--%>
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 : Small market capitalization Why would

    Why would stocks perform better in the month of January than other months of the year, and discuss whether small market capitalization companies outperform large capitalization companies in the short to medium term?

    		•
  • Q : Import cars in equilibrium When the

    When the import car market is in equilibrium prior to the government limits car imports to Q1, the price that buyers will reimburse for an import: (1) Drops/falls from P0 to P1. (2) Is stable, although dealer gains fall by Q0 to Q1. (3) Increases from P0 to P2. (4) Ex

    		•
  • Q : Interest-rate cost A profit-maximizing

    A profit-maximizing firm must not undertake a R&D project for which the: 1) Expected rate of return exceeds its interest-rate cost of funds. 2) interest-rate cost of funds exceeds the expected rate of return. 3) expected returns are in the distant future. 4) the e

    		•
  • Q : Increasing cost industries when

    When resource supply curves facing an industry are positively sloped, in that case the exit of firms which have incurred losses will result in: (w) higher prices and lower output for the industry, although lower average production costs for the surviv

    		•
  • Q : Market clearing price problem The

    The markets in which the current market price surpasses the market clearing price experience: (1) Surpluses. (2) Declining scarcity. (3) Unexpected inventory shrinkage. (4) Shortages. (5) Raised market demands. Find out the right a

    		•
  • Q : Problem on demand curve Give me answer

    Give me answer of this question. Refer to the following diagram. Other things equal, a rightward shift of the demand curve would: A) depreciate the dollar.  B) appreciate the dollar. C) reduce the equilibrium quantity of euros. D) depreciate the euro.

  • Q : Maximum consumer surplus A

    A characteristic Hollywood star derives the maximum consumer surplus from: (i) Calvin Klein underwear. (ii) Water. (iii) Mercedes Benz 600SEs. (iv) DeBeers diamonds. (v) Publicity in "The National Enquirer." Can so

    		•
  • Q : Example of acquisitions of merger The

    The Overpriced Petroleum Extraction Company (or OPEC) has just declared its acquisition of some small firms with facilities which will permit OPEC to process oil via the whole refining procedure, from oil field recovery via transporting and then trading the refined pe

    		•
  • Q : Raise current consumption by rising in

    When interest rates rise, in that case the opportunity costs of: (1) current consumption rise. (2) future consumption rise. (3) current investment decline. (4) government budget deficits decline. (5) saving grows proportionally.

    		•
  • Q : Entrepreneurs implicit cost Can someone

    Can someone please help me in finding out the precise answer from the following question. The entrepreneur’s implicit cost would comprise the: (i) Purchase price of the intermediate goods. (ii) Interest payments on loans. (iii) Value of the owner’s labor.

    		•