--%>
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 : Derived Demand for Labor in competition

    The faddish popularity of Atkins and South Beach diets both, and both of that advise dieters to eat more meat and to decrease the intake of starchy carbohydrates, most likely decreased incomes most sharply for: (1) grocery store clerks. (2) cattle ran

    		•
  • Q : Increase total revenue by increasing

    A monopolist can raise total revenue by increasing output when: (w) demand is elastic. (x) demand is inelastic. (y) demand is unitarily elastic. (z) supply is perfectly elastic. Can someone explain

    		•
  • Q : Value of the marginal product of labor

    The Profit-maximizing firms which operate in the competitive resource and output markets adjust the labor inputs till the wage rate equivalents the: (i) Average revenue from the output. (ii) Output price equivalents the average variable cost. (iii) Marginal utility of

    		•
  • Q : Effect of economic prosperity on demand

    Precisely predicting the effect of economic prosperity upon the demand for mass transit would be excellent facilitated by a good calculates approximately of the: (w) slope of the demand curve for mass transit. (x) price elasticity of

    		•
  • Q : Reduction in demand of Complementary

    Mold that damaged the hamburger crop following a flood would be most probable to decrease the demands for: (i) fried chicken with gravy and mashed potatoes. (ii) Soda pop and bottled water. (iii) Carrots, cucumbers and egg plant. (iv) Ketchup and mustard. (v) Sushi an

    		•
  • Q : Loss in social welfare with quantity

    When pharmaceutical manufacturers conspire to generate only Q1 penicillin, in that case the: (i) purely-competitive firms which produced penicillin would experience economic losses. (ii) resulting excessive antibiotic treatments would produce strains of dru

    		•
  • Q : Elucidate GNI per capita Elucidate GNI

    Elucidate GNI per capita?

    		•
  • Q : Hire labor at any amount in purely

    When this purely competitive firm can hire any amount of labor at pre hour wage of $9 per worker, in this given figure, as it will hire: (1) L2 workers. (2) L3 workers. (3) L4 workers. (4) L5 workers. (5) L<

    		•
  • Q : Monopsony power without wage

    Can someone help me in finding out the right answer from the given options. The Minimum wage laws are most probable to increase the equilibrium employment when a firm has been exercising: (1) Monopoly power and price discrimination. (2) Employee choice in markets for

    		•
  • Q : Positive economic profit and accounting

    Purely competitive equilibrium, in long-run firms normally experience positive accounting profit and economic profit which is: (w) also positive, but smaller. (x) zero. (y) negative, but barely that why. (z) either positive, zero, or negative.