--%>
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 : Where is the price elasticity of supply

    The price elasticity of supply as in below demonstrated figure is unitary within: (w) Panel A. (x) Panel B. (y) Panel C. (z) Panel D.

    Q : Profit-maximizing pure competitor in

    For a profit-maximizing pure competitor in the short-run equilibrium: (w) P = MC = MR. (x) MC = minimum AC. (y) MR > P. (z) only normal profits will be earned. Hey friends please give your opini

    		•
  • Q : Increasing demand for Complementary

    Can someone please help me in finding out the accurate answer from the following question. When tortilla chips go on sale for fifty percent off, then the demand for salsa is most probable to: (1) Stay similar. (2) Reduce. (3) Raise. (d) Raise only when salsa as well g

    		•
  • Q : Problem of asymmetric information

    Provide the solution of this question. The problem of asymmetric information is that: A) neither health care buyers nor providers are well-informed. B) health care providers are well-informed, but buyers are not. C) the outcomes of many complex medical procedures cann

    		•
  • Q : Influence of good on opportunity cost

    The law of demand defines that, all as well constant, consumers will obtain: (i) More of a good, the lower its opportunity cost. (ii) Less of any good, higher the prices of its substitutes. (iii) Advertised goods more often than generic products. (iv) Greater luxuries

    		•
  • Q : Labor union monopoly I have a problem

    I have a problem in economics on Labor union monopoly. Please help me in the following question. As compared to pure competition, beneath a pure labor union monopoly, the wage will tend to: (1) Higher and employment will also be higher. (2) Lower and

    		•
  • Q : Export transactions Select the right

    Select the right answer of the question. U.S. export transactions create: A) a U.S. demand for foreign monies and the satisfaction of this demand decreases the supplies of dollars held by foreign banks. B) a U.S. demand for foreign monies and the satisfaction of this

    		•
  • Q : Individual firm in purely competitive

    In a purely competitive industry, the individual firm: (i) can raise the quantity demanded by lowering the price of its product. (ii) experiences substantial economies of scale. (iii) faces a completely inelastic demand curve. (iv) cannot influence th

    		•
  • Q : Labor Unions-Public Employees I have a

    I have a problem in economics on Labor Unions-Public Employees. Please help me in the following question. Workers who are now permitted to join unions however who still might not legally strike comprise: (1) Civilian federal employees. (2) Medical pro

    		•
  • Q : Economies of scale exist in range of

    Natural monopoly refers to a market or industry in that: (w) economies of scale exist across much of the complete range of market demand. (x) superior management enables a firm to remove its competitors. (y) a firm produces a good protected through pa

    		•