1. Suppose the equilibrium price for an average hospital stay in the absence of insurance is...

1. Suppose the equilibrium price for an average hospital stay in the absence of insurance is $10,000. At that price, 1000 people are hospitalized each year. Now suppose an insurer offers a policy to lower the out of pocket price of a stay to $100, and at that price, 1200 people are hospitalized.

a) How much TOTAL premium revenue must be collected to finance this arrangement?

b) How much premium revenue per hospitalized person must be collected? Would the average person be willing to pay this premium if they were risk averse?

c) Now suppose there are 120,000 people near this hospital, all of whom think they have an equal chance (1%) of being hospitalized. What must the per person premium be now?

Expert Solution

Ans:- In the absence of Insurance, total price for hospital stay in an year would be 10,000*1,000 = 10000000

Now after the introduction of insurer, total price for hospital stay in an year would be 100*1200 = 120000

a- The difference of the hospital stay should be collected in the form of premium revenue which is equal to 10000000-120000=98,80,000 dollars

b- Revenue per hospitalized person would be 98,80,000/1200 = 8233.33 dollars. The average person would be willing to pay this premium if they were risk averse as the total expenditure by them after taking insurance is less than when they dont opt for it.

c- When there are 120,000 people near this hospital and all of them think they have an equal chance(1%) of being hospitalized then the per person premium would be

120,000* X +120000*0.01*100 = 10000000 (premium will be paying by everyone. However only 1% of them will be hospitalized and they will be paying marginal price of 100 dollars )

X= 98,80,000/120000 = 82.33 dollars

Colby Messinger answered 2 years ago

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