--%>
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 : Explain the markets and prices of the

    Explain the markets and prices of the Market System?

    		•
  • Q : Determine the lowest average wages

    Consider a huge group of identically smart and strong industrious workers. All else identical, Adam Smith would predict such that the lowest average wages would be earned through the workers who were in the work that: (1) had the leas

    		•
  • Q : Government policies with respect to the

    Can you explain how different government policies with respect to the recycling of aluminum and paper might account for these different market outcomes?

    		•
  • Q : Requirement of building blocks for a

    Building blocks for a capitalist system consist of: (1) supplies and demands. (2) private property rights. (3) laissez-faire policies. (4) market-determined outputs and prices. (5) All of the above. Please guys hel

    		•
  • Q : The supply curve when each of these

    What happens to the supply curve when each of these determinants changes?

    		•
  • 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 : Define Direct and inverse relationships

    Define Direct and inverse relationships?

    		•
  • Q : Problem on utility function Matt’s life

    Matt’s life is divided into two time periods, young and old, and his utility is a function of two “goods”:  consumption when young and consumption whenever old.  Consumption when young and consumption when old are both of normal goods to Ma

    		•
  • Q : Maximizes profits in a perfectly

    Which of the given is not true for a firm within perfect competition: w) Profit equivalents total revenue minus total cost. x) Price equivalents average revenue. y) Average revenue is greater than marginal revenue. z) Marginal revenue equivalents the

    		•
  • Q : Illustrate the rate of exchange of two

    Illustrate the rate of exchange of two products?

    		•