--%>
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 : Reform National Welfare Before the

    Before the national welfare reform of 1996s, where Aid to Families with Dependent Children [AFDC]: (w) was the principal government program intended to alleviate poverty. (x) was exempt from any form of taxation. (y) generated pressur

    		•
  • Q : Fundamental welfare benefits by

    The incentive to work and earn income is possible to be greatest when the fundamental welfare benefit is ____ and the fundamental welfare benefit is reduced through ____ that the person earns: (w) high, the amount (x) low, the amount

    		•
  • Q : Relative Prices of household

    When a household consumes just x and y, a higher price of y and the stable price of x will make: (i) All goods cheaper relative to the x. (ii) x cheaper relative to the y. (iii) Real family income grow. (iv) Substitution against x the more desirable.

    Q : Demand of goods people willing to buy

    The amount of goods which people are willing and capable to buy is termed as their: (i) Desires. (ii) Demands. (iii) Requirements. (iv) Needs. (v) Wants. Can someone please help me in finding out the accurate answe

    		•
  • 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 : Positively slope of short-run market

    Within purely competitive industries: (w) short-run market supply curves are positively sloped. (x) long-run market supply curves are positively sloped. (y) short-run supply is more elastic than long-run supply. (z) economic profit exceeds accounting

    		•
  • Q : Monopolies over brand name products of

    Several firms have monopolies over brand name products, although face competition from: (w) international cartels. (x) oligopolistic rivals. (y) producers of close substitutes for their products. (z) intra-firm rivalry.

    Q : What is Oligopoly Oligopoly : This is a

    Oligopoly: This is a form of the market in which there are some big sellers of a commodity and a big number of buyers. There is a high degree of interdependence between the sellers regarding their price and output policy.

    		•
  • Q : Economic profits to entrepreneurs

    Economic profits are NOT recompenses to entrepreneurs who: (1) endure business uncertainty. (2) provide society along with economic capital. (3) innovate new goods and technologies. (4) exercise monopoly power or monopsony power. (5)

    		•
  • Q : Avoid losses incurred from predatory

    To drive rivals by a market but ignore losses incurred by predatory pricing, a firm could: (w) cut price below costs but continue to sell similar amount of output. (x) set price equal to average costs, removing incentives for other firms to reenter th

    		•