--%>
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 : Produce a natural monopoly by market

    Market forces tend to produce a natural monopoly while: (1) decreasing costs are small relative to market demand for output. (2) diseconomies of scale are substantial at low levels of output. (3) economies of scale are substantial relative to market d

    		•
  • Q : Define cost Cost : This refers to the

    Cost: This refers to the money expenses acquired on the production of a specified amount of commodity.

    		•
  • Q : Product differentiation in market If

    If new soap operas that, although same to the previous ones, all are advertised as original and new, the TV networks are engaging within: (i) bait and switch. (ii) product differentiation. (iii) monopolistic competition. (iv) dynamic game theory. (v)

    		•
  • Q : Choosing a statistical Model Choosing a

    Choosing a statistical Model: A number of problems arise in determining whether the work is truly rigorous or not. It is important to determine whether the model chosen makes theoretical and intuitive sense. <

    		•
  • Q : Annual total revenue when profit

    When Nostalgia Corporation maximizes profit in its production of Silver Screen DVDs, in that case its annual total revenue will be roughly: (i) $40 million. (ii) $60 million. (iii) $80 million. (iv) $100 million. (v) $120 million.

    		•
  • Q : Various close substitutes and little

    The demand for an exact good tends to be relatively more price elastic when the good: (1) has various close substitutes and very little complements. (2) is taken as a necessity in place of a luxury. (3) is an inferior good. (4) is rel

    		•
  • Q : Scope of spiral and waterfall approach

    Explain the difference in changing the scope between a spiral approach and a waterfall approach?

    		•
  • Q : High prices elasticities of demand

    Taxing private auto travel as well as subsidizing mass transit will most effectively limit auto travel and raise the use of mass transit when the price elasticities of demand for auto travel: (1) and mass transit are low, and the cross-elasticity of d

    		•
  • Q : Zero economic profit in long run When

    When the best a monopolist can do to produce an economic profit of zero, this will: (w) shut down in the long run. (x) shut down in the short run. (y) remain in operation in the long run. (z) raise its price to raise profit.

    Q : Official unemployement Provide the

    Provide the solution of this question. To be officially unemployed a person must: A) be in the labor force. B) be 21 years of age or older. C) have just lost a job. D) be waiting to be called back from a layoff.

    		•