--%>
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 : Quantity Equilibrium I have the

    I have the quantity functions of demand and supply for two different goods, and I have to find the equilibrium of both the goods. Would I make all four functions equal to each other to find the equilibrium for the two goods? Or am I supposed to do something else?

    		•
  • Q : Voluntary verses Involuntary Poverty

    When physically and mentally capable individuals who are born in impoverished families fail to work after they develop up but since they can rely on charity, in that case they are experiencing: (1) involuntary poverty. (2) relative poverty. (3) a vicious cycle of pove

    		•
  • Q : Spread of wage information The

    The Employers frequently discourage the spread of wage information since they fear that: (i) Lower salaried workers might use the information to negotiate the raises. (ii) Firms honor employee’s privacy only when secrecy is reciprocated. (iii) Unions try to orga

    		•
  • Q : Tax on a good tends to make The tax on

    The tax on a good tends to make: (i) Inflationary pressure the govt. can disperse by cutting its spending. (ii) The wedge among prices buyers pay and the prices sellers obtain. (iii) Rises in supply from the viewpoint of buyers. (iv) More quick transa

    		•
  • Q : Shifting of labor demand for Labor The

    The labor demand will shift due to the modifications in all of the given except: (1) Prices of other resources. (2) Prices of the output. (3) MPP (4) Salaries. Can someone please help me in finding out the accurate answer from the

    		•
  • Q : Law of Demand in respect to relative

    I have a problem in economics on Law of Demand in respect to relative price. Please help me in the following question. The law of demand defines that as: (1) Absolute prices rise, quantity demanded raises. (2) Relative prices raise, quantity demanded

    		•
  • Q : Exit industry in long run at wholesale

    This purely competitive peach orchard would most likely exit this industry within the long run when the wholesale price per bushel of peaches fell below: (i) $9.00 per bushel of peaches. (ii) $10.00 per bushel of peaches. (iii) $11.00 per bushel of pe

    		•
  • Q : A monopolist in market power A

    A monopolist: (w) is a price taker in the sale of its product. (x) can charge any price this wishes without reducing profit. (y) is not a price taker into the sale of its product. (z) may or may not be a price taker within the sale of its product.

    		•
  • Q : Production in a competitive market

    Production within a competitive market system tends to be: (1) a process that exploits labor to the maximum. (2) geared to respond to the whims of central planners. (3) relatively efficient and low cost. (4) highly automated because labor costs more t

    		•
  • Q : Produce output by zero marginal reveune

    When LoCalLoCarbo, the favorite corporation of fad dieters,in that case produces output q* [that where is marginal revenue is zero] as: (1) LoCalLoCarbo’s total revenue is at its highest possible level. (2) expanding output to q4 would cause tot

    		•