--%>
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 : Define the term Abstractions in

    Define the term Abstractions in economics?

    		•
  • Q : Argument by Adam Smith for a true

    Within the Wealth of Nations, argument by Adam Smith such that a nation’s true wealth is its capability to: (1) obtain stocks of financial capital. (2) inspire its people’s courage and diligence. (c) give

    		•
  • Q : Meaning of Economic Development

    Question Discuss what "economic development" means in the context of this game? (Hint: How do you win, and what do you have at the end of the game that you did not have at the beginning of the game?)

  • Q : Cost of debt and Equity Cost of debt =

    Cost of debt= (1-tax rate)* interest rate * (debt ÷capital employed)Cost of equity = risk free rate + market premium (equity shareholders funds÷ capital employed)

    		•
  • 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 : How do you account for the dominant

    How do you account for the dominant role of corporations in the U.S. economy?

    		•
  • Q : The federal fiscal stimulus Question:

    Question: Was the stimulus package passed in 2009 as success?  In answering this question the focus should be the articles on the syllabus, but you should also include opinions of other commentators.   Your answer should also describe w

    		•
  • Q : Elucidate the overview of Business Cycle

    Elucidate the overview of Business Cycle?

    		•
  • Q : Real rate of interest Question: Hubbard

    Question: Hubbard argues that the Fed can control the Fed funds rate, but the interest rate that is important for the economy is a longer-term real rate of interest.   How much control does the Fed have over this longer real rate?

  • Q : Forcast 9. The following table shows

    9. The following table shows annual sales data for Stuff Happens, Inc., over the ten-year 1998-2008 period: Year Sales ($ Millions) 1998 $2.0 1999 2.2 2000 2.4 2001 2.6 2002 2.8 2003 3.0 2004 3.2 2005 3.5 2006 3.8 2007 4.1 2008 4.3 A. Calculate the 1998-2008 growth rate in sales using

    		•