--%>
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 budget line Budget line : Budget

    Budget line: Budget line exhibits all combinations of two goods which a consumer can purchase with his income at a specified price.

    		•
  • Q : Occurrence of nominal price lower then

    When the nominal price of apples at a remote orchard is fewer than at a local grocery store, in that case you are more probable to buy at the orchard when: (w) at all possible, because produce is invariably cheaper at the orchard. (x) you desire to bu

    		•
  • Q : Simple circular flow model The simple

    The simple circular flow model illustrates that: A) households are on the buying side of both product and resource markets. B) businesses are on the selling side of both product and resource markets. C) households are on the selling side of the resource market and on

    		•
  • Q : Effects of price controls for a price

    The consequences of price controls would be least discernible for a price ceiling set: (1) above the price equilibrium. (2) below the price equilibrium. (3) in a region of diminishing returns. (4) unfavorable to market companies. (5)

    		•
  • Q : Implicitly weigh marginal cost and

    implicitly weigh marginal cost and marginal benefit

    		•
  • Q : Help The problem of asymmetric

    The problem of asymmetric information is that

    		•
  • Q : Abandonment of perfect competition This

    This needs to be identified that general abandonment of supposition of perfect competition, universal adoption of supposition of monopoly, need to have extremely destructive consequences for economic theory.” 

    		•
  • Q : High economic profits High economic

    High economic profits for firms are least probable to arise by: (1) important market power. (2) “cut-throat” competitive pricing policies. (3) superior products. (4) unusually efficient managers. (5) price-maker behavior.

    Q : Monopsony and Marginal Resource Cost

    The labor monopsonist which doesn’t wage discriminates consists of a marginal resource cost curve [or marginal factor cost curve] which is above the labor supply curve then the firm faces as: (1) Monopsonists encompass market power in the markets for output. (2)

    		•
  • Q : Problem on Horizontal Integration I

    I have a problem in economics on Horizontal Integration. Please help me in the following question. McDonalds makes hamburgers at a number of various locations. This is an illustration of a: (i) Horizontally integrated firm. (ii) Monopoly. (iii) Vertic

    		•