--%>
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 : Loathed monopolization and viewed of

    Adam Smith and most of the typical economists who followed instantly in his footsteps: (i) viewed monopoly as no big problem. (ii) encouraged monopolies due to their research and development abilities. (iii) thought monopoly power was a communist plot

    		•
  • Q : Surpluses in the balance of trade The

    The advocates of laissez-faire policies favor: (i) Govt. control of economy. (ii) Public ownership of all the resources. (iii) Income to be distributed according to requirement. (iv) Surpluses in the balance of trade. (v) Minimal govt. intervention in economy.

  • Q : Write short note on Markets Write short

    Write short note on Markets?

    		•
  • Q : Determine opportunity cost of making an

    The opportunity cost of making an exact alternative is: (i) useful primarily as an indicator of relative prices. (ii) its nominal costs into terms of all other goods. (iii) the information which guides your decision. (iv) measured through the subjecti

    		•
  • 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 : Decreases in opportunity costs of

    The opportunity costs of production and consumption for most resources and goods tend to be decreased by: (w) private monopoly power. (x) price floors. (y) intense competition. (z) price ceilings. Hey friends pleas

    		•
  • Q : Changing rates of Appreciation and

    Elucidate the changing rates of Appreciation and Depreciation?

    		•
  • Q : Introduction of the term Control

    Give a brief introduction of the term Control Principle?

    		•
  • Q : Government expenditures on goods and

    Explain Government expenditures on goods and services and transfer payments?

    		•
  • Q : Summary of what can cause an increase

    Illustrate a summary of what can cause an increase in demand?

    		•