--%>
Assignment Help - homework help

Ambrose’s budget constraint

Question:

Ambrose consumes two goods, peanuts (x1 ) and a composite good (x2). He has a utility functionU = 4 √x1 + x2. This means his MU1 = 2/ √x1 and his MU2 = 1 . The current prices are p1 = 0.5 per kilogram and. p2 = 1. His budget is $20 per month.

(a) Write down Ambrose's budget constraint?

(b) What are the optimal quantities of peanuts and x2 for Ambrose to consume? How much utility will he get?

(c) Suppose that rationing by the government means that Ambrose is allowed to purchase no more that 12 kilograms of peanuts per month. Now how much x1 and x2 will Morgan consume? Show the effect of rationing using a diagram. Be sure to label you diagram completely.

(d) Suppose that instead of rationing peanuts the government decides to tax them. The tax is $0.5 per kilogram. How much x1 and x2 will Morgan consume? How much utility will he get?

(e) How much would Ambrose need to be compensated to make him as well of as if peanuts had not been taxed?

Solution:

a) P1 = 0.5, P2 = 1, m = 20

Therefore, the budget constraint is,

0.5x1 + x2 = 20

b) U = 4 Öx1 + x2. P1 = 0.5, P2 = 1

MRS = MU1/ MU2 = (2/Öx1)/1 = 2/Öx1

Now, MRS = P1/P2 = 0.5/1 = 2/Öx1

  1.   Öx1=2/0.5
  2.   x1 = 4/0.25 = 16
  3.   x2 = (20 - 16x 0.5) = 12

Utility derived = 4(16)0.5 + 12 = 28

c) If x1 is rationed to 12 units, x2 = 20 - 12x 0.5 = 14

351_effect of rationing.png

d) P1 = 0.5 + 0.5 = 1, P2 = 1, m = 20

MRS = P1/P2 = 1/1 = 2/Öx1

  1.   Öx1=2
  2.   x1 = 4
  3.   x2 = (20 - 4x 0.5) = 18

Utility derived = 4(4)0.5 + 18 = 22

e) 4(4)0.5 + x2 = 28

  1.   4 + x2 = 28
  2.   x2 = 28-4 = 24
  3.   Extra money required = 24 - 18 = 6

   Related Questions in Business Economics

  • Q : Illustrate Freedom of enterprise and

    Illustrate Freedom of enterprise and choice exist?

    		•
  • Q : Problem on Legislature budget XY School

    XY School District has a large number of students in need of remedial instruction. The superintendent of XY School System can allocated her budget between purchasing X units of remedial instruction at a price of $2,000/unit and spending an amount ($Y) on all other sch

    		•
  • Q : Cooperative and non-cooperative outcome

    Question: Cineplex and AMC are two rival movie theatre chains. They must each decide whether to set an admission price of $10 or set an admission price of $12; of course, the number of movie goers (and thus their r

    		•
  • Q : What do you mean by Linkages What do

    What do you mean by Linkages?

    		•
  • Q : Define internal rate of return What do

    What do you understand by the term internal rate of return?

    		•
  • Q : U.S. exports create a demand for

    True or false? “U.S. exports create a demand for foreign currencies; foreign imports of U.S. goods generate supplies of foreign currencies.”  Explain.

    		•
  • Q : Nation’s production possibilities curve

    Suppose that, based on a nation’s production possibilities curve, for 10,000 pizzas domestically an economy must sacrifice to get the one additional industrial robot it desires, but can get that robot from another country in exchange for 9,000 pizzas. To the fol

    		•
  • Q : Demand often exceeds supply and supply

    “In the corn market, demand often exceeds supply and supply sometimes exceeds demand.” “The price of corn rises and falls in response to changes in supply and demand.” Among these 2 statements used correctly which in the terms “supply&rdq

    		•
  • Q : Government expenditures on goods and

    Explain Government expenditures on goods and services and transfer payments?

    		•
  • Q : Perfect Competition leads to Allocative

    A perfectly competitive industry achieves allocative efficiency since: w) goods and services are produced at the lowest possible cost. x) services and goods are produced up to the point where the last unit gives a marginal benefit to consumers equivalent to the margin

    		•