--%>
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 : Formally adopt inflation targeting

    Question: Why might it be difficult for the Fed to formally adopt inflation targeting?  Would inflation targeting be a good policy for the Fed in the present economic environment? Answer:

  • Q : Programs exchanged in the market For

    For the question below, utilize the given information. The market for gizmos is competitive, with an increasing sloping supply curve and a downward sloping demand curve. With no govt. intervention, the equilibrium price is $25 and the equilibrium quantity is 10,000 gi

    		•
  • Q : Illustrate the Risks involved with bonds

    Illustrate the Risks involved with bonds?

    		•
  • Q : Consumer and producer surplus in the

    In perfectly competitive market, the market demand and market supply curves are provided by Qd = 1000 −10Pd and Qd = 30Ps. Assume that the government gives a subsidy of $20 per unit to each and every seller in the mark

    		•
  • Q : Explain the following from Hull Explain

    Explain the following from Hull, England a news dispatch: “The fish market here slumped today to what local commentators called a ‘disastrous level’—all because of a shortage of potatoes”.

    		•
  • Q : Cornerstone of typical economic theory

    The cornerstone of typical economic theory derived through the work of Jeremy Bentham was the perception of (i) the wages fund. (ii) natural checks on population. (iii) increasing cost. (iv) utility. (v) surplus value.

    Q : Define Average cost and Marginal cost

    Briefly explain the term Average cost and Marginal cost?

    		•
  • 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?

    		•
  • Q : Decentralized a virtue of capitalism

    The idea which a virtue of capitalism is decentralized its decision making emerged while: (1) social philosophers looked for alternatives to feudal kings like economic regulators. (2) Russian imperialism fostered anti-communist sentiment after World W

    		•
  • Q : Conception of the Invisible Hand by

    Conception of the “Invisible Hand” by Adam Smith relies on mechanisms like those as underpin: (1) William Stanley Jevons’ “sunspot” theory of business cycles. (2) the biological concept of Homeostasis. (3

    		•