--%>
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 : Marginal costs and marginal revenue in

    Can someone help me to solve this problem as given below: A profit maximizing firm will generate where: (w) MR > MC. (x) MC > MR. (y) MR = MC. (z) ATC > P > MC. How can I solve my

  • Q : Financial Asset of Annual Income

    Perpetuity is a: (w) life insurance policy which matures upon retirement. (x) nondepreciable piece of capital. (y) financial asset which pays its owner an annual income forever. (z) pyramid scheme as a chain letter.

    Q : Total revenue exceed total variable

    A firm within a purely competitive industry: (w) will produce only as long as its marginal revenue is greater than its marginal cost. (x) decides what level of output to produce based upon an analysis of total revenues and total costs. (y) produces th

    		•
  • Q : Measurement of below poverty line Below

    Below the poverty line the proportion of the U.S. population is: (w) rises with upturns of the business cycle. (x) has declined, though somewhat erratically, over the past 50 years. (y) has been virtually eliminated by a vigorous “War on Poverty

    		•
  • Q : Bonds and Interest Rates in Long-Term

    When the interest rate increases, in that case the price of a long-term bond: (w) rises faster than a perpetuity bond. (x) falls. (y) does not change. (z) appreciates relatively less than a short term bond. Hello g

    		•
  • Q : Area above price line and below

    I have a problem in economics on Area above price line and below individual demand curve. Please help me in the following question. When a single price is charged for each and every unit of a good, then the area above the price line however beneath an individual&rsquo

    		•
  • Q : Depended price on present value The

    The prospects for getting rich by buying assets at prices substantially below their present values are dampened by the: (w) special advantages you have in securing investment information. (x) lack of competition for information regarding profit opport

    		•
  • Q : Rises price elasticity of demand for a

    The price elasticity of demand for a good will tend to rise as the: (i) number of obtainable substitutes increases. (ii) consumer income level increases. (iii) good is a less significant budget item. (iv) time permitted for response decreases. (v) ela

    		•
  • Q : Proprietorships and Partnerships The

    The advantage of a partnership is: (i) Its ease of organization as compared to the corporation. (ii) Its limited liability. (iii) Its capability to outlive the partner’s death. (iv) The lack of divergences. C

    		•
  • Q : Example of demand curve shifts upward

    Can someone help me in finding out the precise answer from the given options. When consumers become willing and capable to purchase more of a good at each and every possible price, then the: (i) Demand curve shifts up-ward and to right. (ii) Quantity demanded increase

    		•