--%>
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 : Theory of imperfect competition An

    An extensive theory of imperfect competition was initially developed by: (1) John Maynard Keynes. (2) Antoine Augustin Cournot. (3) Joan Robinson. (4) Joseph Schumpeter. (5) Thorstein Veblen. How can I solve my

  • Q : Process of Privatization The

    The Privatization is a process by which ‘for-profit’ business firms: (1) Transform small entrepreneurships into big corporations. (2) Hiring professional administrators to assist manage operations. (3) Vend corporate stocks and bonds to safe the economic c

    		•
  • Q : Collapse of Cartels A purpose NOT often

    A purpose NOT often cited for the collapse of cartels would be: (w) price cheating. (x) inability to deter entry. (y) government prosecution. (z) merger into monopoly. Hey friends please give your opinion for the p

    		•
  • Q : Demand curve at the current market price

    The demand curve faced through a purely competitive firm at the current market price of: (i) negatively sloped. (ii) horizontal. (iii) perfectly inelastic. (iv) rectangularly hyperbolic. (v) positively sloped.

    Q : Basic definition of Production I have a

    I have a problem in economics on Basic definition of Production. Please help me in the following question. Production is the process in which: (i) Technology and human knowledge are utilized to apply energy to convert materials to make them more preci

    		•
  • Q : Political pressure on government

    When the government imposes a price floor upon a product, in that case there may be political pressure for the government: (1) to produce several of the good itself. (2) to restrict the demands of private buyers. (3) to buy and then store some surplus

    		•
  • Q : Problem Regarding to Lorenz Curves A

    A Lorenz curve is a way to demonstrate: (w) that the U.S. has perfect equality of income distribution. (x) a mirror image of a production-possibility curve. (y) the percentages of families receiving different percentages of income. (z) differences wit

    		•
  • Q : Economic profit at profit-maximizing

    HoloIMAGine has patented a holographic technology which makes 3-D photography obtainable to consumers. When HoloIMAGine produces its profit-maximizing output, this is demonstrated as: (w) operating in the long run. (x) realizing an economic profit equ

    		•
  • Q : Income sufficient to physical survival

    The view about all people is entitled to income sufficient to comfortably sustain their physical survival is termed as the: (1) survival standard. (2) contribution standard. (3) needs standard. (4) standard deduction. (5) equality standard.

  • Q : Discounted by an appropriate interest

    A fundamental principle of finance is that the net cash flows expected by an investment are: (w) all future revenues expected by the investment minus the purchase price of the capital. (x) negatively associated to the interest rates related with borrowing investment f

    		•