--%>
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 : Horizontal demand curve facing purely

    The demand curve facing a purely competitive firm is: (w) horizontal. (x) vertical. (y) downward sloping. (z) the horizontal summation of individual demand curves. Can someone explain/help me with best solution abo

    		•
  • Q : Selling footballers-the economic

    State economic arguments on whether a football club must sell a significant player?

    		•
  • Q : Price elasticity of supply problem The

    The price elasticity of supply generally evaluates the ratio of relative: (i) Gain to the amounts firms supply at different prices. (ii) Price increase need to induce a firm to raise output. (iii) Change in the quantity supplied to a associative chang

    		•
  • Q : Variation in demand curve with price

    The demand curve along with price elasticity which definitely varies along the curve is within: (w) Panel A. (x) Panel B. (y) Panel C. (z) Panel D.

    Q : Absolute value of the proportional

    The absolute value of proportional change within labor hired divided through a proportional change within the wage rate is termed as the: (w) income/substitution coefficient. (x) employment wage response. (y) labor force participation rate. (z) elasti

    		•
  • Q : Monetary liability All currency issued

    All currency issued by central bank is its monetary liability. Explain how? Answer: The Central Bank is grateful to back the currency with assets of equivalent valu

    		•
  • Q : Output and equilibrium price Hybrid

    Hybrid Roses is the merely florist in 60 miles of Presidio, Texas. Often, lots of Texans are romantics at heart. Total cost curve of Hybrid is below the demand curve this faces. At its output and equilibrium price, Hybrid will produce

    		•
  • Q : Constant price elasticity plausible for

    Constant price elasticity equivalent to one for socket sets would be mainly plausible for demand curve as: (1) D1D1. (2) D2D2.  (3) D3D3. (4) D4D4. (5) D

    		•
  • Q : Problem on public demand In the year of

    In the year of 1996 McDonald's introduced its Arch Deluxe hamburger, which failed to catch on with the public and was subsequently dropped from the menu. This failure illustrates the idea of: A) consumer sovereignty. B) technological change. C) downsloping demand

    		•
  • Q : Shifting supply of curve by entry of

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

    		•