--%>

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 : Total revenue of monopolistically

    A particular monopolistically competitive firm’s total revenue is probably to increase when this: (w) increases the prices of its products and consumer demand is elastic. (x) maintains its original price even if all of its compe

  • Q : Relationship between APP-MPP If APP is

    If APP is at its maximum, then what is the relationship among MPP and APP? Answer: MPP = APP

  • Q : Quantity demanded and goods price The

    The law of demand defines that there is a negative relationship among: (1) A good’s price and quantity demanded. (2) Limitless demands and inadequate resources. (3) The quantities demanded and supplied. (4) People’s income and demands for

  • Q : Implication of buyers in market

    Describe the implication of big number of buyers in the perfectly competetive market.

  • Q : Efficiency Wages-Expected losses

    Expected losses to the workers from shirking are raised when a firm accepts a policy of: (1) Dividing the productive tasks and hence the division of labor is optimal. (2) Paying the efficiency wages which surpass market-clearing wages. (3) Avoiding the legal liability

  • Q : Define Economics Briefly describe the

    Briefly describe the term economics?

  • Q : Define legal tender money Legal tender

    Legal tender money: Money which is declared legally as the medium of exchange by government is termed as legal tender money.

  • Q : What will occur when government taxes a

    When the government taxes a good, the price consumers currently face is most probably: (w) higher than before the tax. (x) below the price the seller receives. (y) less than average production cost. (z) justified through welfare payments to taxpayers.

    Q : Zero or negative marginal utility of a

    Whenever the marginal utility of a good becomes negative or zero: (i) Goods are transformed to the bads. (ii) Net utility reaches the maximum and then declines. (iii) The maximum total advantages have been squeezed from good. (iv) People are unwilling

  • Q : Types of market economies What are the

    What are the types of market economies?