--%>
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 : Propensity to consume Propensity to

    Propensity to consume: This exhibits the level of consumption at various levels of income in the economy.

    		•
  • Q : Justified investment by paying income

    When the price of each of the given assets is $10,000 and the interest rate is 10%, then investment is most justified for: (1) a perpetuity paying $900 annually. (2) a machine with a 3 year life which can be leased to an outsider for $10 per day. (3) an income stream

    		•
  • Q : Innovating and enduring uncertainty of

    Profits are: (i) rewards for innovating and enduring uncertainty. (ii) economic, not normal, under pure competition. (iii) reduced through monopolistic business practices or structure. (iv) payments for providing capital. (v) payments to resource owne

    		•
  • Q : Marginal Utilities and Demand Prices

    Can someone help me in finding out the right answer from the given options. Rational individual consumers tend to purchase goods until the relative market prices for each and every goods purchased are proportional to all individuals: (i) Cost or benefit ratio. (ii) Op

    		•
  • Q : Price of Substitute goods What occurs

    What occurs to the demand for a good whenever the price of Substitute goods downs?Answer: Whenever the price of substitute good downs, then the demand for the specified good too downs.

    		•
  • Q : Exclusivity ratio of ratio while price

    The percentage change within quantity supplied divided through the percentage change within price is an approx measure of a good's: (w) unitary margin. (x) price elasticity of supply. (y) exclusivity ratio. (z) price elasticity of demand.

    Q : Generates price and a quantity

    All prospective suppliers [sellers] would be in equilibrium when this market for teleporter buttons created a price and a quantity consistent along with: (1) eliminating the shortage Q1-Q3 existing at P3. (2) any point along the demand

    		•
  • Q : Question based on poverty rate Select

    Select the right ans wer of the question. Which of the following would we expect to contain the highest poverty rate? A) white households headed by males B) elderly white households C) white households headed by females D) African-American households headed by femal

    		•
  • Q : Excess in balance of trade When there

    When there is an excess in the balance of trade? Answer: When export > import (that is, when export is greater than import).

    		•
  • Q : Find average income by relatively

    When market demands for agricultural products are relatively price inelastic and relatively income inelastic both, in that case as per capita income raises, the average income of farmers will: (w) increase while supplies of agricultur

    		•