--%>
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 : Illustrate Freedom of enterprise and

    Illustrate Freedom of enterprise and choice exist?

    		•
  • Q : Distribution of endowments 1. We have

    1. We have discussed the importance of resource endowments and institutions for an economy's successful development. a. In this game, what are the resources that make up the endowments, and what defines a given player's endowment o

    		•
  • Q : Assertion for the levying of a tax on

    Use the circular flow model to confirm this assertion for the levying of a tax on air polluters?

    		•
  • Q : Market Economy Define the term Market

    Define the term Market Economy and also state its advantages and disadvantages?

    		•
  • Q : Estimate the impact of education on

    Using a random sample of 670 individuals for the population of people in the workforce in 1976, we want to estimate the impact of education on wages. Let wage denote hourly wage in 1976 U.S. dollars and let educ denote years of schooling. We obtain the following OLS regression line: wage = -0.54

    		•
  • Q : The market system not only accepts

    Explain the statements: The market system not only accepts self-interest as a fact of human existence.

    		•
  • Q : Describe four important areas to

    Describe four important areas to emphasize Expenditures?

    		•
  • Q : Market system & a command economy try

    Contrast how a market system and a command economy try to cope with economic scarcity?

    		•
  • Q : What is the opportunity cost of

    What is the opportunity cost of attending college?  In 2000, nearly 80% of college-educated Americans held jobs, whereas only about 40% of those who did not finish high school held jobs.  How might this difference relate to opportunity costs?

    		•
  • Q : Heterodox cost theory Is Eiteman &

    Is Eiteman & Guthrie’s empirical evidence on the shape of the average total cost curve consistent along with heterodox cost theory?  Discuss it out.

    		•