--%>
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 : Profit margins Examine within your

    Examine within your answer the circumstances that will enable a company to pass on cost increases to customers and protect profit margins. For example- price sensitivity of demand, rising food prices, cotton prices, etc.

    		•
  • Q : Determining opportunity cost Suppose a

    Suppose a doctor has a private clinic in New Delhi and his annual earnings are of Rs10 lakh. When he works in a Government Hospital in New Delhi, his annual earnings are of Rs 8 lakh. Determine the opportunity cost of encompassing a clinic in New Delhi?

  • Q : Make economic profits by

    A profit-maximizing monopolist will certainly be capable to generate economic profits when, at certain level of output: (w) average fixed costs [AFC] are very high. (x) average total costs [ATC] lies above the demand curve. (y) averag

    		•
  • Q : Law of Supply Law of Supply : Supply

    Law of Supply: Supply means the goods provided for sale at a price throughout a particular period of time. This is the capacity and intention of the producers to gen

    		•
  • Q : Definitions of Poverty by Researchers

    Some researchers have attempted to define poverty: (1) as the lowest 20% of the income distribution. (2) through estimates of the fundamental needs for families having various characteristics. (3) by estimating the costs of the minimum caloric intake

    		•
  • Q : Income floor by marginal tax rate A

    A marginal tax rate of 75 percent and an income floor of ____ give in a break-even level of income of $8,000. (w) $2,000. (x) $4,000. (y) $6,000. (z) $16,000. Hello guys I want you

    		•
  • Q : Kinked demand curve about product price

    When an oligopolist is aware about the firm faces a kinked demand curve, this: (1) may cut price along with little expected reaction by rivals. (2) can avoid consumer demand and preferences. (3) may keep product price despite large ch

    		•
  • Q : Economic profits by competitive

    Economic profits produce competitive pressures which cause: (w) each firm’s output to shrink during the short run. (x) an industry’s output to increase. (y) market prices to increase. (z) firms to leave an industry.

    Q : Hicks Model of Collective Bargaining I

    I have a problem in economics on Hicks Model of Collective Bargaining. Please help me in the following question. The period of union strikes and the equilibrium wage rate at conclusion of a strike are the focus of: (i) Taft-Hartley Act of 1948. (ii) B

    		•
  • Q : Felicific calculation of utilitarianism

    The supposition that a ‘felicific calculation’ gives a proficient guide for fitting punishment to the crime committed is an integral portion of: (1) Gresham’s Law that ‘Bad will drive out Good’. (2) Jeremy Bentham’s utilitarianism.

    		•