--%>
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 : Technological advances in producing

    When given resources can now produce additional goods than was previously probable, then there have been a: (1) Stock market boom. (2) Competitive spurt which shrinks entrepreneurial gain. (3) Concavity reversal in the production possibilities frontier. (4) Bigger rel

    		•
  • Q : Introduction of the term capital

    Give brief introduction of the term capital structure? And also write down its principles?

    		•
  • Q : Explain the behavior of the workers Use

    Use the economic perspective to explain the behavior of the workers?  Why do they work so diligently?

  • Q : Problem on productive contribution

    Suppositions underpinning simple production possibilities frontier models don’t comprise a need that: (i) Net resources are fixed. (ii) All resources are efficiently employed. (iii) Technology is steady. (iv) Resource owners are paid according t

    		•
  • Q : An Inquiry in the Nature and Causes The

    The first comprehensive work upon economics written within English was authored through Adam Smith in 1776 year and entitled that “An Inquiry within the Nature and Causes of: (1) Laws of Supply and Demand.” (2) Wealth of Nations.” (3

    		•
  • Q : Comparative Advantage-Mutual exchange

    Mutually beneficial exchange is probable whenever relative production costs vary previous to trade, is a manner to state the law of: (1) Positive profits from trade. (2) Comparative benefit. (3) Specialization and Division. (4) Purchasing power parity

    		•
  • Q : Explain the Market System Specialization

    Explain the Market System Specialization?

    		•
  • Q : Demand supply Newspaper item: “Due to

    Newspaper item: “Due to lower grain prices, consumers can expect retail prices of choice beef to begin dropping slightly this spring with pork becoming cheaper after midsummer,” the Agriculture Department predicted. “This reflects increasing supply,” the department said. Does the statement use th

    		•
  • Q : How government might manipulate its

    Explain how government might manipulate its expenditures and tax revenues to reduce unemployment?

    		•
  • Q : Important source of revenue and major

    What is the most important source of revenue and the major type of expenditure at the Federal level?