--%>
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 : Problem on shortages or surpluses of

    The market is cleared when there are: (i) Buyers left waiting in line. (ii) Surplus supplies of unsold goods. (iii) No surpluses or shortages. (iv) Tendencies for the prices to increase. Can someone please help me in finding out th

    		•
  • Q : Positive relationship by law of supply

    The law of supply defines that there is a positive relationship among: (1) The Price and quantity supplied. (2) Technology and production. (3) Purchases and the accessibility of goods. (4) Supply and the demand it makes.

    Q : Kinked demand curves and sticky prices

    Sticky prices within oligopoly markets are: (w) predicted by the kinked demand curve model. (x) substantiated by many statistical studies. (y) most common for highly differentiated products. (z) a result of price discrimination.

    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 : What is Budget line Budget line : This

    Budget line: This refers to all combinations of goods that a consumer can purchase with his whole income and price of two goods.

    		•
  • Q : Words of Frank Knight In words of Frank

    In words of Frank Knight, risk, not like uncertainty: (w) is totally unpredictable. (x) is a main source of pure economic profits. (y) may be estimated. (z) cannot be taken into account while firms make decisions regarding production and pricing.

    		•
  • Q : Market Form-price taker In which market

    In which market form, the firm is a price taker? Answer: In Perfect competition

    		•
  • Q : Define Fiscal deficit Fiscal deficit is

    Fiscal deficit is equavalent to excess of total expenditure over the sum of revenue and capital receipts excluding borrowings. That is, Fiscal deficit means borrowing of the government. Fiscal Deficit :T

    		•
  • Q : Pure competition and monopolistic

    Monopolistically competitive and purely competitive industries tend to be described by: (i) important economies of scale in production. (ii) many potential buyers and sellers. (iii) horizontal demand curves facing each firm. (iv) conscious interdepend

    		•
  • Q : Accounting profit when implicit cost

    Can someone please help me in finding out the accurate answer from the following question. When implicit cost surpasses implicit revenue and economic profit is zero (0), then accounting profit is: (1) Bigger than zero. (2) Zero. (3) Less than 0 (zero). (4) Not specifi

    		•