

    		•
  • Q : Capitalism-Tightly regulate business I

    I have a problem in economics on Capitalism-Tightly regulate business. Please help me in the following question. The govt. in a purely capitalist state would not: (1) Find out the property rights. (2) Enforce contracts among private parties. (3) Offer

    		•
  • Q : Determine relative price when two

    When the prices for doughnuts and croissants are $.50 and $1 correspondingly: (w) the opportunity cost for one doughnut is two croissants. (x) this is better to buy two doughnuts than one croissant. (y) one croissant will make Pierre twice as happy as one doughnut. (z

    		•
  • Q : How can we calculate EPS How can we

    How can we calculate EPS?

    		•
  • Q : Technological advances in producing

    When given resources can now produce additional goods than was previously probable, then there have been a: (1) Stock market boom. (2) Competitive spurt which shrinks entrepreneurial gain. (3) Concavity reversal in the production possibilities frontier. (4) Bigger rel

    		•