--%>
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 : Substitution Effect-relative price of

    The substitution effect signifies to the change in consumption pattern as: (1) The absolute price of the good modifications. (2) Income changes. (3) The relative price of good changes. (4) The quality of good changes. Can someone p

    		•
  • Q : Higher price at slope of the demand

    When the slope of the demand for wheat is ten, we can predict now that a higher price of wheat will be as: (w) increase total expenditures on wheat. (x) reduce total expenditures on wheat. (y) not influence total expenditures on wheat. (z) More information is required

    		•
  • Q : Market Power and the Demand for Labor

    Can someone help me in finding out the right answer from the given options. The lack of competition in the product market outcomes in: (1) Less labor being hired than when the markets were competitive. (2) More labor being hired than when the markets were competitive.

    		•
  • Q : Depreciation expense The Realto Theatre

    The Realto Theatre purchased a new projector costing $37,000 on January 1, 2010. Since of changing technologies, the projector is predictable to last five years after which it will be obsolete and contain a salvage value of $1,000 as a collectors item. Compute the

  • Q : Discount coupons and trip afforded by

    Relative to people along with lower incomes, and high-income families be likely to shop for groceries less often and use fewer discount coupons, although buy more throughout each trip, since: (w) their superior access to transportatio

    		•
  • Q : Define cost Cost : This refers to the

    Cost: This refers to the money expenses acquired on the production of a specified amount of commodity.

    		•
  • Q : Changes in dollar receipts from sales

    The change within a firm’s dollar receipts from sales when this produces and sells one additional unit of output is termed as: (w) price. (x) marginal revenue. (y) average revenue. (z) contribution to overhead. Can anybody su

    		•
  • Q : Problem on Labor Unions and Wages The

    The Industrial unions try to accomplish wage rates above the competitive level through: (i) Limiting the supply of labor to the industry. (ii) Raising the supply of labor. (iii) Raising the productivity of the labor in an industry. (iv) Member’s agreeing to work

    		•
  • Q : Increase in Income Tax Progressivity

    When this figure demonstrated Lorenz curves for distribution of income after taxes and transfers, in that case it is UNTRUE of the Lorenz curves demonstrated in this demonstrated figure that: (1) line 0E0' represents a Lorenz curve of

    		•
  • Q : Shapes of yield curves in marketplace

    What are the three basic shapes of yield curves in the marketplace?

    		•