--%>
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 : Financial investments-traceable by most

    Most of the U.S. capital investment is traceable to the financial investments by households, that is one way that private individuals: (i) Turn into capitalists. (ii) Save. (iii) Evade taxes. (iv) Avoid the circular flow of resources and income.

    Q : Reasonable analytic objection to land

    A reasonable analytic objection to the argument which full taxation of economic rents would not hinder allocative efficiency is about: (w) reducing income streams by rents does reduce the incentive of the resource owner to acquire the transaction cost

    		•
  • Q : Demand curve when taxes shifted forward

    Taxes will be shifted forward completely when supply is positively sloped as well as the demand curve is, there contrary to economic reasoning: (1) perfectly inelastic. (2) perfectly elastic. (3) unitarily elastic. (4) flatter than supply.

  • Q : Question on elasticity of demand Select

    Select the right ans wer of the question. The demand for agricultural products is: A) relatively elastic with respect to price. B) relatively inelastic with respect to price. C) relatively elastic with respect to income. D) downward sloping to the individual farmer, b

    		•
  • Q : Define Inferior good Inferior good : It

    Inferior good: It is a good for which, other things equivalent, a rise in income leads to a reduction in demand.

    		•
  • Q : Problem on quantity of Whopper Slushees

    When Adam Smith’s invisible hand executed with no government intervention, this market would be in equilibrium and quantity of Whopper Slushees demanded the quantity supplied would be equivalent at: (i) Price P1. (ii) Quantity Q1. (iii) Price P3. (iv) Quantity Q

    		•
  • Q : Relationship between MPS and multiplier

    Relationship between MPS and multiplier:K=1/1-MPC = 1/MPS or inverse relationship between MPS and the size of multiplier.

    		•
  • Q : Problem regarding Craft Unions Can

    Can someone help me in finding out the right answer from the given options. The craft unions historically tried to systematize all the workers in: (1) A specific company, in spite of size. (2) The United States. (3) The specific broad industry. (4) Relatively highly s

    		•
  • Q : Price increases and price cut in

    Within the kinked-demand-curve model, there the firm faces: (w) a less elastic demand curve for price increases as well as a more elastic demand curve for price cuts. (x) a more elastic demand curve for price increases and a less elastic demand curve

    		•
  • Q : Market structure of unregulated monopoly

    An unregulated monopoly is a market structure: (w) which is especially inefficient when price discrimination is practiced. (x) inhabited by several firms, all selling identical goods. (y) composed of a single firm which controls the production and pri

    		•