--%>
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 : Monopolies over brand name products of

    Several firms have monopolies over brand name products, although face competition from: (w) international cartels. (x) oligopolistic rivals. (y) producers of close substitutes for their products. (z) intra-firm rivalry.

    Q : Collective Bargaining-managers and

    The strikes tend to be resolved after worker’s savings trickle down to a discomfort region and there is an exhaustion of: (i) Public tolerance, causing government to set the fair settlement. (ii) Managers and inventories, causing the firms to increase their offe

    		•
  • Q : External costs and external benefits

    Question: (a)         Explain the impact of external costs and external benefits on resource allocation; (b)     

    		•
  • Q : Standard economic reasoning for price

    In the given figure as in below, demand curve D0D0: (w) has price elasticity of infinity. (x) is possibly for a luxury good. (y) is unitarily price elastic. (z) seems contrary to standard economic reasoning.

    Q : General law of demand I have problem in

    I have problem in this question based on law of demand. Provide me correct answer of this. Described the circumstances in which the "general law of demand" not hold?

    		•
  • Q : Long run problem In long run , the

    In long run, the actions of successful speculators tend to rise: (i) Gains and raise consumer’s costs. (ii) Output and decrease the volatility of prices. (iii) Corruption and Bribery in government. (iv) The volatility of both prices and outputs.

    		•
  • Q : Rent controls fix rent in equilibrium

    Rent controls which fix rents below equilibrium will NOT: (w) maintain monetary rents down. (x) create shortages of rental housing. (y) stimulate non-market allocations of rental housing. (z) maintain the opportunity costs of housing down.

  • Q : Synonym for the economists term utility

    I have a problem in economics on Synonym for the economist’s term utility. Please help me in the following question. The reasonably close by synonym for the economist’s term utility is: (1) Consumption. (2) Marginalism. (3) Discontentment. (4) Satisfaction

    		•
  • Q : Positive relationship by law of supply

    The law of supply defines that there is a positive relationship among: (1) The Price and quantity supplied. (2) Technology and production. (3) Purchases and the accessibility of goods. (4) Supply and the demand it makes.

    Q : Problem related to rises japanese yen

    Normal 0 false false

    		•