--%>
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 : Signaling definition Can someone please

    Can someone please help me in finding out the accurate answer from the following question. Job applicants employ polished resumes explaining education, skills and work experience, accompanied by the supportive letters of recommendation letters as tools in the procedur

    		•
  • Q : High demand facing relatively

    Total revenue for Macho Man fake mustaches increased after the price raised from $15 to $17, showing that demand faced throguh Macho Man was: (i) relatively elastic. (ii) relatively inelastic. (iii) unitarily elastic. (iv) perfectly elastic. (v) perfe

    		•
  • Q : Effects of deceptive accounting

    Whenever stockholders who made big financial investments in Enron prior to the mid-1990s suffered huge losses during the year 2001-2002 since of deceptive accounting practices and insider trading, they were the victims of problem termed as: (1) Adverse selection (2) M

    		•
  • Q : Weakest and least efficient producers

    Cartels are generally supported most strongly by: (w) the largest and most efficient producers in the industry. (x) the weakest and least efficient producers in the industry. (y) buyers of the output of the industry. (z) consumer advocate groups.

    		•
  • Q : Differnt types of demand and supply i

    i want to understand different market competitions using graphs and solving some problems

    		•
  • Q : Employment distinguish between full

    distinguish between full employment and under employment

    		•
  • Q : Value of the Average Product Hulk is

    Hulk is the fitness counselor who coaches 5 clients at a time in the exercise groups at Beefcake Body Builders. His hourly salary is $17, and Beefcake charges Hulk’s clients $20 for each and every hour-long conditioning session. Average value of the product Hulk

    		•
  • Q : Determine prices for demand of buyers

    Buyers' demand prices would be ____ and sellers' supply prices would be ____ when the U.S. restricted car imports to Q1. (w) P2 and P1. (x) P0 and P2. (y) P0 and P

    		•
  • Q : Substitutes and Complements The

    The increase in the price of a good generally also rises the: (i) Demands for its substitutes. (ii) Supply of its complements. (iii) Purchasing power of the consumer incomes. (iv) Demand for its complements. Can someone please help

    		•
  • Q : Determine the equilibrium prises When

    When both sellers and potential buyers suppose prices for rider lawn mowers to raise as summer approaches, in that case throughout March and April (in the short run), the equilibrium: (w) price falls but quantity changes are ambiguous. (x) price rises

    		•