--%>
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 : How can we calculate EPS How can we

    How can we calculate EPS?

    		•
  • Q : Circular flow model of the private

    I have a problem in economics on Circular flow model of the private sector. Please help me in the following question. The simple circular flow model of private sector doesn’t comprise: (i) Firms. (ii) Product markets. (iii) Government agencies.

    		•
  • Q : Characterized contestable markets

    Industries that are described as "contestable": (w) will experience long-run economic profits equal to zero. (x) are difficult for firms to enter, but not to exit. (y) are difficult for firms to exit, but not to enter. (z) will charge prices greater t

    		•
  • Q : Describe Financial Leverage Briefly

    Briefly describe Financial Leverage? In what manner it is calculated? What does low or high financial leverage signify?

    		•
  • Q : State of good or service at last unit

    Which of the given describes a situation in which each good or service is produced up to the point where the last unit gives a marginal benefit to consumers equivalent to the marginal cost of producing this? w) productive efficiency.

    		•
  • 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 : Effects of that depreciation or

    Would a decline in U.S. consumer income or a weakening of U.S. preferences for foreign products cause the dollar to depreciate or appreciate?  Other things equal, what would be the effects of that depreciation or appreciation on U.S. exports and imports?

    		•
  • Q : Rightward shift of PPC What was

    What was rightward shift of PPC point out? Answer: It points out growth of the resources.

    		•
  • Q : External factors which influencing the

    Write down the external factors which influencing the capital structure?

    		•
  • Q : Examples and Applications of

    What are the Examples and Applications of International Trade?

    		•