--%>
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 : Elucidate the growth record of the

    Elucidate the growth record of the United States?

    		•
  • Q : Heterodox approach for more production

    From the heterodox approach, what options does the enterprise need to produce more output? What effect do these options put on its cost structure?

    		•
  • Q : Discuss the economic aspects of ticket

    Discuss the economic aspects of ticket scalping also identifying the gainers and losers?

    		•
  • Q : Problem on Infrastructure The state

    The state legislature has voted to develop a grant-in-aid policy to try and induce local communities to devote more resources to improving their infrastructure. Town O = Has an operating budget of $2 million; currently spends a tot

    		•
  • Q : Need urgent help need urgent help in

    need urgent help in business economics, please suggest

    		•
  • Q : Market Economy Define the term Market

    Define the term Market Economy and also state its advantages and disadvantages?

    		•
  • Q : Problem on productive contribution

    Suppositions underpinning simple production possibilities frontier models don’t comprise a need that: (i) Net resources are fixed. (ii) All resources are efficiently employed. (iii) Technology is steady. (iv) Resource owners are paid according t

    		•
  • Q : How do households dispose of their

    How do households dispose of their income?

    		•
  • Q : Rise in participation of women in the

    Which two of the six reasons listed in the Last Word do you think are the most important in explaining the rise in participation of women in the workplace? Explain your reasoning.

    		•
  • Q : Adopting policy of paying efficiency

    The expected losses to workers by shirking are increased while a firm adopts a policy of: (1) dividing productive tasks therefore the division of labor is optimal. (2) paying efficiency wages that exceed market-clearing wages. (3) avoiding legal liability from not wri

    		•