--%>
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 : Price discrimination by monopoly power

    A firm can practice price discrimination when this: (i) confronts a perfectly elastic demand curve. (ii) is a pure quantity adjuster. (iii) has several monopoly power and is capable to separate its customers in various groups with different elasticiti

    		•
  • Q : Decrease the burden of sales tax on low

    To decrease the burden of a sales tax upon low income households, in that case: (i) goods along with high income elasticities should be taxed. (ii) goods along with low income elasticities should be taxed. (iii) goods along with high income elasticities must be exempt

    		•
  • Q : Generating utility through production I

    I have a problem in economics on Generating utility through production. Please help me in the following question. The production generates utility by making a good more precious in: (1) Possession. (2) Time. (3) Form. (4) Place. (5) All the above.

    Q : Determine market demand in curve The

    The market demand curve as in demonstrated figure for Christmas trees is: (i) curve A. (ii) curve E. (iii) curve F. (iv) curve G. (v) curve J.

    Q : Increase profits of quantity selling by

    When a monopolist was selling a quantity which marginal revenue [MR] is greater than marginal costs [marginal costs [MC] in that case this could increase profits by: (w) raising price. (x) increasing output. (y) raisi

    		•
  • Q : Illustrates average variable cost curve

    LoCalLoCarbo has become the favorite of fad dieters. There in curve E shows: (1) LoCalLoCarbo’s marginal cost curve. (2) LoCalLoCarbo’s average variable cost curve. (3) LoCalLoCarbo’s average total cost curve. (4) the market demand curve facing LoCal

    		•
  • Q : Various kinds of capital goods Supply

    Supply curves for different kinds of capital goods are usually: (w) perfectly elastic. (x) perfectly inelastic. (y) upward sloping. (z) downward sloping. Can anybody suggest me the proper explanati

    		•
  • Q : Market demand function The market  for

    The market  for good X consists  of 2 consumers. consumer  1',s demand  for good X is: X1 :  15 - 3Px + 0.5PY + .02I1I1 and I2 a

    		•
  • Q : Unit of Account function of money Unit

    Unit of Account function of money: The Unit of Account function of money is also termed as the measure of value function. Money as a unit of account signifies a standard unit for quoting the prices. This makes money a powerful medium of comparing the

    		•
  • Q : Substitution effects resulting from

    The Law of Demand mainly relies heavily on the: (1) Buying power consequences of relative price modifications. (2) Substitution effect resultant from the relative price changes. (3) Increase in opportunity costs as income is worn out. (4) Principle of the non satiety.

    		•