--%>
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 : Problem based on ATC-MR and MC If $4 is

    If $4 is Firm B's profit-maximizing price, its: A) ATC must be $4. B) MC must be $4. C) MR must be $4.  D) MC must be zero. Help me to get

    		•
  • Q : Surviving for maximum profits in

    Supposing that the competitive firms should seek the maximum profits to survive signifies that: (1) Firm do not make trial-and-error decisions. (2) Each and every firm always seeks the maximum gain and nothing else. (3) Competition is very profitable.

    		•
  • Q : Pepsi and Coke market Some of the

    Some of the consumers strongly prefer Pepsi and some strongly prefer Coke. Thus there is no single market for colas. This statement is true or false ? Explain.This statement is false. Although some people have strong preferences for a specific

    		•
  • Q : Question related to Gross domestic

    Proprietors' income $ 20, Compensation of employees 300, Consumption of fixed capital 15, Gross investment 80, Rents 10, Interest 20 ,Exports 30, Imports 50, Corporate profits 25, Taxes on production and imports 5 ,Net foreign factor income 0 ,Statistical discrepancy

    		•
  • Q : Expectations about future housing prices

    The market demand curve for latest houses would shift in response to a modification in: (i) Housing prices. (ii) The costs of lumber. (iii) Construction technology. (iv) Expectations regarding future housing prices.

    Q : Social opportunity cost of resource

    Economic rent is: (w) income received by a factor owner in excess of the social opportunity cost of supplying the resource. (x) the difference between a firm’s revenues and the sum of the fixed and variable costs of production. (y) a form of eco

    		•
  • Q : Standard of Income Distribution

    According to the requirements standard of income distribution: (w) marginal productivity is easily measured. (x) people’s needs are proportional to their marginal products. (y) income must be distributed in proportion to people’s needs. (z

    		•
  • Q : Social welfare function What do you

    What do you mean by a social welfare function? If you assume that such a function exists, what properties of social optima would be considered by you? Discuss such properties.

    		•
  • Q : Proportion of total costs I have a

    I have a problem in economics on Proportion of total costs. Please help me in the following question. Demand for the labor is more elastic as the: (1) Bigger labor costs is as proportion of net costs. (2) Shorter the time-interval considered. (3) Bigg

    		•
  • Q : Interdependent economy I am facing

    I am facing problem in this question. Help me in find out correct answer of this economic based question. Explain interdependent economy?  Illustrate it by using an input-output table and model.

    		•