--%>
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 : Price floors with government purchases

    Suppose the U.S. wheat market is primarily in a stable equilibrium upon S0D0. Assume now that the government institutes a legal price floor at P3 per bushel of wheat. When the government will buy and store any resulting surplus

    		•
  • Q : Define fixed cost Fixed cost : Fixed

    Fixed cost: Fixed costs refer to cost that remains constant as output modifies. For example: rent

    		•
  • Q : Monopolists maximize profits Maximizing

    Maximizing the net social benefits from a specified stock of resources does NOT need that: (i) price equals marginal cost for all goods. (ii) marginal social benefit equals marginal social cost [MSB = MSC]. (iii) no one can be made better off unless s

    		•
  • Q : Official poverty rate for income

    For U.S. families official poverty rates are: (w) higher than in most other countries. (x) very similar for different types of families. (y) higher for the middle class than for lower class families. (z) lower than in most other countries if poverty i

    		•
  • Q : Exploitation and the Wage Rate Assume a

    Assume a neither firm possessing both the monopsony power as an employer and the market power in its output market, however which can neither wage discriminate nor price discriminate. In the equilibrium in its labor market for workers, of the given va

    		•
  • Q : Output From the heterodox approach,

    From the heterodox approach, what options does the enterprise need to produce more output? What effect do these options put on its cost structure?

    		•
  • Q : Average cost per unit of production

    When Prohibition Corporation maximizes profit within its production of St. Valentine’s Day software, there average cost per unit of it produced will be roughly: (i) $4 per copy. (ii) $10 per copy. (iii) $18 per copy. (iv) $24 per copy. (v) $32 per copy.

  • Q : Coefficient of elasticity of relatively

    Please help me to solve the problem that is given below: A relatively price elastic demand curve would consist of a coefficient of elasticity of as: (w) ep = 1. (x) ep > 1. (y) ep < 1. (z) ep

    		•
  • Q : Operating in state-Right-to-Work Laws

    When it is illegal to necessitate union membership as a condition of employment for firm, then the firm: (1) Needs all the employees to sign the yellow dog contracts. (2) Can’t sign an agency shop agreement with the union. (3) Can need settlement before workers

    		•
  • Q : Powerful negative externalities in

    Potentially powerful negative externalities are mainly overwhelmingly a decisive argument against permitting laissez faire policies and supplies to govern the production and market demands and distribution of: (1) avian flu antivirus shots. (2) public

    		•