Suppose that the price elasticity for hip replacement surgeries is 0.4. Further

Question

Suppose that the price elasticity for hip replacement surgeries is 0.4. Further suppose that hip replacement surgeries are originally not covered by health insurance and that at a price of $50,000 each, 10,000 such surgeries are demanded each year.


Instructions: Enter your answers as whole numbers.


a. Suppose that health insurance begins to cover hip replacement surgeries and that everyone interested in getting a hip replacement has health insurance. If insurance covers 50 percent of the cost of the surgery, by what percentage would you expect the quantity demanded of hip replacements to increase? (Hint: Do not bother to calculate the percentage changes using the midpoint formula. If insurance covers 50 percent of the bill, just assume that the price paid by consumers falls 50 percent.)


___________percent.


What if insurance covered 90 percent of the price?


Instructions: Round your answer to 1 decimal place.


__________percent.


b. Suppose that with insurance companies covering 90 percent of the price, the increase in demand leads to a jump in the price per hip surgery from $50,000 to $80,000. How much will each insured patient now pay for a hip replacement surgery?


   $___________


Compared to the original situation, where hip replacements cost $50,000 each but people had no insurance to help subsidize the cost, will the quantity demanded increase or decrease?


Increase


By how much?

________ surgeries.

Explanation / Answer

Price elasticity hip replacement surgeries = 0.4

At $50,000, 10,000 surgeries are demanded each year with no health insurance cover.

a. Now, insurance covers 50% of hip replacement costs, which means the percentage reduction in price is 50% (-)

PED = % change in quantity demanded / % change in price

0.4 = % change in quantity demanded / (0.5)

Percentage change in hip replacement surgeries demanded = 0.4 x 0.5 = 0.20

Percentage change in surgeries demanded = Increases by 20 percent.

If health insurance covered 90% of the price:

Percentage change in quantity demanded = 0.4 x 0.9 = 0.36

Percentage change in surgeries demanded = 36 percent

b. How much will each insured patient now pay for a hip replacement surgery?

Insurers pay 90% of the increased price of surgery which is $80,000 x 90%

Price paid by insured patient = $80,000 - $72,000 = $8,000.

Where hip replacements cost $50,000 each but people had no insurance to help subsidize the cost

Will increase by 40 percent, by 4000 surgeries.

*****

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