--%>
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 : Sunk cost Give the answer of following

    Give the answer of following question. Which of the following sayings associate most closely to the idea of sunk costs? 1) Don't cry over spilt milk. 2) A bird in the hand is worth two in the bush. 3) He who hesitates is lost. 4) Show me the money.

    		•
  • Q : Advertising for higher prices Brand

    Brand name aspirin sells on higher prices than generic aspirin since: (w) higher prices mean higher quality. (x) they are chemically superior. (y) they cost more to produce. (z) advertising campaigns relate the brand name along with quality.

  • Q : Annual total revenue of production When

    When Prohibition Corporation maximizes profit in its production of St. Valentine’s Day software, so annual total revenue of it will be around: (1) $140 million. (2) $250 million. (3) $320 million. (4) $420 million. (5) $1 billio

    		•
  • 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 : Average variable costs of pure

    Average variable costs per generic brick of this pure competitor equal approximately: (i) $.02 (2 cents per brick). (ii) $.04 (4 cents per brick). (iii) $.07 (7 cents per brick). (iv) $.09 (9 cents per brick).

  • Q : Bond Theorem Applications What are Bond

    What are Bond Theorem Applications and also write down its consequences?

    		•
  • Q : Reason of Financial Intermediation The

    The fundamental reason for financial intermediary’s presence is to: (1) Facilitate beginning new business firms by employing internal financing. (2) Help business organizations comply with laws needing the financial intermediation. (3) Minimize

    		•
  • Q : Income effect dominating substitution

    The personal supply of labor is characterized by the income effect which dominates the substitution effect if: (1) Trina retires to beach condo subsequent to working for the city for 42-years. (2) Members of a rock band give up touring for a year subsequent to their s

    		•
  • Q : Functions of price mechanism What are

    What are the various functions of price mechanism in a free market economy?

    		•
  • Q : Industrial Unions-organizing workers

    Can someone help me in finding out the right answer from the given options. Industrial unions are proposed to organize all the workers in: (i) A specific company. (ii) The United States. (iii) Particular skill or the craft. (iv) Particular occupation. (v) Specific ind

    		•