--%>

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 : Rising the level of utility Kelly

    Kelly spends his whole food budget on steak and doughnuts, and could trade 2 pounds of steak for 4 doughnuts devoid of changing his level of satisfaction. When the price of doughnuts is 50 cents and steak is $2.00 per pound, Kelly will most likely adjust by: (i) Incre

  • Q : International federal or agreements and

    Consider goods for that various people are willing and capable to pay much more than the costs of production therefore widespread shortages exist. International federal or agreements, state and local laws as well as regulations are probably key factor

  • Q : Maximize profit by monopolistic

    Monopolistic competitors maximize profit through: (w) adjusting output at a given price. (x) adjusting price for a given output. (y) adjusting output and price. (z) cheating. Can someone explain/help me with best s

  • Q : Effect on total revenue by raises price

    A price raise from $6 to $8 would effect in: (1) a decrease in total revenue. (2) an increase in total revenue. (3) no change in total revenue. (4) consumers buying more pizza. (5) pizza parlors selling more pizza.

  • Q : Constant price elasticities in

    Perfectly inelastic demand curves include constant price elasticities equivalent to zero as well as: (i) cannot exist within the real world across the full range of possible prices. (ii) happen more often than any other type. (iii) are horizontal line

  • Q : Short run for production I have a

    I have a problem in economics on Short run for production. Please help me in the following question. In short run for production: (1) Both variable and fixed costs exist. (2) Productive capacity might be adjusted. (3) Unprofitable firms shut down. (4) No fresh workers

  • Q : Potential inefficiencies and inequities

    Whenever someone paying for the service can’t completely monitor the behavior or aims of the person offering the service, there are potential inequities and inefficiencies caused by the: (1) Moral hazard. (2) Adverse selection. (3) Utilitarianism. (4) Principal-

  • Q : Define normal goods Normal goods:

    Normal goods: Normal goods are such goods whose demand increases with the increase in income of consumer.

  • Q : Problem on implicit belief in a moral

    Can someone please help me in finding out the accurate answer from the following question. Assume that when faced with the Faustian option [that is, a deal with the devil] of torturing an naive child in the interest of securing world peace and an end to global hunger,

  • Q : Cartel Select the right answer of the

    Select the right answer of the question. We would expect a cartel to achieve: A) both allocative efficiency and productive efficiency. B) allocative efficiency, but not productive efficiency. C) productive efficiency, but not allocative efficiency. D) neither allocati