--%>
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 : Correcting deflationary gap Describe

    Describe the role of given in correcting deflationary gap in an economy. A) Govt. ExpenditureB) Legal Reserve Ratio

    		•
  • Q : Product differentiation in market If

    If new soap operas that, although same to the previous ones, all are advertised as original and new, the TV networks are engaging within: (i) bait and switch. (ii) product differentiation. (iii) monopolistic competition. (iv) dynamic game theory. (v)

    		•
  • Q : Margin requirements for deflationary gap

    Elucidate the role of margin requirements for correcting deflationary gap.

    		•
  • Q : Problem on surplus inventories When the

    When the market price for soccer balls is above the intersection of supply and demand curves, then: (1) Shortages of soccer balls will be extensive. (2) Pressure will exist to raise the price of soccer balls. (3) Salaries paid people who make soccer balls are probable

    		•
  • Q : Minimizes economic losses by

    When it is feasible for total revenue to cover all variable costs, an unregulated monopoly which does not price discriminate maximizes economic profits or else minimizes losses through producing the r

    		•
  • Q : Post tax and post transfer income

    As measured through post tax and post transfer income patterns, from World War II, then the U.S. has created: (w) no progress in reducing the gap in between the rich and poor. (x) substantial progress in reducing the gap in between rich and poor. (y) moderate progress

    		•
  • Q : Long run equilibrium for purely

    When a purely competitive industry is into long run equilibrium, in that case for the typical firm: (a) P = FC = TC = MC = MR = AR = AC. (b) P = AR = MR = SRMC = SRAC = LRMC = LRAC. (c) pure economic profits reward especially effectiv

    		•
  • Q : Perfect price elasticity in the short

    In a purely competitive industry, it tends to be perfect price elasticity within the short run: (w) market demand curve. (x) market supply curve. (y) demand for the good by a single consumer. (z) demand curve facing a single firm.

    		•
  • Q : Exploitation and the Wage Rate Assume a

    Assume a neither firm possessing both the monopsony power as an employer and the market power in its output market, however which can neither wage discriminate nor price discriminate. In the equilibrium in its labor market for workers, of the given va

    		•
  • Q : How Accounting profits differ from

    Can someone please help me in finding out the accurate answer from the following question. The Accounting profits differ from economic profits in such a manner that: (1) Accounting profits take into account of opportunity costs, whereas economic profits take into acco

    		•