--%>
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 : Competitive theory of prices Normal 0

    Normal 0 false false

  • Q : Implication of perfect knowledge

    Describe the implication of perfect knowledge regarding market beneath perfect competition.

    		•
  • Q : Risk-Return-Diversification The below

    The below table presents the three possible states for stocks A and B returns. (a) De

    		•
  • Q : Exploitation and the wage rate problem

    Assume a neither firm possessesing both the monopsony power as an employer and market power in its output market, however which can neither wage discriminate nor the price discriminate. In equilibrium, in its labor market for the workers, the following variables the m

    		•
  • Q : Agricultural demand The demand for

    The demand for agricultural products is: A) relatively elastic with respect to price. B) relatively inelastic with respect to price. C) relatively elastic with respect to income. D) downward sloping to the individual farmer, but perfectly elastic to farmers as a group.

    		•
  • Q : Marginal Utilities and Demand Prices

    Can someone help me in finding out the right answer from the given options. Rational individual consumers tend to purchase goods until the relative market prices for each and every goods purchased are proportional to all individuals: (i) Cost or benefit ratio. (ii) Op

    		•
  • Q : Production by a strategy of extensive

    Fakery is a pretentious start-up firm within the monopolistically-competitive costume jewellery industry. But Fakery is most probable to try to gain control over pricing whereas limiting its production by a strategy of: (1) lobbying C

    		•
  • Q : Opportunity costs in different prices

    While a firm is NOT able of price discrimination: (w) various prices are charged for units of remotely related goods. (x) only opportunity costs are reflected in various prices for units of similar good. (y) any short term profit stimulates long run l

    		•
  • Q : Average revenue and marginal revenue

    In spite of of the amount sold, price equals for a price-taker firm on both average: (i) revenue and marginal revenue. (ii) variable cost and marginal cost. (iii) fixed cost and average variable cost. (iv) total cost and marginal revenue.

  • Q : What will happen when a supply of curve

    When a supply curve is positively sloped, a raise in demand will increase the equilibrium price as well as: (w) raise the quantity supplied. (x) raise supply. (y) decrease the quantity supplied. (z) decrease supply.

    		•