--%>
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 : Marginal revenue product problem

    Siberian Software vends custom programs to the multinational corporations. Its programs are coded in a remote region. In equilibrium, the Siberian’s programmers produce a marginal revenue product equivalent to around: (i) $21 per hour. (ii) $25 per hour. (iii) $

    		•
  • Q : Elastic and Inelastic demand An

    An increase in the price of goods, outcomes in an increase in expenses on it. This demand is elastic or inelastic? Answer: Inelastic since there is direct relation

    		•
  • Q : Price discriminate raises output and

    When a monopolist which does not price discriminate raises its output, the firm’s total revenue: (w) should rise. (x) will rise when demand is elastic. (y) will rise when demand is inelastic. (z) will rise when marginal revenue = 0.

  • Q : Inefficient economic monopolists

    Monopolists are frequently considered inefficient since they set: (w) MR = MC to maximize profits. (x) P > MSC. (y) MSR < MSC. (z) output where average revenue equals price [AR = P] as well as marginal revenue equals marginal cost [MR = MC].

    		•
  • Q : Public Goods and Service Why does a

    Why does a good or service become a public good or service?

    		•
  • Q : Trends in Income Distribution The year

    The year in that a long-run trend towards greater equality within the U.S. income distribution was reversed, therefore income since then has become less equally distributed, it was roughly: (w) 1945. (x) 1960. (y) 1975. (z) 1990.

    Q : How market demand curve is obtained I

    I have a problem in economics on market demand curve. Please help me in the following question. The market demand can be obtained via the: (1) Summation of all the quantities demanded whenever market is in equilibrium. (2) Vertical summation of each a

    		•
  • Q : Types of market economies What are the

    What are the types of market economies?

    		•
  • Q : Demand for labor by monopolist Can

    Can someone please help me in finding out the accurate answer from the following question. The demand for the labor by a monopolist in product market is its: (i) Value of the marginal product (or VMP) curve. (ii) Marginal revenue of product (or MRP) curve. (iii) Its m

    		•
  • Q : Minimum legal price in intersection of

    When a minimum legal price of a good is set below the intersection of the supply and demand curves there will be: (1) shortages and pressures for decreases in price. (2) pressures for increases in price and the emergence of black mark

    		•