--%>
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 : Basic supply determinants of other than

    Illustrate the 6 basic supply determinants of other than price?

    		•
  • Q : Utility with food coupons Question: In

    Question: In Vancouver the Salvation Army encourages people to make food voucher donations to panhandlers instead of simply giving them cash. You can buy a food voucher for $5 and give it to a panhandler who can use it to purchase food. The Sa

    		•
  • Q : Comparative advantage in production I

    I have a problem in economics on Comparative advantage in production. Please help me in the following question. The oranges are grown in Florida and potatoes are grown in Maine mainly since: (i) orange-grower’s in Maine have not lobbied effectiv

    		•
  • Q : Problem regarding supplies-demands and

    The new supply and demand curves within University City are S0 and D0. But after the county commission imposed a $3 per six-pack excise tax upon beer: (1) demand fell to D1 from the perspectives of beer dealers. (2) co

    		•
  • Q : Illustrate the Law of supply Illustrate

    Illustrate the Law of supply?

    		•
  • Q : Real exchange rate Question: To

    Question: To determine the real exchange rate, what two pieces of information do you need in addition to the nominal exchange rate? Answer:

    Q : Costs for a firm Question:  (a)      

    Question:  (a)       Complete the following table of costs for a firm.  (Note: enter the figures in the MC  column between outputs of  0 and 1, 1 and 2, 2 and 3, etc.) 

    		•
  • Q : Describe the Slope of a nonlinear curve

    Describe the Slope of a nonlinear curve?

    		•
  • Q : Current Account captures international

    Question The Current Account captures international fund flows due to net income on (past) investments, net transfers, and i._______________________________, general

    		•
  • Q : Explain and give an illustration

    Explain and give an illustration of (a) the fallacy of composition; and (b) the “after this, therefore because of this” fallacy.  Why are cause-and-effect relationships difficult to isolate in the social sciences?

    		•