--%>
Assignment Help - homework help

Demand curve for peanuts

Question:

a) Johnny consumes peanuts (x1) and a composite good (x2). His utility function is U = x1x2. His marginal utilities are MU1 = x2 and MU2 = x1. Johnny's budget is $20 and the price of the composite good is $1. Derive Johnny's demand function for peanuts.

b) Ambrose consumes 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 price of the composite good is p2 = 1. His budget is $20 per month. Derive Ambrose's demand function for peanuts. How does it compare with Johnny's demand curve for peanuts?

Solution:

a) U = x1x2

MRS = MU1/MU2 = x2/x1

Now, MRS = P1/P2 = P/1 = x2/x1 => x2 = 2Px1 {taking P1 = P}

Putting this value in budget equation:

Px1 + x2 = 20

  1.   Px1 + 2Px1 = 30
  2.   Px1 = 10
  3.   x1 = 10/P
  4.   x2 = 20

b) U = 4 Öx1 + x2.

MRS = MU1/ MU2 = (2/Öx1)/1 = 2/Öx1

Now, MRS = P1/P2 = P/1 = 2/Öx1

  1.   Öx1=2/P
  2.   x1 = 4/P2

Therefore, Ambrose's demand for peanuts does not depend upon his income, while Johnny's demand for peanuts does depend upon his income.

   Related Questions in Microeconomics

  • Q : Expected rate of return on R&D

    All of the following rise the expected rate of return on R&D expenditures, except: A) patents. B) trademarks. C) imitation by others. D) trade secrets

    		•
  • Q : Downward-sloping demand curve The law

    The law of demand is graphically demonstrated by: (1) Movement all along the supply curve. (2) The downward-sloping demand curve. (3) The rightward shift of demand curve. (4) Shifting of production possibilities. C

    		•
  • Q : Nondiscriminating monopoly Tell answer

    Tell answer of this question.Refer to the following data for a nondiscriminating monopolist. At its profit-maximizing output, this firm will be operating in the: 1) perfectly elastic portion of its demand curve. 2) perfectly inelastic portion of its demand curve. 3)

    		•
  • Q : Coefficient of price elasticity Why the

    Why the coefficient of price elasticity of demand is is negative?

    		•
  • Q : Impact of economy according to price

    If price ceiling or price floor were removed what is the impact on the economy?

    		•
  • Q : Perfectly Competitive market condition

    In which market condition, the effect of an individual seller is (0) zero? Answer: In Perfectly Competitive market condition.

    		•
  • Q : Positively sloped demand curve of

    When your income is positively and closely tied to the price of a specific product, a raise in its price might cause: (1) The income effect which, in severe conditions, yields a positively sloped demand curve. (2) You to go bankrupt. (3) The powerful positive substitu

    		•
  • Q : Quantity supply or demand to changes in

    When a measure of the responsiveness of one variable to other (for example, quantity supplied [or demanded] to changes within price), elasticity: (w) provides no criterion for identifying responsiveness. (x) depends on the units used to express change

    		•
  • Q : Nonexistent market supply and power

    HoloIMAGine has patented a holographic technology which creates 3-D photography obtainable to consumers. There is a market supply curve for HoloIMAGine technology: (w) nonexistent since price-maker firms simultaneously set prices as well as quantities

    		•
  • Q : Advantage of law of equivalent marginal

    Behavior most compatible along with the law of equivalent marginal advantage occurs while: (w) shoppers exhaust their budgets upon nondurables and services. (x) every firm uses similar markup over cost to set prices. (y) identical twins work in evenly

    		•