--%>
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 : Predictable Flows of Income Vigorous

    Vigorous competition for predictable flows of income recommends that federal agricultural subsidies will tend to be rapidly: (1) spent because most farmers lack sufficient budgeting skills. (2) capitalized within higher prices for farm land. (3) slash

    		•
  • Q : Raise Interest Rates with Investment

    Interest rates will rise when: (1) the supply of loanable funds grows. (2) the average maturities of corporate bonds issued decreases. (3) most households decide to decrease the liquidity of their portfolios of assets. (4) households increasingly defe

    		•
  • Q : Economic theories Economic theories: A)

    Economic theories: A) are useless because they are not based on laboratory experimentation. B) that are true for individual economic units are never true for the economy as a whole. C) are generalizations based on a careful observation of facts. D) are abstractions an

    		•
  • Q : Measurement of below poverty line Below

    Below the poverty line the proportion of the U.S. population is: (w) rises with upturns of the business cycle. (x) has declined, though somewhat erratically, over the past 50 years. (y) has been virtually eliminated by a vigorous “War on Poverty

    		•
  • Q : When is demand perfectly price inelastic

    Demand is perfectly price inelastic when the quantity demanded for Pixie’s cheesy fried grits is of: (w) zero. (x) P4. (y) P2. (z) More information is required.

    Q : Substitute goods in cross-elasticity of

    The cross-elasticity of demand among any pair of goods is positive when the goods are: (i) luxuries. (ii) necessities. (iii) complements. (iv) substitutes. Hey friends please give your opinion for the problem of

  • Q : Determine water elasticity of production

    When 200,000 gallons of water are applied per acre, 4 tons are harvested by each acre of linguini trees yearly, but cutting back to 160,000 gallons causes the crop per acre to reduce to 2 tons yearly. Then water elasticity of linguini production is as

    		•
  • Q : Contribution standard of income

    The contribution standard of income distribution: (w) sets the least efficient incentives for production. (x) is the distribution standard most compatible along with pure capitalism. (y) minimizes individual economic freedom. (z) is very complimented

    		•
  • Q : Least possible cost for primary economy

    The least possible costs of alternative outcomes to the primary economic question of “what?” can be represented with the production possibilities curve through: (1) The slopes of movements all along the curve. (2) Shifting the curve up by

    		•
  • Q : Profit Maximization-Labor Markets If,

    If, after hiring the very last worker, the firm's profit is similar as it was before the last worker was hired, then the firm must: (1) Hire more workers to raise gain. (2) Layoff certain workers to raise the gain. (3) Not hire any more workers. (4) Shut down in short

    		•