--%>
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 : Nominal interest rates in market

    Nominal interest rates are most largely and directly determined within markets for: (1) loanable funds. (2) newly issued stock. (3) foreign exchange. (4) securitized assets. (5) long term government bonds. Please c

    		•
  • Q : Expansion of increasing cost industries

    Expansion of the industry in increasing cost industries causes: (w) increases in each firm’s costs at every level of output. (x) decreases in each firm’s costs at every level of output. (y) all firms to suffer long-run economic losses. (z)

    		•
  • Q : Examples of Labor

    The contracts needing employment after some worker’s jobs have been made obsolete through automation are illustrations of: (i) Blacklisting. (ii) Labor-reducing protectionism. (iii) Check-off provisions. (iv) Yellow dog contracts. (v) Feather-bedding.

  • Q : Negative-positive coefficient in

    When you compute cross-elasticity of demand, what are you trying to find out?  What do a negative coefficient and a positive coefficient imply?

    		•
  • Q : Shifting supply of curve by entry of

    When the price for Christmas trees is initially P1, in that case in the long run: (w) firms will neither enter nor exit this industry. (x) entry of firms will shift curve supply curve A to the right. (y) exit of firms will shift supply curve A to the left.

    		•
  • Q : Workers volunteered to work in purely

    Even though workers volunteered to work as "for free", such purely competitive firm would never hire more than: (i) L2 workers. (ii) L3 workers. (iii) L4 workers. (iv) L5 workers. (v) L6 workers.<

    		•
  • Q : Labor Productivity The American workers

    The American workers tend to be much productive than their counterparts in the South America or Asia in part as they have: (i) Superior natural genetic endowments. (ii) Access to the better sports programming, that promotes the team-work. (iii) More capital to work wi

    		•
  • Q : Demand curve facing monopolistically

    The demand curve that facing a monopolistically competitive firm is: (1) perfectly elastic within the short run. (2) perfectly inelastic due to numerous substitutes for its product. (3) less elastic than the demand curve facing a comp

    		•
  • Q : Problem on coefficient of income

    Refer to the following diagrams give the answer of following question. In which case would the coefficient of income elasticity be positive? 1) A 2) B  3) C  4) D    

    Q : Separation of the Economic Functions

    Separation of ownership or stockholders by control (management) into modern giant corporations tends to divide the economic functions of: (w) capitalists. (x) union leaders. (y) entrepreneurship. (z) bureaucrats. I

    		•