--%>
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 : Inconsistent of demand with standard

    The curve which is so inconsistent along with standard consumer theory which is based only on the substitution result, this could not possibly be a demand curve for any standard kind of consumer good is: (1) curve D1D1. (2) curve

    		•
  • Q : Accounting profit when implicit cost

    Can someone please help me in finding out the accurate answer from the following question. When implicit cost surpasses implicit revenue and economic profit is zero (0), then accounting profit is: (1) Bigger than zero. (2) Zero. (3) Less than 0 (zero). (4) Not specifi

    		•
  • Q : Can the value of APS be negative Can

    Can the value of APS be negative:Yes, the value of APS is negative; when there are dissavings.

    		•
  • Q : Effect of future consumption on

    When households become increasingly willing to defer current consumption in order that they can enjoy greater future consumption, in that case the: (1) interest rate rises. (2) equilibrium investment level rises. (3) present value of

    		•
  • Q : New entrance in limit pricing model of

    Within the limit pricing model of strategic behavior, there the demand curve facing a new entrant will be: (w) horizontal. (x) the difference between industry demand and incumbent sales at each price. (y) the difference between the new entrant's outpu

    		•
  • Q : Industrial Unions-organizing workers

    Can someone help me in finding out the right answer from the given options. Industrial unions are proposed to organize all the workers in: (i) A specific company. (ii) The United States. (iii) Particular skill or the craft. (iv) Particular occupation. (v) Specific ind

    		•
  • Q : Federal agricultural subsidies Federal

    Federal agricultural subsidies tend to be rapidly: (w) spent because most farmers lack sufficient budgeting skills. (x) capitalized in higher prices for farm land. (y) slashed while pressure mounts to cut the federal deficit. (z) absorbed from rising

    		•
  • Q : Operation in the short run of fixed

    The curves demonstrated in this figure reflect that: (i) operation in the short run since fixed costs can be measured in the graph. (ii) a disequilibrium that will force some competitors to exit this market. (iii) how firms innovate new technologies in response to pro

    		•
  • Q : Deadweight Losses and Taxation Whenever

    Whenever a tax on a good outcome less government revenue than the sum of the losses of producer and consumer surpluses due to tax, economists state that the tax has caused a/an: (1) Administrative loss. (2) Market failure. (3) Economic loss. (4) Bureaucratic loss. (5)

    		•
  • Q : Definition of Consumer Surplus The

    The difference among the price a consumer would have been eager to pay for the commodity and the price consumer really has to pay is termed as: (i) Gain. (ii) The substitution effect. (iii) The income effect. (iv) Consumer surplus.