--%>
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 : Income elasticity and inferior goods

    Raises in real income that causes the demands for: (i) inferior goods to shift upward and to the left. (ii) normal goods to shift upward and to the right. (iii) substitute goods to shift upward and to the right. (iv) complementary goods to decline mor

    		•
  • Q : Earn high incomes in purely competitive

    Into a purely competitive market economy, people along with rare and valuable talents would earn high incomes due to: (w) monopsonistic exploitation. (x) interest maximization. (y) economic rent. (z) transfer payments.

    Q : Generate economic profit by a firm

    A firm is most certain to be capable to generate an economic profit when: (1) this is a monopoly. (2) entry within its industry in the short run is prevented through barriers to entry. (3) its marginal costs are less than the marginal costs of its com

    		•
  • Q : Problem on long run competitive

    The technology is such that LAC is minimized at firm’s output equivalent to 10 and minimum LAC is Rs. 15. Assume that the demand schedule for the product is given as shown:

    Q : Problem on Labor Union Goals Can

    Can someone please help me in finding out the accurate answer from the following question. The higher union wages would be least likely to pursue: (1) Higher union initiation fees. (2) Mandatory retirement programs

    		•
  • Q : Maximizes profit at total economic of

    When the wholesale price P = $8 per bushel of peaches, it purely competitive peach orchard maximizes profit via producing ___ bushel of peaches at a total economic of profit or loss of $___. (i) zero; loss; -$4,000. (

    		•
  • Q : Long run entry of supply curve When the

    When the price for cranberries is primarily P1, in that case in the long run: (w) firms will neither enter nor exit this industry. (x) entry of firms will move curve supply curve A to the right. (y) exit of firms will move

    		•
  • Q : Analytic Time in economic theory of

    In economic theory of production: (1) Average fixed costs equally drop as the capacity of firm rises. (2) Technology can be varied wholly. (3) The choices available to firm raise as longer periods are considered. (4) Firms which do not cover all the h

    		•
  • Q : Income elasticity of demand The income

    The income elasticity of demand for mass transit of 0.6 signifies that the demand for mass transit: (1) Is a requirement. (2) Is a luxury. (3) Will increase at a slower rate than income. (4) Will drop/fall when personal incomes increases average.

    		•
  • Q : Define multiplier Multiplier : It is

    Multiplier: It is the number by which change in investment should be multiple in order to find out the resultant change in income and output.

    		•