--%>
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 : Screening-derived demand Can someone

    Can someone please help me in finding out the accurate answer from the following question. Boris, who functions a local landscaping company, needs each of the potential employee to lift a 200 pound tree before being hired full-time. This need is an illustration of: (1

    		•
  • Q : Importance of study of the model of

    The study of the model of pure competition is very significant since this: (w) explains the behavior of most U.S. firms. (x) gives the underpinnings for supply and demand. (y) helps explain why government economic policy is essential. (z) gives a rati

    		•
  • Q : Define price floor Price floor : Price

    Price floor: Price floor refers to the lowest amount price fixed by the government over the market determined price and hence the producers of the necessary items such as wheat, rice and so on might not experience losses.

    		•
  • Q : Price taker in the context of a firm

    What is meant by the word price taker in the context of a firm? Answer: It means that firm does not contain any control over the price and it has to pursue that pri

    		•
  • Q : What is Budget line Budget line : This

    Budget line: This refers to all combinations of goods that a consumer can purchase with his whole income and price of two goods.

    		•
  • Q : Pure competition in product and

    When no goods generate external costs or benefits within their consumption or production and when the income distribution is deemed acceptable, in that case economic efficiency is promoted through: (w) government inte

    		•
  • Q : Amount of Tax of Initial Demand Assume

    Assume that D0 is the initial demand curve for land in this demonstrated figure, and a land tax at a rate of t is imposed. Trying by the landlord to pass the tax forward to the renter, which will cause the: (i) supply curve of housing to sh

    		•
  • Q : Long-run purely competitive industry

    For a purely competitive industry in the long-run: (w) neither net entry nor net exit of firms will arise. (x) firms will experience significant economies of scale. (y) the typical firm’s economic profit will exceed its accounting profit. (z) th

    		•
  • Q : Pure competition in modern U.S. economy

    Within the modern U.S. economy, there pure competition is: (w) characteristic of all resource markets. (x) rare in product markets. (y) most common for public utilities. (z) strictly regulated throguh government. I

    		•
  • Q : Positively sloped demand curve of

    When your income is positively and closely tied to the price of a specific product, a raise in its price might cause: (1) The income effect which, in severe conditions, yields a positively sloped demand curve. (2) You to go bankrupt. (3) The powerful positive substitu

    		•