--%>
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 : Total variable costs of

    This profit-maximizing competitive firm’s total variable costs or TVC as in illustrated figure can be computed area as: (i) 0P3fq4. (ii) P2P1de. (iii) P3P2ef. (iv) 0P2eq4. (v) aced.

    Q : Problem on utility-maximizing bundle

    Jane consumes only apples and chocolate.  She is always willing to trade 1piece of chocolate for exactly 3 apples. Her income is $200.  She can buy apples for $1 each and chocolate for $2 per piece.a. To Jane, apples and chocolate are (circle 1):

    		•
  • Q : Founder of Utilitarianism I have a

    I have a problem in economics on Founder of Utilitarianism. Please help me in the following question. The utilitarianism founder in England was: (i) Rupert Brooke. (ii) Jeremy Bentham. (iii) Thomas Dewey. (iv) John Stuart Mill. (v) Adam Smith.

    Q : Quantity of good supplied-Law of supply

    The law of supply states that the amount of a good supplied is: (i) Legally governed by the production regulations. (ii) Inversely related to its absolute price. (iii) Recognized by the consumer tastes in the free market economy. (iv) Positively relat

    		•
  • Q : Labor market-Monopsony power Can

    Can someone please help me in finding out the accurate answer from the following question. The firm probable to encompass significant monopsony power in its labor market would be: (1) Big cotton farm in the Texas hiring migrant workers. (2) Textile manufacturer in Hon

    		•
  • Q : Altering the value of place for better

    The trucker who hauls fresh oranges from Florida to the New York raises the value of oranges by directly and productively changing their: (i) Time of consumption. (ii) Location or Place. (iii) Ownership or Possession. (iv) Form and substance.

    Q : Determine constant slope of demanded

    The slope of this illustrated figure of demand curve for DVD games is: (w) constant. (x) greater at high prices than at low prices. (y) lower at low prices than at high prices (z) unitarily elastic.

    Q : Disadvantages of mixed economy system

    Tell me what are the disadvantages of mixed economy system?

    		•
  • Q : Annual total costs When Nostalgia

    When Nostalgia Corporation maximizes profit in its production of Silver Screen DVDs, in that case its annual total costs will be around: (i) $45 million. (ii) $65 million. (iii) $85 million. (iv) $105 million. (v) $125 million. <

    		•
  • Q : Practicing joint profit maximization A

    A cartel is: (w) any large multinational corporation like OPEC. (x) a group of oligopolists practicing conscious parallelism of action. (y) a group of firms which practices joint profit maximization. (z) a multinational firm along with government subs

    		•