--%>
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 : Laissez-faire philosophy of government

    As per to the laissez-faire philosophy of government,: (1) economy works best while all investment decisions are centralized. (2) market system works best along with only minimal government intervention. (3) government must be restricted to stabilizin

    		•
  • Q : Rivalry for various types of resources

    Intermediaries ultimately prosper only when they give a service of decreasing: (1) demand for a good (2) prices paid to manufacturers of a good. (3) transaction costs. (4) rivalry for various types of resources. (5) cut-throat competition into markets

    		•
  • Q : Cooperative and non-cooperative outcome

    Question: Cineplex and AMC are two rival movie theatre chains. They must each decide whether to set an admission price of $10 or set an admission price of $12; of course, the number of movie goers (and thus their r

    		•
  • Q : Introduction of the term Cost of

    Give a brief introduction of the term Cost of preference shares?

    		•
  • Q : Explain about the Payments for using

    Payments for the use of land, capital and labor are respectively termed as: (w) rent, wages and profits. (x) rent, interest and wages. (y) dues, profits and depreciation. (z) fruit, profits and money.

    Q : What are the limitations of Circular

    What are the limitations of Circular Flow Model?

    		•
  • Q : What problem does barter entail What

    What problem does barter entail?

    		•
  • Q : Utilitarianism of Jeremy Bentham The

    The utilitarianism of Jeremy Bentham is generally closely akin to the philosophies of: (1) Epicurianism and hedonism. (2) pragmatism and instrumentalism. (3) asceticism and stoicism. (4) dialecticism and materialism. (5) fundamentalism and predestinat

    		•
  • Q : Introduction of the term Operating

    Give a brief introduction of the term Operating Leverage?

    		•
  • Q : Positive Balance of Payments Question:

    Question: "Things will look good for the US if we could just get to where we are consistently running a positive Balance of Payments." Briefly comment on this

    		•