--%>
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 : Elasticity of demand curve In which

    In which form of market, the demand curve is more elastic and why? Answer: Demand curve is more elastic under monopolistic since of the availability of close substitute.

    		•
  • Q : Unexpected inventory growth of price

    These supply and demand curves within the sugar market specify that: (w) a price floor of P0 for sugar will cause a surplus. (x) a price ceiling of P2 will cause a shortage. (y) the market clears while quantity equals Q0

    		•
  • Q : Capital resources Select which of the

    Select which of the following lists includes only capital resources (and therefore no labor or land resources)? 1) an ice arena; a professional hockey player; hockey uniforms. 2) the owner of a new startup firm; a chemistry lab; a researcher. 3) a hydroelectric dam; w

    		•
  • Q : Inefficiency of market equilibrium When

    When firms have market power although do not price discriminate perfectly, in that case the market equilibrium will be inefficient since: (w) P = AC = MC. (x) total revenue equals total costs [TR = TC]. (y) MSB = P > MC = MSC. (z)

    		•
  • Q : Value of the Average Product Hulk is

    Hulk is the fitness counselor who coaches 5 clients at a time in the exercise groups at Beefcake Body Builders. His hourly salary is $17, and Beefcake charges Hulk’s clients $20 for each and every hour-long conditioning session. Average value of the product Hulk

    		•
  • Q : Price discriminate A monopolist selling

    A monopolist selling several di erent products can sometimes "price discriminate" by bundling her products together. Here's an example. Suppose the U of C is planning to o er a series of two concerts. The rst program in the series consists of music by Chopin; the second, music by Stravinsky

    		•
  • Q : Stable Competitive Economy Into a

    Into a stable competitive economy without innovation, transaction, or uncertainty costs, all accounting profits would be: (w) pure economic profits. (x) payments required to secure owner-provided resources. (y) pure e

    		•
  • Q : Is binge drinking an economic trouble

    This binge drinking exercise observes why excessive drinking might be an economic trouble and the possible influences of government policy.

    		•
  • Q : Controlling costs in the short run

    Executives at the helms of monopolies that may pay little attention to controlling costs within the short run, but during the long run the monopoly will tend to be operated into a technically efficient fashion since: (w) the firm will

    		•
  • Q : Under negative income tax the net income

    Under the negative income tax system demonstrated in this figure, where a family of four all along with earned income of $60,000 yearly would have a net [after-tax] income of: (1) $37,500 per year. (2) $42,500 per year. (3) $50,000 per year. (4) $55,0

    		•