--%>
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 : Labor Union Goals-Minimum employment

    Can someone please help me in finding out the accurate answer from the following question. When a union achieved the maximum possible hourly wage: (i) All of the members would be pleased. (ii) Employment would as well be maximized. (iii) Employment would be at minimum

    		•
  • Q : Problem of Income Effects on paychecks

    I have a problem in economics on Income Effects on paychecks. Please help me in the following question. Whenever prices are increased and your paycheck does not alter the purchasing power of your pay refuses. This is an instance of the: (1) Substituti

    		•
  • Q : Equilibrium in long-run purely

    When a purely competitive industry is into long-run equilibrium: (i) firms try to maximize profit. (ii) P = ATC. (c) P = MC. (iii) economic profit is zero. (iv) All of the above. Can someone explai

    		•
  • Q : Utility function notes on separable

    notes on separable utility function in microeconomics

    		•
  • Q : Total revenue and profit Monsieur

    Monsieur Cournot has a monopoly on an artesian well from that flows tasty spring water along with medicinal properties. To ignore variable costs, he insists which customers bring their own pails as well as fill them personally. When C

    		•
  • Q : Critics of negative income tax Critics

    Critics of negative income tax (NIT) proposals most generally argue that: (a) economic rents should be taxed at a rate of 100%. (b) in-kind services should be above and beyond generous income assistance. (c) no NIT plan would be flexible enough to sol

    		•
  • Q : Needs of Wage Discrimination Can

    Can someone please help me in finding out the accurate answer from the following question. The Wage discrimination needs a firm to possess: (1) Monopsony power. (2) Monopoly power. (3) Oligopoly power. (4) None of these—no po

    		•
  • Q : Social opportunity cost of resource

    Economic rent is: (w) income received by a factor owner in excess of the social opportunity cost of supplying the resource. (x) the difference between a firm’s revenues and the sum of the fixed and variable costs of production. (y) a form of eco

    		•
  • Q : Marginal Utilities and Demand Prices

    Can someone help me in finding out the right answer from the given options. Rational individual consumers tend to purchase goods until the relative market prices for each and every goods purchased are proportional to all individuals: (i) Cost or benefit ratio. (ii) Op

    		•
  • Q : Inter-temporal Costs and Benefits

    Harvey is currently a Junior Analyst at a financial firm.  His annual salary is $30,000, and past experience leads him to believe that the real (inflation adjusted) value of his salary will remain at that level in the future.  (Assume he is paid at the end o

    		•