--%>
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 : Set price equal to produce output

    Assume that HoloIMAGine’s patents for holographic technology lapsed, as well as entry of new competitors within this market eroded the demand for HoloIMAGine technology, even though the firm retains several market power since competitors’

    		•
  • Q : Influence of drought in market price

    Severe drought outcomes in a drastic fall in the output of wheat. Examine how will it influence the market price of wheat? Answer: As an outcome of severe drought,

    		•
  • Q : Complementary goods problem When a

    When a price cut for licorice gummy bears decreases the demand for tuna fish ice cream, then: (i) tuna fish ice cream and licorice gummy bears are both complementary goods. (ii) Price scrambles for tuna fish ice cream will diminish the demand for licorice gummy bears.

    		•
  • Q : Marginal and average revenue-market form

    In which market form is the marginal and average revenue of a firm always equivalent? Answer: Average and marginal revenue of a firm are for all time equivalents beneath perfect competition.

    		•
  • Q : What will occur when government taxes a

    When the government taxes a good, the price consumers currently face is most probably: (w) higher than before the tax. (x) below the price the seller receives. (y) less than average production cost. (z) justified through welfare payments to taxpayers.

    Q : Illustrate progressive tax rates The

    The burden of taxation would become additional progressive when federal taxes were reformed in that case: (1) fewer business firms were capable to evade corporate profit taxes. (2) steeper taxes were levied on that harmful goods as alcohol and tobacco. (3) the proport

    		•
  • Q : Defined Welfare Recipients By

    By description, a family of four receives welfare when it: (1) pays a smaller share of taxes than its share of benefits from government. (2) lives below the poverty line. (3) includes a student attending college on an academic scholar

    		•
  • Q : Effects of Globalization on Indian

    What do you mean by globalization and its effects on the Indian economy?

    		•
  • Q : Marginal cost by price discriminate

    When a monopolist which does not price discriminate maximizes profit and charges a price equal to marginal cost, this will: (i) minimize average cost and generate zero economic profit. (ii) minimize average cost and generate a positiv

    		•
  • Q : Occurrence of Adverse Selection When an

    When an NFL football team obscures information regarding damage to a former all-pro linebacker’s knees prior to trading him to the other team, the team which receives that player loses since of: (1) Immoral hazard. (2) Malfeasance. (3) Perverse selection. (4) Ad

    		•