--%>
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 : Least consistent demand curve with

    The demand curve which is least consistent along with the existence of a substitution consequence is within: (w) Panel A. (x) Panel B. (y) Panel C. (z) Panel D.

    Q : Law of demand is price in the law of

    is price in the law of demand an absolute or relative price

    		•
  • Q : Decreasing cost industries When average

    When average production cost for Plastibristle Inc. falls like market demand increases and more firms go into the industry, Plastibristle is within:  (1) an economically efficient industry. (2) a purely competiti

    		•
  • Q : Income rate variation in Loren curve

    When you were unconcerned about the welfare of other people and your income rated you onto the top two percent of the population, then you would be happiest while the Lorenz curve for your country resembled as: (1) li

    		•
  • Q : Equality Standard of Income Distribution

    When the equality standard of income distribution were adopted: (w) people would be paid the values of their marginal products. (x) family incomes would be identical for families of all sizes. (y) poets and engineers would have the same incomes. (z) g

    		•
  • Q : Profit Maximization and the Demand for

    Each and every profit-maximizing firm which can cover its variable costs will hire the labor: (1) Just to the point of the diminishing returns. (2) Just to the point where MRP = ARP for the final worker hired. (3) Beyond the point of the diminishing r

    		•
  • Q : Pretax -posttax and transfer

    Refer to the following diagram. If line b represents the pretax and transfer distribution of income in the United States, we would expect the post-tax and transfer distribution to be: A) line a. B) line b, because taxes and transfers have no effect on income distribut

    		•
  • Q : Uniting individual sellers of labor Can

    Can someone help me in finding out the right answer from the given options. Economically, the labor unions can be thought of as: (1) Motivating competition between workers for jobs. (2) Raising the flexibility of the nominal wages. (3) Attempts to cartelize and unite

    		•
  • Q : Comparison of competitive and

    If compared to competitive advertising, in that case informative advertising tends to: (1) help consumers make more satisfying choices. (2) be a waste of resources. (3) increase transaction costs. (4) be less efficient than competitiv

    		•
  • Q : Purely-competitive and constant-cost

    When this firm is typical into this purely-competitive of constant-cost industry, as in demonstrated figure in long-run equilibrium for cranberries will be attained at a market price of: (i) P1. (ii) P2. (iii) P<

    		•