--%>
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 : Distribution of income and wealth in a

    Of the given options, the economist whose theories pivoted least upon the distribution of income and wealth (class conflict) in a capitalist system would have been: (1) Adam Smith. (2) David Ricardo. (3) Karl Marx. (4

    		•
  • Q : Main advantage of EVA The main

    The main advantage of using EVA is that it is simple to calculate and understand. It uses simple measures like operating profits and cost of capital terms which are widely known and accepted in the financial arena. It helps the managers to assess thei

    		•
  • Q : Theory of wages according to Adam Smith

    Least consistent along with Adam Smith’s theory of wages would be the suggestion that wages vary positively along with the: (w) effort required to learn skills necessary to accomplish particular types of work. (x) stability of employment and the

    		•
  • Q : Introduction of the term Cost of

    Give a brief introduction of the term Cost of preference shares?

    		•
  • Q : Case study plz find the attachment and

    plz find the attachment and dont compromise on quality,, no similarity n need to be done according to requierment...

    		•
  • Q : Describe unanticipated inflation

    Describe unanticipated inflation?

    		•
  • Q : Founder of modern economics The person

    The person along with, arguably, the top claim to the name “founder of modern economics”: (1) John Stuart Mill. (2) Karl Marx. (3) John Maynard Keynes. (4) Joan Robinson. (5) Adam Smith. Hello guys I wa

    		•
  • Q : What are the Functions of money Explain

    Explain in short the functions of money? Answer: (A) Medium of exchange: Money can be employed to make payments for all transactions of services and goods.

    		•
  • 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 : Heterodox approach for more production

    From the heterodox approach, what options does the enterprise need to produce more output? What effect do these options put on its cost structure?

    		•