Question

**** Only Need answers for questions g and h****

Suppose that, in the absence of insurance, the daily demand for visits to a clinic is given by Qd = 200 – 0.5P, where c is the coinsurance rate and P is the price charged by the clinic.

a) Calculate the quantity demanded when P is $100.

b) Calculate daily revenues when P is $100.

Now assume that customers pay a coinsurance rate, c. You will need to modify the demand function to account for the coinsurance.

c) Calculate the quantity demanded when P is $100 and the coinsurance rate is 0.4.

d) Calculate the daily revenue for the values given in (c).

e) Calculate the quantity demanded when P is $100 and the coinsurance rate is 0.8.

f) Calculate the daily revenue for the values given in (e).

Assume the clinic’s daily capacity is 100 customers.

g) Calculate the price the clinic should set to exactly use its entire capacity when there is no coinsurance (i.e., the co-coverage rate is 1).

h) Calculate the price the clinic should set to exactly use its entire capacity when there is a coinsurance rate of 0.8

Answers:

1. 150
2. 15000
3. 110
4. 11000
5. 70
6. 7000

Answer 1

g) Calculate the price the clinic should set to exactly use its entire capacity when there is no coinsurance (i.e., the co-coverage rate is 1).

Answer:

Assumption given in question is that the clinic’s daily capacity is 100 customers. So our Demand Qd is fixed at 100.

Demand Function is  Qd = 200 - 0.5P

Substituting value of Qd as 100, we get:

100 = 200 - 0.5P

0.5P = 100

P = 200

So, in absence of coinsurance, the clinic should set a price of $200.

h) Calculate the price the clinic should set to exactly use its entire capacity when there is a coinsurance rate of 0.8

Answer:

Here, coinsurance rate of 0.8 is also applied in addition to fixed demand of 100 customer per day.

In view of coinsurance, the Demand Function changes to Qd = 200 - 0.5P - Pc ; where c is coinsurance rate.

Substituting values in the equation above, we get:

100 = 200 - 0.5P - 0.8P

1.3P = 100

P = 76.92

So, with a coinsurance of 0.8, the clinic should set a price of $ 76.92