--%>
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 : Unitarily elasticity in supply curve At

    At point b, in demonstrated figure the supply curve into this graph is: (w) perfectly elastic. (x) elastic, but not perfectly that why. (y) unitarily elastic. (z) inelastic.

    Q : Definition of law of demand Definition

    Definition of law of demand: It is the claim that, other things equivalent, the quantity demanded of a good drops/falls whenever the price of the good increases.

    		•
  • Q : National Income in Equality Standard As

    As per the equality standard of income distribution: (w) people should be paid according to their needs for income. (x) income should be distributed to resource owners. (y) justice requires national income to be divided equally. (z) people should be p

    		•
  • Q : Problem regarding rise in quantity

    Can someone please help me in finding out the accurate answer from the following question. The raise in the quantity supplied of frozen vegetarian lasagna would be most probable to outcome from raise in the: (i) cost of ingredients in the vegetarian lasagna. (ii) Numb

    		•
  • Q : When is demand more elastic at a price

    Along this demonstrated in below demand curve for DVD games, demand is more elastic at a price of: (w) $10. (x) $6. (y) $1. (z) zero.

    Q : Trade Restrictions of import and export

    Quotas that restricted U.S. imports of foreign steel between 2001 and 2004 because of the: (w) prices paid by U.S. car buyers to rise. (x) price of gasoline to rise sharply. (y) profits of U.S. steelmakers to drop. (z) quantities of European imports t

    		•
  • Q : Income distribution line in Lorenz curve

    When line 0C0' shows the 1975 U.S. income distribution, in that case the 2005 income distribution would most likely be most probable: (1) line 0A0'. (2) line 0B0'. (3) line 0C0'. (4) line 0D0'. (5) line 0E0'.

  • Q : Price hike in short run I have a

    I have a problem in economics on Price hike in short run. Please help me in the following question. In short run, the demand curve for the potatoes will not be influenced by price hikes for: (i) Potatoes. (ii) Bread. (iii) Rice. (iv) Steak.

    Q : Monopsonistic labor market-wage

    In the monopsonistic labor market in which wage discrimination is not possible, the raise in the minimum wage: (i) Essentially outcomes in less employment and higher wages. (ii) Might result in both the higher level of employment and the higher wage rate. (iii) Unifor

    		•
  • Q : Production-Altering the chemical and

    Can someone please help me in finding out the accurate answer from the following question. The production which modifies the chemical or physical structures of a good produces utilities of: (1) Substance. (2) Place and time. (3) Form. (4) Possession.

    		•