--%>
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 : Change in supply and a change in the

    Distinguish between a change in supply and a change in the quantity supplied?

    		•
  • Q : Higher opportunity costs of attendance

    Economics professors would attribute students’ higher rates of attendance on days while examinations are administered to the: (w) intensified needs to learn valuable material. (x) higher opportunity costs of missing set relative to other schedul

    		•
  • Q : Decreases in opportunity costs of

    The opportunity costs of production and consumption for most resources and goods tend to be decreased by: (w) private monopoly power. (x) price floors. (y) intense competition. (z) price ceilings. Hey friends pleas

    		•
  • Q : Key model of price-specie flow mechanism

    The key model underpinning David Hume’s price-specie flow mechanism which most mercantilists failed to grasp is termed today as: (i) the equimarginal principle. (ii) the wages-fund doctrine. (iii) the quantity theory of money. (iv) partial equil

    		•
  • Q : Illustrate the term Positive and

    Illustrate the term Positive and Normative Economics?

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

    How can we calculate EPS?

    		•
  • Q : Restriction of laissez-faire government

    A laissez-faire government is restricted to finding: (1) property rights within a simple fashion and to enforcing private contracts. (2) market prices which guarantee equitable resource allocations. (c) how resources will be allocated efficiently. (4)

    		•
  • Q : Problem regarding to intermediaries and

    Society gains from the activities of intermediaries which succeed within: (1) falling uncertainty and transaction costs for last consumers. (2) arbitrating strikes and defending workers’ rights. (3) creating productive jobs for unskilled workers

    		•
  • Q : Introduction of the term Cost of capital

    Give a brief introduction of the term Cost of capital?

    		•
  • Q : What are patent rights Patent rights :

    Patent rights: It is a unique license or right granted to a company or an Individual to make a specific product or utilize a specific technology.

    		•