--%>
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 : 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 : Problem on Substitution Effect The cost

    The cost of cashmere plummets and most of the people start employing this once costly material as pillow covers and to knit sweaters for their pets. This is an illustration of: (i) The income effect. (ii) The change in preferences and taste. (iii) The law of diminishi

    		•
  • Q : Substitution effect on supply curves

    One of the reasons for positive relationship among relative price and quantity supplied is the: (1) Technology effect, whereby bigger firms generate at lower average costs than the smaller firms. (2) Substitution effect, whereby firms switch among for

    		•
  • Q : Economic losses generate competitive

    Economic losses in an industry generate competitive pressures which cause: (1) industry output to fall. (2) market price to decrease. (3) each firm’s short-run output to increase. (4) rising costs for industry inputs. (5) firms to expand product

    		•
  • Q : Profit-maximizing output for economic

    Babble-On maintains world-wide patents for software which translates any of 314 spoken languages in text, along with automatic audio and text translations within any of the other three-hundred-thirteen languages. When Babble-On produces its profit-maximizing o

    		•
  • Q : Short run supply of an industry The

    The cranberry industry’s short-run supply is demonstrated as: (i) curve A. (ii) curve B. (iii) curve E. (iv) curve F. (v) curve G.

    Q : Interest rate of annual income When

    When perpetuity pays annual income of $50, in that case at an interest rate of 4 percent its price is: (w) $1000. (x) $1250. (y) $1400. (z) $1800. Hello guys I want your advice. Pl

    		•
  • Q : Influence of short run supply In short

    In short run, the supply of Pinot Noir from the viewpoints of oenophiles who fancy it would be influenced least by: (i) The offspring of late baby boomers arriving the legal age to buy alcohol. (ii) Imposition of a maximum tax for each and every bottle of wine generat

    		•
  • Q : Structure conduct performance paradigm

    From about 1890 till 1970 year, the “structure-conduct-performance paradigm” dominated theories regarding how firms behave in various types of markets. The term here “performance” in this context refers to those things as: (i)

    		•
  • Q : Positional Goods Consider things like

    Consider things like yachts, tattoos, mansions, Harley-Davidsons or bling. Whenever the satisfaction derived from the good depends just weakly on an intrinsic attributes of the good and much strongly on how the good signals group membership or the status, power or soc

    		•