--%>
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 : Normal accounting profit The only

    The only profit earned within the long run through a purely competitive firm is of: (w) normal accounting profit. (x) offset by short term losses. (y) created by exceptionally astute managers. (z) unrelated to its opportunity costs.

    Q : Relatively price elastic demand For

    For Cournot’s Spring Water the demand is relatively price elastic at: (i) point a. (ii) point b. (iii) point c (iv) point d. (v) point e.

    Q : What is production function Production

    Production function: It is the technological relationship among input and output of a firm and is termed as production function.

    		•
  • 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 : Total costs incur by profit-maximizing

    Hybrid Roses is the merely florist in 60 miles of Presidio, Texas. When total fixed costs (for example, rent and utilities) are $9 per hour, that profit-maximizing monopolist will incur total costs of around: (w) $20 per hour. (x) $27

    		•
  • Q : Determine present value of future income

    The present value of future income is: (1) calculated by multiplying future income by the percentage interest rate. (2) higher, the higher the interest rate. (3) lower, the higher the interest rate. (4) unaffected by the interest rate. (5) purely obje

    		•
  • Q : Time and opportunity cost in

    The time and other opportunity costs incurred in obtaining information regarding products and prices and in that case driving to and from markets are illustrations of: (1) mobilization costs. (2) contracting costs. (3) transactions co

    		•
  • Q : Bilateral Monopoly-Collective Bargaining

    Can someone help me in finding out the right answer from the given options. The potential range of negotiable price or wage solutions whenever both the seller and buyer contain substantial economic clout is recognized in the: (1) Bargaining model devised by the John H

    		•
  • Q : Corporations account problem I have a

    I have a problem in economics on Corporations account problem. Please help me in the following question. The Corporations account for roughly ______ of U.S. business revenues. (i) 1/4. (ii) 1/2. (iii) 1/6. (iv) 5/6. (e) All the above.

    Q : Effect of future consumption on

    When households become increasingly willing to defer current consumption in order that they can enjoy greater future consumption, in that case the: (1) interest rate rises. (2) equilibrium investment level rises. (3) present value of

    		•