--%>
Assignment Help - homework help

Market demand function

The market  for good X consists  of 2 consumers. consumer  1',s demand  for good X is:

X1 :  15 - 3Px + 0.5PY + .02I1

I1 and I2 are incomes of consumer 1 and 2, respectively.  Px and Py are the prices of goods X and Y, respectively.

a. What is the equation  for the market  demand  function  for X? Graph the two individual demand curves and the market  demand  curve  for the case which  I1 : $2000, I2: $3000, and Py:$ 10.

b. Suppose Px rises  from $5 to $5.05. What is the market price elasticity of demand?

c. Suppose  income  is redistributed so that each consumer  has $2500. If Px: 5 and Py: 10, how much does the quantity of X demanded  change because  of the redistribution?

E

Expert

Verified

a) Equation for consumer 1: X1= 15-3Px + 0.5 Py +0.2I1

Equation for consumer2:  X2= 15-3Px + 0.5 Py + 0.2 I2

Market demand curve is  calculated by aggregating the individual demand curves.

So, By adding the two demand curves we get:  X*=30-6Px +Py + 0.2I1+ 0.2I2

Put the value of Py and I1 and I2.

X*= 30 -6Px + 10 + 0.2(2000) + 0.2(3000) is the market demand curve for the good X

Individual Demand curves will be:

X1= 15-3Px +5 + 400 or X1= 420-3Px
X2= 15-3Px+ 5 +600 or X2= 620-3Px
X*= 30-6Px + 10+ 1000 or X*= 1040-6Px

b. For market   price  elasticity we use market demand curve:

X*= 1040- 6Px

Elasticity:
dx/dp(p/x)=
dx/dp= -6
-6(5/1010)=-0.029

P= original price-which is 5(that is price before the price change)
X= orginal  quantity: quantity demanded at original price of 5= 1040-6(5)=1010
And dx/dP=slope of market demand curve

c. Now each consumer has 2500. So, Put the values In the market demand curve:

X*= 2040-6Px
If Px=6
Then X* demanded will be 2004
And Earlier it would be: X*= 1040-36= 1004
So the change in quantity demanded will be: 1000

   Related Questions in Microeconomics

  • Q : Cost structure characteristic in purely

    When Cling Peach Orchards has a cost structure characteristic of peach orchards into this purely competitive industry, when the long run new competitors would most likely enter the market providing the wholesale price per bushel of peaches exceeded: (

    		•
  • Q : Elasticity and demand of monopolist

    When a monopolist produces output where demand is unitarily elastic, in that case marginal revenue equals: (1) price. (2) infinity. (3) negative infinity. (4) one. (5) zero. I need a good answer on the topic of

  • Q : Proportion of total costs I have a

    I have a problem in economics on Proportion of total costs. Please help me in the following question. Demand for the labor is more elastic as the: (1) Bigger labor costs is as proportion of net costs. (2) Shorter the time-interval considered. (3) Bigg

    		•
  • Q : Demand for Complementary Goods Can

    Can someone help me in finding out the right answer from the given options. Reductions in the price of tea are most probable to raise the demands for: (i) Lemons, ice cubes and sugar. (ii) Cola, coffee and hot cocoa. (iii) Mint juleps, Daiquiris and moonshine. (iv) Va

    		•
  • Q : Marginal productivity theory about

    John Bates Clark's marginal productivity theory gives details that the marginal productivity of resources finds out: (w) the true value of human life. (x) an equitable distribution of tax burdens. (y) the income distr

    		•
  • Q : Bilateral Monopoly problem The

    The bilateral monopoly is in operation when: (i) Firm is the only employer of the certain labor force and a union is just the supplier of the labor for that organization. (ii) The firm is the mere producer of the two complementary goods. (iii) The monopolist sells a g

    		•
  • Q : Create demand and supply tables Suppose

    Suppose the demand and supply for milk is described by the following equations: QD =  600 - 100P;  QS = - 150 + 150P, where P is price in dollars, QD is quantity de

    		•
  • Q : Calculating economic profit for first

    Assume that the banker is employed at an annual salary of $60,000. She as well has financial assets worth of $40,000 which earns $1,500 per year in interest. She too owns a commercial building that she rents out for $20,000 per year. Now assume that she quits this job

    		•
  • Q : College loan-Rational Ignorance Assume

    Assume that a student takes out a college loan which needs 12% annual interest, however later learns that his aunt makes loans to the family members at 5% interest. The student has suffered from the problem termed as: (1) Rational ignorance. (2) Blind indifference. (3

    		•
  • Q : Define Capital expenditure Capital

    Capital expenditure: Any expenditure which will lead to formation of an asset or reduction in liability. This is financed out of capital receipts of government. Illustrations: Expenses on construction of roads, canals, bridges, grant of loans by the c

    		•