--%>
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 : Define price elasticity of supply with

    The supply curve which would best reflect the supply of 1940 a Packard 180 limousine is as: (i) supply curve S1. (ii) supply curve S2. (iii) supply curve S3. (iv) supply curve S4. (v) supply curve S5.

  • Q : Needs a goal of maximizing by

    The long run survival of a purely-competitive firm needs a goal of maximizing: (i) managerial salaries. (ii) total costs. (iii) economic profits. (iv) total revenue. (v) fixed costs to minimize variable costs. How

    		•
  • Q : Exploitation of Labor-average revenue

    The Exploitation might not exist even when the wage a worker is paid is less than worker’s: (1) Average revenue product. (2) Marginal revenue product. (3) Marginal factor cost. (4) The value of marginal product. Can someone p

    		•
  • Q : Collective Bargaining-John Hicks model

    I have a problem in economics on Collective Bargaining-John Hicks model. Please help me in the following question. Sir John Hick’s model of the collective bargaining doesn’t describe: (1) Final wage settlements. (2) The period of strikes.

    		•
  • Q : Oligopolistic firms by intersecting two

    In this illustrated figure kinked demand curve model, there two demand curves intersect at point a since the other oligopolistic firms: (w) are rapid to follow both price increases and price decreases by rival firms. (x) will follow p

    		•
  • Q : Problem on Equilibrium condition

    Reduction in the size of average American family is most probable to: (i) Erode rates of the technological advancement. (ii) Raise the demand for disposable diapers. (iii) Decrease women’s labor force participation rates. (iv) Increase the contribution of family

    		•
  • Q : Strategic Barriers to Entry The

    The successful employment of expensive marketing techniques through established competitors in an oligopoly: (w) encourages entry by other profit maximizing firms. (x) raises the minimum efficient scale of production for new entrants. (y) acts as a re

    		•
  • Q : Positively sloped long run industry

    A purely competitive industry produces a positively-sloped long-run industry supply curve when the industry: (i) includes only firms which experience diseconomies of scale. (ii) is an increasing cost industry. (iii) experiences technological advances

    		•
  • Q : Increasing supply problem Whenever the

    Whenever the equilibrium in the figure shown move from point a to point b, raised supply has taken only in the market illustrated in: (i) Panel A. (ii) Panel B. (iii) Panel C. (iv) Panel D.

    Q : Competition from poor substitutes A

    A firm in an industry which is a pure monopoly faces as: (w) many competitors from into the industry. (x) competition from only poor substitutes produced in other industries. (y) a market demand curve which is horizontal. (z) prosecution when it impor

    		•