--%>
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 : Coefficient of cross-elasticity of

    When a price hike from $15 to $20 for DVD disks causes sales of DVD players to reduce from 100 to 50 units, in that case the coefficient of cross-elasticity of demand among these goods is approximately: (w) 1/10. (x)  10. (y)  7/3. (z) 

    		•
  • Q : Income elasticity of demand when

    When diamond sales jump from 3 to 13 million carats yearly while a strong recovery increases national income from $12.0 trillion to $13.2 trillion, in that case the income elasticity of demand for diamonds is: (1) 0.76. (2) 1.52. (3)

    		•
  • Q : Price below perfect competition Who

    Who decides price beneath perfect competition? Answer: Price under perfect competition is recognized by the forces of market demand and supply in business.

    		•
  • Q : When is not total annual revenue

    As per this demonstrated figure in below, unless something changes the total annual revenue of Robot Butlers, Inc. Can’t exceed: (1) $10,000. (2) $20,000. (3) $100 million. (4) $200 million. (5) $400 million.

  • Q : World price in market When for wheat

    When for wheat the world price is $10 per bushel, and Del, who one owns the biggest wheat farm into North Dakota, will work at: (i) point a. (ii) point b. (iii) point c. (iv) point d. (v) point f.

    Q : Prevent operating in long run by

    A monopolist will prevent operating within the long run unless its economic profit is: (i) zero. (ii) positive. (iii) greater than accounting profit. (iv) zero or greater. (v) zero or less. I need a good answer on

    		•
  • Q : Monopolist maximizes profit When a

    When a monopolist maximizes the profit in the product market, it will: (i) Hire labor till the marginal revenue product equivalents the marginal resource cost. (ii) Hire the labor till the value of marginal product equivalents the marginal resource cost. (iii) Pay a w

    		•
  • Q : Compare firms with substantial market

    Compared to Firms A and B as well as C, Firm D is: (1) a firm along with substantial market power. (2) a pure price taker and quantity adjuster. (3) least possible to generate economic profit in the long run. (4) a total revenue maximizer when it produces output level

    		•
  • Q : Production possibility history of World

    Can someone help me in determining the right answer from the given options. Through the onset of World War-II, the United States: (i) Expanded the military output just by increases taxes rigorously. (ii) Moved in the direction of its production possibilities frontier.

    		•
  • Q : Demand of consumers-supply of seller

    Consumers’ demand prices and sellers’ supply prices may be different in equilibrium due to: (w) arbitrage. (x) expectations about availability. (y) the invisible hand. (z) government subsidies or tax wedges.