The extended demand function of good Y is: Q d Y = 1200 – 10 P Y + 20 P X + 0.2

Question

The extended demand function of good Y is:

QdY = 1200 – 10 PY + 20 PX + 0.2 M

where:    QdY = quantity demanded of good Y

               PY = Price of good Y

               M = Average consumer income

               PX = Price of related good X (related in consumption to good Y)

a) If M = 20,000 and PX = 10, what is the reduced demand function for good Y? For what range of prices is this linear demand curve price elastic? What will happen to revenues for the suppliers of good Y as the price of good Y decreases within this range?

b) Continue with part a. How many units of good Y do the suppliers of good Y have to produce to maximize their revenues? What would be maximum revenues for the suppliers of good Y? Calculate the value of the price elasticity of demand at the middle point on this demand curve (use the point formula).

Continue using the reduced demand equation from part a,

    If M = 20,000, PX = 10, and PY = 400 then QdY = ________

    If M = 20,000, PX = 10, and PY = 420 then QdY = ________

c) Use these two prices and quantities demanded to calculate the value of the price elasticity of demand between these two points on the demand curve for good Y (use the arc elasticity formula). Show your work and interpret your answer. What will happen to revenues for the suppliers of good Y as the price of good Y decreases from PY = 420 to PY = 400? WHY?

you found that when:

M = 20,000, PX = 10, and PY = 400 then QdY = ________

Now let’s suppose that the average consumer income increases from 20,000 to 30,000 but the price of good X remains constant at 10 and the price of good Y remains constant at 400. Then, if

M = 30,000, PX = 10, and PY = 400 then QdY = ________

d) Use these two average consumer income levels and associated quantities demanded of good Y to calculate the value of the income elasticity of the demand for good Y (when

PX = 10 and PY = 400). Show your work and interpret your answer. Based on the value of the income elasticity of demand you just estimated, what type of good is good Y? WHY?

You found that when:

M = 20,000, PX = 10, and PY = 400 then QdY = ________

Now let’s suppose that the price of good X decreases from 10 to 5 (but income remains constant at 20,000 and the price of good Y remains constant at 400). Then, if

M = 20,000, PX = 5, and PY = 400 then QdY = ________

e) Use these prices of good X and the quantities demanded of good Y to calculate the cross-price elasticity of the demand of good Y when the price of good X decreases from 10 to 5 (and PY = 400 and M = 20,000). Show your work and interpret your answer. Based on the value of this cross-price elasticity of demand you just estimated, what type of goods are X and Y? WHY?

Explanation / Answer

answer a)

If M = 20,000 and PX = 10, the reduced demand function for good Y is

QdY = 1200 – 10 PY + 20 PX + 0.2 M

=1200-10PY+20*10+0.2*20000

=1200+200+4000-10PY

=5400-10PY

It is price elastic for prices greater than 10

The revenues of the suppliers will increase as a result of fall in prices of good Y.

b) PY=540-1/10QY

TR=P*Q

=(540-1/10QY)*Q

=540Q-1/10Q2

at maximum profits MR=0

540-1/5Q=0

540=1/5Q

QY=2700

PY=270

Maximum revenues=270*2700

=729000

At the middle point of demand curve elasticity of demand=1 i.e unitary

  If M = 20,000, PX = 10, and PY = 400 then QdY = ___1400_

    If M = 20,000, PX = 10, and PY = 420 then QdY = __1200______

answer c) PY=400 QY=1400

PY=420 QY=1200

Ed=change in quantity demanded/change in price

=200/20 *400/1400

=2.85

As price falls from 420 to 400 TR increases from 504000 to 560000 as commodity Y has more elastic demand ,fall in price leads to more increase in demand.

M = 20,000, PX = 10, and PY = 400 then QdY = _1400_______

Now let’s suppose that the average consumer income increases from 20,000 to 30,000 but the price of good X remains constant at 10 and the price of good Y remains constant at 400. Then, if

M = 30,000, PX = 10, and PY = 400 then QdY = ____3400____

answer d) income elasticity of demand = change in quantity/change in money income

=2000/10000 *20000/1400

=2.85

since income elasticity is greater than one commodity Y is a luxury good.

M = 20,000, PX = 10, and PY = 400 then QdY = 1400________

M = 20,000, PX = 5, and PY = 400 then QdY = ____1300____

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