--%>
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 : Union-Nonunion Wage Differentials I

    I have a problem in economics on Union-Nonunion Wage Differentials. Please help me in the following question. All else equivalent, when employment in an industry raises, the average wage differential gap among union and non-union workers: (1) Narrows.

    		•
  • Q : Government programs influencing

    Government programs assuring farmers minimum legal price floors which surpass equilibrium market prices will outcome: (1) Cheaper food for consumers. (2) Scarcities of food and the potential for famine. (3) Surplus demand in food markets. (4) Maximum equilibrium price

    		•
  • Q : Define Fiscal deficit Fiscal deficit is

    Fiscal deficit is equavalent to excess of total expenditure over the sum of revenue and capital receipts excluding borrowings. That is, Fiscal deficit means borrowing of the government. Fiscal Deficit :T

    		•
  • Q : Price cross-elasticities of demand When

    When the price of thermal underwear is increased from $12 to $18 per pair, because of the quantity of cross country snow skis to decline by 1,200 to 800 pairs annual, such goods are ____ and the price cross elasticity of demand equiva

    		•
  • Q : Marginal social benefit and costs under

    Under pure competition, there is marginal social benefit will equivalent marginal social cost unless: (w) “hit and run” entrepreneurs prosper. (x) economic profits are zero. (y) there are externalities. (z) entrepreneurs a

    		•
  • Q : Exploitation on resource suppliers Can

    Can someone help me in finding out the right answer from the given options. When resource suppliers are paid less than the values of their marginal products (or VMPs), they are stated to be: (i) Monopolistic. (ii) Exploited. (iii) Monopsonistic. (iv) In equilibrium.

    		•
  • Q : Determine relatively price elasticity

    A price elasticity of demand of 2.0 implies that at that point, the demand curve is: (w) income elastic. (x) relatively price elastic. (y) relatively price inelastic. (z) unitarily price elastic. I need a good answ

    		•
  • Q : Needs of families by poverty line

    The official “poverty line” computed by the federal government is the income level needed to meet the perceived fundamental needs of families along with differing characteristics as size, location, etc. Therefore, it is based on: (1) a rel

    		•
  • Q : Monopolist in an output market Can

    Can someone please help me in finding out the accurate answer from the following question. The labor monopsonist who is as well a monopolist in an output market: (1) Always makes huge profits. (2) Hires more units of the labor when

    		•
  • Q : Political pressure on government

    When the government imposes a price floor upon a product, in that case there may be political pressure for the government: (1) to produce several of the good itself. (2) to restrict the demands of private buyers. (3) to buy and then store some surplus

    		•