--%>
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 : Question on Federal Reserve Choose the

    Choose the right answer from following. How many members the Board of Governors of the Federal Reserve has ? A) 5 B) 7 C) 9  D) 14

    		•
  • Q : Demonstrate supply curve for price

    The quantity supplied is ever more sensitive as output increases, therefore the price elasticity of supply raises as the price raises for the supply curve demonstrated in: (w) Panel A. (x) Panel B. (y) Panel C. (z) Panel D.

  • Q : Problem on merging firms Elucidate how

    Elucidate how the efficiency might increase when two firms merge? Answer: If the two firms merge, their joined efficiency is expected to enhance owing to:

  • Q : Transformation of Predictable Income

    The transformation of predictable income streams within wealth is termed as: (i) monetization. (ii) financial arbitrage. (iii) capitalization. (iv) seignorage. (v) capital accumulation. How can I solve my E

    		•
  • Q : Consequence of vigorous price

    Product differentiation is least probable to be a consequence of: (i) model year changes for carmakers. (ii) corporate logos. (iii) advertising. (iv) vigorous price competition. (v) showy packaging. Can someone exp

    		•
  • Q : Expectations and Demand problem The

    The demand for durable consumer good tends to rise if: (1) Supply rises. (2) Aggregate expenses rise. (3) Consumers predict price hikes or scarcities in the future. (3) Consumers predict surpluses in future. Choose the precise answ

    		•
  • Q : Illustrates the initial point of

    RoboMatic’s RoboMaids have turn into the hottest innovation in consumer electronics since colour television. The initial point Robomatic requires to see in its quest to maximize profit is: (1) point e. (2) point f. (3) point g.

    		•
  • Q : Resource prices Refer to the following

    Refer to the following diagrams, in which AD1 and AS1 are the "before" curves and AD2 and AS2 are the "after" curves. Other things equal, a decrease in resource prices is depicted by:1) panel (A) only. 2) panel (B) only. 3)

    		•
  • Q : Words of Frank Knight In words of Frank

    In words of Frank Knight, risk, not like uncertainty: (w) is totally unpredictable. (x) is a main source of pure economic profits. (y) may be estimated. (z) cannot be taken into account while firms make decisions regarding production and pricing.

    		•
  • Q : Change in total revenue by market power

    When a monopolist raises price, it: (w) always increases its revenue. (x) always reduces its revenues. (y) doesn't influence its revenue. (z) may increase, decrease, or not change total revenue. I need a good answe

    		•