--%>
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 : Law of diminishing returns for a good

    The point is inevitably reached where an individual derives less extra enjoyment from the extra units of any good. This is mainly well-suited with: (i) Supply curves that slope-up and to right. (ii) Concave (or bowed out) production possibilities frontiers. (iii) The

    		•
  • Q : Reduce total revenue when demand is

    Boosting the price for Pixie’s cheesy fried grits by P2 to P3 will: (w) increases total revenue since demand within inelastic. (x) increase total revenue since demand is elastic. (y) reduce total revenue since demand is inelastic. (z) reduce total revenue since demand

    		•
  • Q : Marginal Resource Costs The word

    The word ‘marginal resource costs’ or ‘marginal factor costs’ signifies to the: (1) Additional cost included in generating an additional resource. (2) Additional cost included in generating an additional unit of the resource. (3) Additional cos

    		•
  • Q : Describe "in-market" mergers Describe

    Describe "in-market" mergers?An in-market merger is one which takes place among two banks operating in the similar geographic area, normally a city or metropolitan area. The merged institution frequently ends up with more than one branch in the

    		•
  • Q : Quantity Equilibrium I have the

    I have the quantity functions of demand and supply for two different goods, and I have to find the equilibrium of both the goods. Would I make all four functions equal to each other to find the equilibrium for the two goods? Or am I supposed to do something else?

    		•
  • Q : Problem on demand-Purchasing goods I

    I have a problem in economics on demand-Purchasing goods. Please help me in the following question. The quantity of good consumers will purchase beneath different conditions are termed as consumer: (i) Requirements. (ii) Entitlements. (iii) Wants. (iv

    		•
  • Q : Wage Discrimination-supply labor curve

    The employer with monopsony power which as well had the capability to wage discriminate perfectly would confront the marginal factor cost of the labor curve: (i) Similar to the supply of labor curve it faces. (ii) Lower than the supply of labor curve it faces. (iii) H

    		•
  • Q : Middle relative income define by Census

    The Department of the Census defines middle relative income as experienced while a family: (w) has adequate income to buy the fundamental food clothing and shelter required for survival. (x) would like to enhance their personal welfar

    		•
  • Q : Price charging by minimizing average

    See a monopolist which cannot price discriminate but that maximizes profit. When this firm produces the level of output where is average cost at its minimum that will charge a price: (i) equal to marginal cost and generate zero economic profit. (ii) e

    		•
  • Q : Total revenue when a price increases

    For hamburgers the demand is relatively elastic. When the price of hamburgers increases, in that case: (i) the quantity demanded will go up. (ii) its demand will increase. (iii) total revenue will increase. (iv) total revenue will reduce.