Question

As a manager of Children's Museum of Indianapolis, you face the following monthly demand curve for its annual membership:
Qd= 1,000-4P
where Qd is the quantity demanded of annual memberships and P is the unit-price of annual membership. The Following table derived from the above demand function above shows how Qd and TR (total Revenue) change with P

P	Qd	TR
$50
$75
$100
$125
$150
$175
$200

a) Fill in the table
b) Suppose that the CEO of the museum wants to increase the membership price from $125 to $150.
i) Use the midpoint method to calculate the price elasticity of demand for the price increase. Is the demand elastic, unitary or inelastic for the price change?
ii) What would be your recommendation to her?
c) Suppose the supply function is given as Qs= 4P

Answer 1

a) Qd= 1,000-4P

P	Qd	TR
50	800	$40000
75	700	$52500
100	600	$60000
125	500	$62500
150	400	$60000
175	300	$52500
200	200	$40000

b)

i) If  the CEO of the museum wants to increase the membership price from $125 to $150.

Midpoint method of elasticity= [(Q2-Q1)/{(Q1+Q2)/2}]/[(P2-P1/{(P1+P2)/2}]

Where P1= $125, P2= $150

Q1= 500, Q2= 400

Ed= [(400-500)/{(500+400)/2}]/[(150-125)/{(150+125)/2}]

Ed={(-100/450)/(25/137.5)}=0.22/0.1818= (-)1.22

Since Ed>1 , it means that demand is elastic . SO the revenue would decrease when price increases.

ii) My recommendation to her is to keep the price at $125, because the revenue there is maximum . The revenue reduces as we move to $150. So its better to keep price at $125 in order to earn maximum revenue.

c) Qs= 4P and we have the demand curve as Qd= 1,000-4P

Equating demand and supply

4P= 1,000-4P

8P= 1000

P= $125

So Q= 4(125)= 500 units