--%>
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 : Economic profits by potential customers

    When you lease a building for five years and rapidly achieve economic profits since it is located conveniently for potential customers: (1) you could capitalize some of these pure profits when you sold your business along with a sublease at the ending

    		•
  • Q : Labor Unions-Public Employees I have a

    I have a problem in economics on Labor Unions-Public Employees. Please help me in the following question. Workers who are now permitted to join unions however who still might not legally strike comprise: (1) Civilian federal employees. (2) Medical pro

    		•
  • Q : Problem of dockworkers on hiking the pay

    When you were in the ski boat business, your net revenues from selling given numbers of boats would be least influenced by: (i) Govt. increasing fees for boat licenses. (ii) Rises in prices for jet skis. (iii) Pay hikes for dock-workers. (iv) Vacation

    		•
  • Q : Functions of Profits and Losses The

    The functions of profits into a market economy do NOT comprise: (1) stimulation for firms to be innovative and efficient. (2) compensating savers for delays of consumption. (3) signaling changing business conditions. (4) inducing mimi

    		•
  • Q : Long-run equilibrium price and output

    Long-run output and equilibrium price combinations describe a purely competitive industry’s: (w) demand curve. (x) long-run supply curve. (y) expansion path. (z) contract curve. I need a good answer on the to

    		•
  • Q : State the relationship between MPC and

    State the relationship between MPC and multiplier? Answer: The value of multiplier differs directly with MPC.  K=1/1 - MPC.

  • Q : Formally effective a cartel To form and

    To form and effectively keep a cartel over time needs that the: (w) bulk of output be produced and sold by a minute number of cartel members. (x) product be relatively heterogeneous. (y) demand for the product be highly elastic. (z) government totall

    		•
  • Q : Break-even level of income The

    The break-even level of income for four member of family under the negative income tax system demonstrated in this figure is: (1) $15,000 per year. (2) $30,000 per year. (3) $45,000 per year. (4) $60,000 per year. (5) $75,000 per year

    		•
  • Q : Economists conceive of any resource

    Economists can’t conceive of any resource or product for which the: (i) Price elasticity of demand is zero (0) and the demand curve is vertical. (ii) Price elasticity of supply is zero (0) and supply curve is vertical. (iii) Income elasticity of

    		•
  • Q : Help In the quintile distribution of

    In the quintile distribution of income, the term "quintile" represents

    		•