--%>
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 : Variation of supply of loanable funds

    The supply of loanable funds varies positively along with the: (w) willingness of people to defer consumption into the future. (x) profitability and productivity of new capital investments. (y) price of the output which new capital will produce. (z) f

    		•
  • Q : Negatively transactions costs in

    The site value of the physical location of an enterprise tends to be very negatively associated to the: (w) transactions costs incurred by the firm’s customers and resource suppliers. (x) fertility of a parcel of land. (y) physical characteristi

    		•
  • Q : Operating the economy of production

    I have a problem in economics on the topic of Production. Please help me in the following question. The economy operating on its production possibilities frontier is as: (1) At full employment. (2) Technologically proficient. (3) Maximizing the output

    		•
  • Q : Market clearance according to Economists

    Can someone help me in finding out the right answer from the given options. The Economists state that a market is cleared when the price is in such a manner that: (i) Each and every good produced is sold. (ii) Quantity and Price are equal. (iii) Surplus demand surpass

    		•
  • Q : Marginal Utilities and Demand Prices

    Can someone help me in finding out the right answer from the given options. Rational individual consumers tend to purchase goods until the relative market prices for each and every goods purchased are proportional to all individuals: (i) Cost or benefit ratio. (ii) Op

    		•
  • Q : Shifting supply of curve by entry of

    When the price for Christmas trees is initially P1, in that case in the long run: (w) firms will neither enter nor exit this industry. (x) entry of firms will shift curve supply curve A to the right. (y) exit of firms will shift supply curve A to the left.

    		•
  • Q : Characteristic firms of purely

    At market price P0, this purely competitive industry’s characteristic firms will earn: (i) positive economic profit. (ii) negative economic profit. (iii) zero economic profit. (iv) negative accounting profit. (v) important dividends f

    		•
  • Q : Equilibrium price in setting minimum

    Setting a minimum price floor above the equilibrium price will: (w) raise the equilibrium price. (x) create excess demand at the minimum price. (y) create excess supply at the minimum price. (z) clear the market at the minimum price.<

    		•
  • Q : Attribute Demand Curve for Bonds A

    A demand curve for bonds moving to the right is probably to be attributable to: (w) a business cycle recession. (x) lower expected (future) interest rates. (y) an increase into the expected rate of inflation. (z) an increase in the liquidity of altern

    		•
  • Q : Curing shortages in the market Can

    Can someone help me in finding out the right answer from the following options. Curing shortages in the market for ice-cream needs: (1) Rises in the price of ice-cream. (2) Reduction in the supply of ice-cream. (3) Rises in the demand for ice-cream. (d) Reduces in the

    		•