--%>
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 : Rule of thumb for office rent Is there

    Is there any rule of thumb for office rent or on lease per gross income? If yes, then explain?

    		•
  • Q : Critics of current welfare programs

    Critics of current welfare programs who desire the welfare system scaled down tend to argue which welfare reform should give: (1) whatever this takes to lift all people out of poverty. (2) poor people with incentives to work. (3) nothing; there should

    		•
  • Q : Price discriminate by unregulated

    Unregulated monopolistic firms which do not price discriminate do NOT: (i) have power as price makers. (ii) dominate the supply side of the market. (iii) select profit maximizing price/quantity combinations from the market demand curv

    		•
  • Q : Price elasticity and market power The

    The price elasticity of demand equals one when this firm produces where total revenue is: (i) $72,000 per period. (ii) $80,000 per period. (iii) $96,000 per period. (iv) $100,000 per period. (v) $144,000 per period.

    Q : Value of commodities and services The

    The value of services and commodities is frequently decomposed into value in: (1) Dollars and value in Euros. (2) Absolute value and prices in relative prices. (3) House-holds and value in organizations. (4) Utilization and value in exchange.

  • Q : Generates price-quantity consistent for

    All prospective demanders [buyers] would be within equilibrium when this market for teleporter buttons created a price and a quantity consistent along with: (1) eliminating the shortage Q1-Q3 existing at P3<

    		•
  • Q : Curing scarcities of good Curing

    Curing scarcities in the market for ice cream needs: (i) Rises in the price of ice cream. (ii) Reduces in the supply of ice cream. (iii) Rises in the demand for ice cream. (iv) Reduction in the price of ice cream. (v) Burden of a price floor.

  • Q : Oligopoly and economic welfare in long

    In an oligopoly, as opposite to monopolistic or pure competition, industry output within the long run is probable to be: (1) lower along with reduced prices. (2) about similar but with higher prices. (3) lower and with higher prices.

    		•
  • Q : Medium of Exchange function of money

    Medium of Exchange function of money: Money as a medium of exchange signifies money as a means of the payment for exchange of services and goods. The Goods and services are exchanged for money whenever people sell things. Money is exchanged for goods

    		•
  • Q : Define change in demand Change in

    Change in demand: When change in demand takes place due to change in factor other than price, it is termed as change in demand.

    		•