--%>
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 : Resource market in equilibrium When the

    When the resource market demonstrated in this figure is into equilibrium: (1) owners of these resources currently receive no economic rents. (2) economic rent is specified from trapezoid Oade. (3) the rectangle Obde measures consumer surplus by the fi

    		•
  • Q : Problem regarding to trade barriers for

    When the import market was within equilibrium before the Japanese government began subsidizing all autos exported by the amount dg, in that case U.S. car buyers would be: (w) pay P2 for a car previouslszy priced at P0. (x) suffer Q0 to

    		•
  • Q : Rental check of pure economic rent The

    The part of your monthly rental check which shows pure economic rent is that that pays only for the use of the landlord's: (w) land. (x) capital. (y) labor. (z) entrepreneurial skills. I need a goo

    		•
  • Q : Price charging by minimizing average

    See a monopolist which cannot price discriminate but that maximizes profit. When this firm produces the level of output where is average cost at its minimum that will charge a price: (i) equal to marginal cost and generate zero economic profit. (ii) e

    		•
  • Q : Certainty and severity of punishment in

    Rising the certainty and severity of punishment decreases cheating on an examination. This statement signifies: (i) Unrealistic expectations regarding student honesty. (ii) Purely normative visions of behavior. (iii) Misplaced cynicism since this issu

    		•
  • Q : Set price equal to produce output

    Assume that HoloIMAGine’s patents for holographic technology lapsed, as well as entry of new competitors within this market eroded the demand for HoloIMAGine technology, even though the firm retains several market power since competitors’

    		•
  • Q : Define demand curve where quantity

    At the whole prices where quantity demanded is zero, there the: (w) slope of the demand curve is zero. (x) price elasticity of demand is zero. (y) supply curve has infinite slope. (z) price elasticity of demand is imperfectly defined.

    Q : Short-run losses of shuts down firm

    When a firm shuts down, short-run losses of it equals total: (w) implicit costs. (x) variable costs. (y) fixed costs. (z) resource costs. I need a good answer on the topic of Economics problems. Pl

    		•
  • Q : Voluntary verses Involuntary Poverty

    When physically and mentally capable individuals who are born in impoverished families fail to work after they develop up but since they can rely on charity, in that case they are experiencing: (1) involuntary poverty. (2) relative poverty. (3) a vicious cycle of pove

    		•
  • Q : Reduction in demand of Complementary

    Mold that damaged the hamburger crop following a flood would be most probable to decrease the demands for: (i) fried chicken with gravy and mashed potatoes. (ii) Soda pop and bottled water. (iii) Carrots, cucumbers and egg plant. (iv) Ketchup and mustard. (v) Sushi an

    		•