--%>
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 : Compare average household income How

    How you compare the average household income of the different countries?

    		•
  • Q : Long-run In the long-run, an increase

    In the long-run, an increase in consumer desire for strawberries is most likely to:

    		•
  • Q : Elimination of exploitation The removal

    The removal of exploitation of labor [that is, wage payments beneath the value to society of each and every individual worker’s productive contribution] is automatic when business decision makers: (1) Should set wages via collective bargaining agreements with th

    		•
  • Q : Price elasticity of demands for moving

    Moving from point d to point e beside demand curve D, the price elasticity of demands of DVDs of video games at equal: (a) 0.8. (b) one. (c) 1.10. (d) 1.25. (e) 2.50

    Q : Present Value and Rates of Return When

    When the rate of return you calculate on an asset exceeds the interest rate: (1) competition for profit must make its price fall rapidly. (2) the price must fall rapidly. (3) the market is in long term equilibrium. (4) you should igno

    		•
  • Q : Rental check of pure economic rent The

    The part of your monthly rental check which shows pure economic rent is that that pays only for the use of the landlord's: (w) land. (x) capital. (y) labor. (z) entrepreneurial skills. I need a goo

    		•
  • Q : Average total costs above the demand

    A profit-maximizing monopolist will necessarily incur economic losses when, at every feasible level of output as: (w) average fixed costs [AFC] are very high. (x) average total costs [ATC] lies above the demand curve. (y) average tota

    		•
  • 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 : Elasticity of Demand for Labor Can

    Can someone help me in finding out the right answer from the given options. Absolute value of the proportional change in labor hired divided by the proportional change in the wage rate is termed as the: (1) Income or substitution coefficient. (2) Employment salary or

    		•
  • Q : Saving schedule Refer to the given

    Refer to the given figure.Choose the right answer from following. If the relevant saving schedule were constructed: A) saving would be minus $20 billion at the zero level of income. B) aggregate saving would be $60 at the $60 billion level of income. C) its slope woul

    		•