--%>
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 : Elasticity and Revenue At the point of

    At the point of unit elasticity beside the demand curve then a firm faces: (w) profits are always maximized. (x) total revenue is certainly at a maximum. (y) total costs are minimized. (z) All of the above. I need

    		•
  • Q : Labor markets profit maximization When,

    When, after hiring the very last worker, the organization’s profit is similar as it was before the last worker was hired, then the firm must: (1) Hire more workers to raise the profit. (2) Layoff some workers to raise the profit. (3) Not appoint any more workers

    		•
  • Q : Excess demand for commodity When do we

    When do we state that there is an excess demand for a commodity in the market?

    		•
  • Q : Reform or revision of the welfare system

    The most important reform / revision of the welfare system within the past half century occurred throughout the administration of President as: (1) Richard Nixon [1971]. (2) Jimmy Carter [1978]. (3) Ronald Reagan [1984]. (4) Bill Clinton [1996]. (5) G

    		•
  • Q : Economic profit of purely-competitive

    This purely-competitive lumber mill experiences on the average day is an: (w) economic profit of about $340. (x) economic loss of roughly $150. (y) accounting profit of less than $300. (z) accounting loss of more than $100.

    Q : Short-run supply curve of a purely

    Short-run supply curve of a purely competitive firm is the positively sloped segment of: (a) its long run sales revenue curve. (b) its marginal fixed cost curve. (c) its average profits curve. (d) its average total cost curve. (e) its MC curve above t

    		•
  • Q : Division of Labor I have a problem in

    I have a problem in economics on Division of Labor. Please help me in determining the right answer from the following question. Shannon brewing an espresso drinks whereas Kelly bakes the croissants at their coffee shop are an illustration of: (i) Comp

    		•
  • Q : Describe price elasticity of demand

    Price elasticity of demand: The Price elasticity of demand refers to the degree of responsiveness of the quantity demanded to modifications in price. Ed = (ΔQ/Δ P) x (P/Q)

    		•
  • Q : Problem of asymmetric information

    Provide the solution of this question. The problem of asymmetric information is that: A) neither health care buyers nor providers are well-informed. B) health care providers are well-informed, but buyers are not. C) the outcomes of many complex medical procedures cann

    		•
  • Q : Importance of Store of Value function

    Importance of Store of Value function of money: People save a portion of their earnings for utilization in future. But in what form? Money fulfills this requirement of the people. Money as a store of value signifies that money is an asset and can be s

    		•