--%>
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 : Expected Rate of Inflation What is the

    What is the Expected Rate of Inflation. Illustrate the term.

    		•
  • Q : Diseconomies of scale problem Can

    Can someone help me in finding out the right answer from the given options. When the average production costs rise as the total production of a firm rises, the firm is experiencing: (1) economies of scale. (2) Economies of scope. (3) Diseconomies of scope. (4) Disecon

    		•
  • Q : Net income by negative income tax Under

    Under the negative income tax system demonstrated in this figure, a family of four along with no earned income would have a net after-tax income of: (1) $15,000 per year. (2) $10,000 per year. (3) $5,000 per year. (4) $2,500 per year. (5) $0 per year.

    		•
  • Q : Wages for workers and economic rent The

    The monthly check which you pay to your landlord shows: (w) interest for use of the landlord’s capital, and wages for maintenance workers, economic rent depends on the location and amount of land as well as perhaps, several economic profit (when there is any mon

    		•
  • Q : Determine absolute value of price

    Since this demand curve for DVD games is a straight line, and its slope: (w) is constant, although the absolute value of price elasticity of demand falls as output increases. (x) varies to compensate for changes within elasticity. (y) is constant, alt

    		•
  • Q : Problem on Illegal Union Strategies Not

    Not between strategies historically employed by some unions however now illegal in the United States are: (i) Jurisdictional strikes centered on which the unions will stand for a firm’s staff. (ii) Agency shop contracts forcing the non-union staff to pay ‘

    		•
  • Q : Derived Demand for Labor in competition

    The faddish popularity of Atkins and South Beach diets both, and both of that advise dieters to eat more meat and to decrease the intake of starchy carbohydrates, most likely decreased incomes most sharply for: (1) grocery store clerks. (2) cattle ran

    		•
  • Q : Short-run shut-down point for profits

    Short-run shut-down point of the cranberry farm occurs at a price of: (i) P1. (ii) P2. (iii) P3. (iv) P4. (v) Not computable from these figures.

    Q : Output level of profit maximizing of

    The profit maximizing competitive firm in illustrated graph will: (i) produce output level q5. (ii) minimize total costs by producing output level q3. (iii) experience fixed costs equal to 0P3fq4. (iv) produce output level q4. (v) inevitably experienc

    		•
  • Q : Prevent operating in long run by

    A monopolist will prevent operating within the long run unless its economic profit is: (i) zero. (ii) positive. (iii) greater than accounting profit. (iv) zero or greater. (v) zero or less. I need a good answer on

    		•