--%>
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 : Screening-derived demand Can someone

    Can someone please help me in finding out the accurate answer from the following question. Boris, who functions a local landscaping company, needs each of the potential employee to lift a 200 pound tree before being hired full-time. This need is an illustration of: (1

    		•
  • Q : Words of Economic Rent about David

    David Ricardo: (w) was the originator of the theory of pure economic rent onto land. (x) believed that land rent was earned since land would not be available at a zero price. (y) observed that marginal land which is just barely helpful commands positi

    		•
  • Q : Product differentiation in gain

    Monopolistic competitors: (1) base decisions on the anticipated reactions of their many individual competitors. (2) can easily enter but not exit industries. (3) may sometimes act like monopolists and gain economic profits in the short run because of

    		•
  • Q : Labor union and an unregulated public

    I have a problem in economics on Labor union and an unregulated public utility. Please help me in the following question. While comparing an influential labor union and an unregulated public utility firm like cable TV, both might: (1) Be considered as the monopolists.

    		•
  • Q : Problem on numbers of Buyers Even when

    Even when each household’s demand curve didn’t shift, the market demand for the butter would increase if there were a raise in: (1) House-hold income. (2) People’s preferences for the butter. (3) Population. (4) Price of margarine.

    		•
  • Q : Determine average production cost by an

    When Robomatic Corporation maximizes profit in its production of RoboMaids, its average production cost per robot will be roughly: (1) $3,000 per robot. (2) $5,000 per robot. (3) $7,000 per robot. (4) $9,000 per robot. (5) $11,000 per robot.

  • Q : Define saving function Saving function

    Saving function: The relationship among saving and income is termed as saving function.

    		•
  • Q : Non discriminating firm-monopsony power

    The non discriminating firm with monopsony power in labor market confronts the: (1) Wage rate which consistently surpasses the marginal revenue. (2) MRP less than w. (3) MFC which surpasses w. (4) Monopolistic seller of firm's output. (5) MRP more tha

    		•
  • Q : Single monopoly in market A monopoly is

    A monopoly is a single: (w) seller of differentiated products. (x) producer of a good for that there are no close substitutes. (y) producer of a good for that there are several substitutes. (z) buyer of products into the market.

    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

    		•