--%>
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 : Determine total revenue when prices fall

    As the price falls by P4 to P3 to P2 to P1 beside such demand curve for Pixie's cheesy fried grits, then total revenue: (w) always rises. (x) always falls. (y) rises then falls. (z) falls then rises.

    Q : Problem of dockworkers on hiking the pay

    When you were in the ski boat business, your net revenues from selling given numbers of boats would be least influenced by: (i) Govt. increasing fees for boat licenses. (ii) Rises in prices for jet skis. (iii) Pay hikes for dock-workers. (iv) Vacation

    		•
  • Q : Problem regarding analyzing persistent

    In analyzing persistent shortages within the U.S. market for adoptable children: (w) children are most reasonably considered investment goods. (x) children might reasonably be functioned as consumer goods. (y) lower prices charged adopting families would result within

    		•
  • Q : Problem on Closed Shops Can someone

    Can someone please help me in finding out the accurate answer from the following question. The firm which operates beneath a closed shop agreement: (i) Produces more gains than the firm beset through union strikes. (ii) Is less beneath organized labor's control than t

    		•
  • Q : Experiencing the Economies of Scope A

    A soft drink bottler which finds it cost efficient and gainful to deliver the chips and other snack foods all along with cola would be experiencing: (i) Economies of scope. (ii) Positive psychic income. (iii) Economies of scale. (iv) Economies of structure. (v) Diseco

    		•
  • Q : Experiencing the economies of Scale Let

    Let assume that an auto manufacturer which can produce 10 cars at an average cost of $8000 per car. When the manufacturer enlarges output to 100 cars, then the average cost of production falls to $5000 per car. This firm is experiencing the: (1) Raised demand. (2) Eco

    		•
  • Q : Occurrence of socially optimal

    The socially optimal production of penicillin arises while quantity: (a) Q1 is produced and sold at price P1. (b) Q1 is produced and sold at price P3. (c) Q2 is produced and sold at price P2<

    		•
  • Q : Comparative Advantage in opportunity

    The most important declines in opportunity costs of multiple goods for the consumers and greatest rises in the value of net production for all societies everywhere tend to be realized whenever production is organized in accord by: (1) The optimal clas

    		•
  • Q : Increment in quantity demanded by price

    A demand curve has a slope which would be expressed as like $5/ (1 extra ton demanded) when a: (w) 5 % price cut raises quantity demanded by 1 %. (x) $5 price cut increases quantity demanded by 2000 lbs. (y) $5 price hike boosts quantity supplied by 2

    		•
  • Q : Labor Unions and Union membership I

    I have a problem in economics on Labor Unions-Union membership. Please help me in the following question. The union membership is most widespread among: (1) White collar workers. (2) Managers and Supervisors. (3) Blue collar workers. (4) Young, upward

    		•