--%>
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 : Define multiplier Multiplier : It is

    Multiplier: It is the number by which change in investment should be multiple in order to find out the resultant change in income and output.

    		•
  • Q : Linear demand curves and elasticity

    When price falls and quantity rises along a negatively-sloped linear demand curve: (1) total revenues fall till elasticity equals zero, then this rises. (2) demand is decreasingly price elastic. (3) there is a contrad

    		•
  • Q : Supply in short-run equilibrium When a

    When a purely competitive industry is within short-run equilibrium, this: (w) should also be in long-run equilibrium. (x) won’t be in long-run equilibrium. (y) may or may not be within long-run equilibrium. (z) will experience m

    		•
  • Q : Purely competitive or monopolies or

    Compared to either purely competitive firms or oligopolists, monopolies are: (w) more probable to consider the possible reactions of other firms. (x) oblivious to the actions of other firms. (y) less likely to engage

    		•
  • Q : Market clearance according to Economists

    Can someone help me in finding out the right answer from the given options. The Economists state that a market is cleared when the price is in such a manner that: (i) Each and every good produced is sold. (ii) Quantity and Price are equal. (iii) Surplus demand surpass

    		•
  • Q : Monetary liability All currency issued

    All currency issued by central bank is its monetary liability. Explain how? Answer: The Central Bank is grateful to back the currency with assets of equivalent valu

    		•
  • Q : Discrimination and Income Differentials

    By 2000, the differential among the rich and the poor which can be attributed to economic discrimination was computed at: (w) approximately 60 percent. (x) approximately 30 percent. (y) under 10 percent. (z) zero.

  • Q : Incurs total costs by profit

    This profit-maximizing brickyard as in illustrated figure incurs total costs of approximately: (i) $1200 daily. (ii) $1300 daily. (iii) $1400 daily. (iv) $1530 daily (v) $1600 daily.

    Q : Monopolist maximizes profit When a

    When a monopolist maximizes the profit in the product market, it will: (i) Hire labor till the marginal revenue product equivalents the marginal resource cost. (ii) Hire the labor till the value of marginal product equivalents the marginal resource cost. (iii) Pay a w

    		•
  • Q : Follow Lower Bond Price Lower bond

    Lower bond prices follow through higher: (w) interest rates. (x) real estate speculation. (y) present value of future income by the bonds. (z) growth rates of national income. Please choose the right answer from ab

    		•