--%>
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 : Instance of Implicit Costs Can someone

    Can someone help me in finding out the most right answer from the given options. The instance of an implicit cost would be: (i) Salaries paid to the employees. (ii) Payments for repairs on the company-owned machine. (iii) Rent paid on building company utilizations. (i

    		•
  • Q : Creating externalities to spread costs

    In efforts to offset specific failures of the private sector, government policy within a mixed-capitalist economy would be least reasonably intended at an objective of: (1) creating externalities to spread the costs of various activities across all me

    		•
  • Q : Raise current consumption by rising in

    When interest rates rise, in that case the opportunity costs of: (1) current consumption rise. (2) future consumption rise. (3) current investment decline. (4) government budget deficits decline. (5) saving grows proportionally.

    		•
  • 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 : Relationship between APP-MPP If APP is

    If APP is at its maximum, then what is the relationship among MPP and APP? Answer: MPP = APP

    		•
  • Q : Reading Production Possibilities

    I have a problem in economics on reading the Production Possibilities Frontiers graph. Please help me in determining the right answer from the following question. The graph below depicts the mythical country of the Sandwichia’s:

    Q : Business strategies in market Assume

    Assume that technological advances considerably lower costs for Honda. Hence which of the given statements is true: (w) when Honda lowers prices, rivals will rightfully accuse the firm of predatory pricing (x) when Honda raises prices, rivals will rightfully accuse th

    		•
  • Q : Labor-Leisure Tradeoffs When leisure is

    When leisure is a normal good, then the demand for leisure: (i) Differs directly with the income. (ii) Has declined sharply as World War II. (iii) Is positively associated to the average age of population. (iii) Shifts left-ward as an outcome of technological advances

    		•
  • Q : Uncertainty and Decision-making I have

    I have a problem in economics on Uncertainty and Decision-making. Please help me in the following question. The error of omission would be: (i) The failure of an individual to invest in Microsoft 20 years ago. (ii) Individual cheating on a test. (iii)

    		•
  • Q : Profit-maximizing output to maximizes

    HoloIMAGine has patented a holographic technology which creates 3-D photography obtainable to consumers. So HoloIMAGine’s: (w) lowest possible average total cost arises at precisely the output where profit is maximized. (x) market supply curve is the same to its

    		•