--%>
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 : Why is speculation unlike arbitrage

    Speculation is unlike arbitrage since: (1) speculative buyers always break even. (2) speculation causes increased costs. (3) speculators bear no risk. (4) positive returns for speculators are not sure. (5) competitive speculation equa

    		•
  • Q : Limitation of intermediaries for

    Intermediaries do not classically: (w) reduce transaction costs. (x) absorb risk. (y) try to make profits. (z) cause prices to be more volatile. I need a good answer on the topic of Economic problems. Please give m

    		•
  • Q : Factor Price Equalization theorem

    Please answer each of the exercises below. While you may work together on the homework, you must turn in your own work (in your own words). Homework must be handed in at the beginning of class on the due date unless other arrangements have been made. No late homework will be accepted. Homework wi

    		•
  • Q : Gains from Exchange- Practice and

    When a world famous concert pianist is as well the world's fastest short order cook, he would most likely gain the most financially through devoting: (i) Full time to frying burgers (ii) Full time to piano practice and concerts. (iii) Half-time cooking and half-time p

    		•
  • Q : Specialization and trade according to

    Not between concepts explained in Adam Smith’s Wealth of Nations was the conception which net benefits occur from: (1) specialization and trade according to comparative advantage. (2) the division of labor in production processes. (3) reliance o

    		•
  • Q : Determine relative price when two

    When the prices for doughnuts and croissants are $.50 and $1 correspondingly: (w) the opportunity cost for one doughnut is two croissants. (x) this is better to buy two doughnuts than one croissant. (y) one croissant will make Pierre twice as happy as one doughnut. (z

    		•
  • Q : Perfect competition leads the economic

    The perfectly competitive market structure benefits consumers since: w) firms do not generate goods at the lowest possible price within the long run. x) firms are forced through competitive pressure to be as efficient as possible. y) firms add a much

    		•
  • Q : Describe Financial Leverage Briefly

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

    		•
  • Q : Fixed costs and Variable cost

    Questions: 1: Which of the following are likely to be fixed costs and which variable costs for a chocolate factory over the course of a month?  Explain your choice.

    Q : Describe unexpected deflation Describe

    Describe unexpected deflation?

    		•