--%>
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 : Earning zero economic profit Within a

    Within a monopolistically competitive industry along with no barriers to entry, long run equilibrium will be reached along with the firms into the industry: (1) maximizing total revenue. (2) producing their most efficient outputs. (3)

    		•
  • Q : Relative Income to Measures and

    From 1976 year, after adjusting income for taxes and transfers, the relative income group which, according to the Department of the Census, which has decreased most markedly like a percentage of the U.S. population ha

    		•
  • Q : Higher value for the Gini index A

    A higher value for Gini index tends to be related with: (w) decreases in the equality of the distribution of income or wealth. (x) decreases in the population’s total amount of income or wealth  (y) reduced overall curvature of the Lorenz c

    		•
  • Q : Influence on the total cost of plans of

    For a negative income tax the break-even level of income plan (NIT) is: (1) negatively related to the plan’s basic income floor. (2) positively related to the negative income tax rate. (3) a main influence on the total cost of t

    		•
  • Q : Relationship between MPP and APP If MPP

    If MPP equivalent to APP, what will you state regarding APP? Answer: APP is at its maximum and steady or constant.

    		•
  • Q : Example of a vertical merger An example

    An example of the vertical merger would be: (i) Merging the Oscar Myer hot dog Company with Wrangler Jeans Company and Aquafina Water Company. (ii) The log cabin architecture firm merging with the logging company and construction company. (iii) Merger between Wachovia

    		•
  • Q : Short run operation and long run

    When Presidio, Hybrid Roses and Texas boomed learned which its rent and utilities had soared upward by $9 per hour hence a new five-year lease would now cost $60 per hour, therefore this monopolist will: (w) continue to realize positive economic profi

    		•
  • Q : Problem regarding Minimum Wage Laws I

    I have a problem in economics on Problem regarding Minimum Wage Laws. Please help me in the following question. The consequence of minimum wage legislation on the teenagers has most likely been: (i) Greater unemployment. (ii) Greater employment. (iii) Full employment.

    		•
  • Q : Supply of labor curve problem Can

    Can someone please help me in finding out the accurate answer from the following question. Employer with the monopsony power which as well had the ability to wage discriminate perfectly would tackle a marginal factor cost of labor

    		•
  • Q : Marginal revenue when market price

    When the market price of a good is $50 and a purely competitive firm raises its output from 20 units, marginal revenue of it is: (w) $50. (x) $1000. (y) $2.50. (z) $0.40. I need a good answer on th

    		•