--%>
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 : Describe unequal burdens of

    Describe unequal burdens of unemployment exist?

    		•
  • Q : Way to determine nature price of Adam

    “Natural price” by Adam Smith of a good was eventually determined through: (1) the amount of capital used within production in the short run. (2) long-run average costs of production, that Adam Smith believed to be the amo

    		•
  • Q : Exchange and Specialization I have a

    I have a problem in economics on Exchange and Specialization. Please help me in getting the right answer from the following question. Sarah the wheat farmer would be most probable to trade for fruit from the Kathy's orchard if: (i) Sarah's opportunity

    		•
  • Q : Illustrate the characteristics of the

    Illustrate the characteristics of the Market System?

    		•
  • Q : Calculate Equilibrium Quantity and Price

    1. The owner of a firm calculates that next year's profit will be $1,000. Each successive year profit will increase by 10% (i.e. year 2: $1100; year 3: $1210 and so on.) At the end of the 5th year the firm could be sold for $20,000. A) if the appropriate di

    		•
  • Q : Illustrate the advantage of corporate

    Illustrate the advantage of corporate form of organization?

    		•
  • Q : Describe the Personal distribution of

    Describe the Personal distribution of income?

    		•
  • Q : Introduction of the term Timing

    Give a brief introduction of the term Timing Principle?

    		•
  • Q : Explanation of theory of pricing for

    The theory of pricing for particular goods explained in Adam Smith’s Wealth of Nations is most consistent along with: (1) mercantilist doctrine. (2) Richard Cantillon’s distinction between “value in

    		•
  • Q : Concepts of Economic system argues by

    For Economic system argues by Adam Smith relies heavily upon all the given concepts EXCEPT: (w) market expansion will be facilitated through capital accumulation. (x) prices will be driven to the lowest point at that production can ev

    		•