--%>
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 : A legal price floor and revenues Assume

    Assume that the U.S. wheat market is firstly into equilibrium on S0D0. Now assume the government institutes a legal price floor at P3 per bushel of wheat. When the government does nothing else, one outcome will be such

    		•
  • Q : Problem concerning Exploitation I have

    I have a problem in economics on Problem concerning Exploitation. Please help me in the given question. Whenever resource suppliers are salaried less than the values of their marginal products [or VMPs], then they are stated to be: (i) Monopsonistic.

    		•
  • Q : Decrease the burden of sales tax on low

    To decrease the burden of a sales tax upon low income households, in that case: (i) goods along with high income elasticities should be taxed. (ii) goods along with low income elasticities should be taxed. (iii) goods along with high income elasticities must be exempt

    		•
  • Q : Potential advantage of Proprietorships

    Beth and Anna each own a florist shop. After many years of rivalry, they make a decision to team up and make a partnership. The potential advantage of such a union would be that: (1) They can divide up duties and become more proficient. (2) Their partnership profits n

    		•
  • Q : Share of wages problem Can someone

    Can someone please help me in finding out the accurate answer from the following question. The elasticity of demand for the labor tends to rise as there are increases in the: (i) Amount of capital utilized in a production procedure. (ii) Rate of automation in industry

    		•
  • Q : Substitutes and Complements The

    The increase in the price of a good generally also rises the: (i) Demands for its substitutes. (ii) Supply of its complements. (iii) Purchasing power of the consumer incomes. (iv) Demand for its complements. Can someone please help

    		•
  • Q : Tendencies of price floors creating

    Price floors create tendencies for: (1) shortages since buyers demand more than firms produce. (2) lobbying through sellers for their elimination. (3) net increases within the satisfactions of consumers. (4) surpluses since firms creates more when hou

    		•
  • Q : Quantity demanded in Substitution

    I have a problem in economics on Quantity demanded in Substitution process. Please help me in the following question. The sales growth resultant from price cuts for a good reflects rises in: (i) Quantity demanded. (ii) Demand. (iii) Quantity supplied.

    		•
  • Q : Engage market power in price

    If this is possible, firms along with market power engage in price discrimination to: (i) defy civil rights legislation. (ii) help consumers. (iii) help the community. (iv) increase their profits. (v) reduce production costs.

  • Q : Problem on labor monopsonist Can

    Can someone please help me in finding out the accurate answer from the following question. The labor monopsonist will hire labor up to the point where marginal: (i) Revenue product of the labor equivalents the wage. (ii) Resource c

    		•