--%>
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 : Perfectly price elasticity of supply

    The supply of textile employees in China is possibly most like the perfectly price elastic supply curve within: (w) Panel A. (x) Panel B. (y) Panel C. (z) Panel D.

    Q : Concept of Production Possibilities

    The Production possibilities frontiers describe the concepts of: (1) A trade-off between inflation and unemployment. (2) Positive economics versus the normative economics. (3) Scarcity, opportunity costs, and reducing returns. (4) Absolute advantages

    		•
  • Q : Problem on sellers utility function The

    The economy consists of a single buyer and a single seller. The buyer has the utility function b ln xB1 + xB2 with b ≤ 10. The seller has the

    		•
  • Q : Positive economic loss Can someone help

    Can someone help me in finding out the right answer from the given options. Sara left her high strain job at hospital as the neurosurgeon making $250,000 yearly to launch ‘Flowers-to-Go’, a new firm. Sara still feels similar quantity of stress; therefore s

    		•
  • Q : Meritocracy in System of Distribution

    An emphasis onto socioeconomic mobility based upon equality of opportunity, independently of inheritances of land or else physical capital, which is a centerpiece of a system of distribution termed as: (1) meritocracy. (2) laissez faire capitalism. (3

    		•
  • Q : Illustration of production process The

    The Physical space is an illustration of the: (i) An input in the production procedure. (ii) The constraint on the production. (iii) The labor used up in production. (iv) An output of production procedure. Can someone please help m

    		•
  • Q : Perfectly facing of all price takers

    All price-taker firms face absolutely: (w) elastic demand curves. (x) unitary supply curves. (y) inelastic demand curves. (z) inelastic output curves. Hey friends please give your opinion for the problem of

  • Q : In-Kind Transfer Payments Medicare,

    Medicare, rent subsidies, Medicaid, and food stamps are examples of: (w) transfers in-kind. (x) cash transfers. (y) human capital programs. (z) negative income taxes. Can anybody suggest me the proper explanation for given problem

    		•
  • Q : Lowest possible price in transaction

    Is the assertion such that "Everyone all the time buys everything at the lowest possible price" right? Have you paid more than you had to for any good yet, after permitting for all transaction costs?

    		•
  • Q : Question on economic cost Select the

    Select the right answer of the question. Which of the following is not an economic cost? A) wages. B) rents. C) economic profits. D) normal profits.

    		•