--%>
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 : Signals for sellers Can someone help me

    Can someone help me in finding out the right answer from the given options. The signals for sellers to lower the market price comprise: (i) Fast depletion of goods from the retail store shelves. (ii) Producers encompass more orders than they can hold.

    		•
  • Q : Economically inefficient level of output

    A monopolist produces an economically inefficient level of output since: (i) the difference among marginal revenue [MR] and marginal costs [marginal costs [MC] is maximized. (ii) P > average total costs [ATC], therefore MSB < MSC. (iii) all cons

    		•
  • Q : Market interest rate at break-even

    When land that rents for $100,000 yearly can be bought for $800,000 now, it will be a break-even investment when the market interest rate is: (i) 6%. (ii) 10%. (iii) 12.5%. (iv) 15%. (v) 8%. Can anybody suggest me the proper explan

    		•
  • Q : Output level on marginal revenue and

    When the firm produced at output level q2, this produced where: (w) MR = MC. (x) MR > MC. (y) MR < MC. (z) P < MC.

    Q : Annual total costs When Nostalgia

    When Nostalgia Corporation maximizes profit in its production of Silver Screen DVDs, in that case its annual total costs will be around: (i) $45 million. (ii) $65 million. (iii) $85 million. (iv) $105 million. (v) $125 million. <

    		•
  • Q : Income rate variation in Loren curve

    When you were unconcerned about the welfare of other people and your income rated you onto the top two percent of the population, then you would be happiest while the Lorenz curve for your country resembled as: (1) li

    		•
  • Q : Relative Prices of household

    When a household consumes just x and y, a higher price of y and the stable price of x will make: (i) All goods cheaper relative to the x. (ii) x cheaper relative to the y. (iii) Real family income grow. (iv) Substitution against x the more desirable.

    Q : Responding higher prices for heating

    Can someone help me in finding out the right answer from the given options. Canadians would ultimately be likely to respond to higher prices for heating oil and natural gas through (i) Turning up their electric blankets and insulating their houses more carefully. (ii)

    		•
  • Q : Different forms of capital account

    Different forms of capital account transactions: A) Private Transactions: There are transactions which affect the liabilities and assets of individuals.

    Q : Normal profit Normal profit signifies

    Normal profit signifies zero economic profit. Explain why?

    		•