--%>
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 : Define cyclical fluctuations Define

    Define cyclical fluctuations?

    		•
  • Q : The Federal corporate income tax Use

    Use the circular flow model to confirm this assertion for a 2% reduction in the Federal corporate income tax.

    		•
  • Q : Market efficiency while transaction

    Transaction costs tend to be decreased and markets are more efficient when: (w) the government subsidizes a good. (x) inter-market price differentials are eliminated through arbitrage. (y) taxes are used to give for social wants. (z) regulations close

    		•
  • Q : Raising consumer surplus problem For

    For the question below, utilize the given information. The market for gizmos is competitive, with an increasing sloping supply curve and a downward sloping demand curve. With no govt. intervention, the equilibrium price is $25 and the equilibrium quantity is 10,000 gi

    		•
  • Q : Problem on private resource ownership

    Relative to most of the other countries, the United States encompasses historically relied more greatly on: (1) Public resource ownership and private income distribution. (2) Decentralized decision making and private resource ownership. (3) Exports of textiles, automo

    		•
  • Q : International Trade & Globalization

    Question: 1.   Long-term Growth, International Trade & Globalization a.   In terms of understanding the importance of trade to an economy, the most impor

    		•
  • Q : Gross domestic product Question Would

    Question Would "Victory Points" be a measure of player's "GDP"? If not, then how would you calculate a player's GDP?

  • Q : Ambrose’s budget constraint Question:

    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 an

    		•
  • Q : Describe double coincidence of wants

    Double coincidence of wants: This means that one person's wishing to buy and sell should coincide with another person’s wish to buy and sell.

    		•
  • Q : Difference between normal and inferior

    Difference between normal goods and inferior goods. Give illustration.

    		•