--%>
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 : Constant price elasticities in

    Perfectly inelastic demand curves include constant price elasticities equivalent to zero as well as: (i) cannot exist within the real world across the full range of possible prices. (ii) happen more often than any other type. (iii) are horizontal line

    		•
  • Q : Increase output to increase profit When

    When the last unit produced and sold adds $100 to revenue of a firm and $75 to its costs, this will: (a) increase output to increase profit. (b) reduce output to increase profit. (c) maintain similar level of output to maximize profit. (d) shut down.

    Q : Breaks even point Hey friends I need

    Hey friends I need your help to solve out this problem regarding to a purely competitive firm breaks even while: (w) MR = MC (x) TR = TC (y) MC > MR (z) TR > TC. Can someone suggest me the ri

    		•
  • Q : Economy in Bulgaria What is the economy

    What is the economy in Bulgaria like?

    		•
  • Q : Problem on Minimum Wage Laws The

    The Minimum wage legislation is UNLIKELY to aid: (i) Skillful workers who compete with untrained workers. (ii) Untrained workers who don’t lose their jobs. (iii) Buyers of goods which are more capital intensive associative to the buyers of labor intensive goods.

    		•
  • Q : Minimum possible economic losses Hello

    Hello guys I want your advice. Please recommend some views for below illustrated figure of Economics problem that for this profit-maximizing pure competitor, area Pbgh signifies: (1) fixed cost (TFC). (2) average fixed cost (AFC). (3)

    		•
  • Q : Development and Distribution of Income

    Compared to other relatively prosperous developed nations, the United States: (w) has greater inequality in the distribution of its wealth and national income. (x) enjoys the lowest cost medical care and the best average public health. (y) has been the most aggressive

    		•
  • Q : Productivity related problem Other

    Other things equal, an improvement in productivity will: A) shift the aggregate demand curve to the left. B) shift the aggregate supply curve to the left. C) shift the aggregate supply curve to the right. D) increase the price level.

    		•
  • Q : Characteristics of Entrepreneurship The

    The Characteristics common to most of the successful entrepreneurs do not comprise: (1) Vision and timing. (2) Conviction and action. (iii) Luck and the bureaucratic one-upmanship. (iv) Determination and workaholics. Can someone pl

    		•
  • Q : Increasing-cost industries average

    Within increasing-cost industries average there are: (w) production costs fall as output increases. (x) production costs rise as the number of firms in the industry grows. (y) production costs rise when the number of firms into the industry falls. (z)

    		•