Suppose that the price elasticity for hip replacement surgeries is 0.4. Further
ID: 1209497 • Letter: S
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 70 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 70 percent of the bill, just assume that the price paid by consumers falls 70 percent.)
What if insurance covered 95 percent of the price?
Instructions: Round your answer to 1 decimal place.
b. Suppose that with insurance companies covering 95 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?
By how much?
Explanation / Answer
(a) Price elasticity = 0.4
Insurance covers the 70 percent of the bill.
This means that price has decreased by 70%.
When price decreases, quantity demanded increases.
Price elasticity = % change in quantity demanded/% change in price
0.4 = % change in quantity demanded/70
% change in quantity demanded = 28
Thus, the quantity demanded of hip replacement will increase by 28 percent.
Price elasticity = 0.4
Insurance covers the 95 percent of the bill.
This means that price has decreased by 95%.
When price decreases, quantity demanded increases.
Price elasticity = % change in quantity demanded/% change in price
0.4 = % change in quantity demanded/95
% change in quantity demanded = 38
Thus, the quantity demanded of hip replacement will increase by 38 percent.
(b) (i) Price of hip surgery has increased from $50,000 per surgery to $80,000 per surgery.
So,
New price = $80,000 per surgery
Insurance covers 95% of price.
Amount covered by insurance = (95/100) * $80,000 = $76,000
Amount each insured person will pay = Price - Amount covered = $80,000 - $76,000 = $4,000
So, each insured patient will now pay $4,000 for a hip replacement surgery.
Price elasticity = 0.4
Original demand (Q) = 10,000 surgeries
Original price (P) = $50,000
New price (P1) = $4,000
Calculate percentage change in price -
% change in price = [(P1 - P)/P] * 100 = [(4,000 - 50,000)/50,000] * 100 = -92%
Negative sign indicates that price has decreased. However, negative sign can be ignored.
So, percentage change in price equals 92 percent.
Price and quantity has inverse relationship. As price has decreased, quantity demanded will increase.
So, the quantity demanded of hip replacement surgery will increase.
Calculate % change in quantity demanded -
Price elasticity = % change in quantity demanded/% change in price
0.4 = % change in quantity demanded/92
% change in quantity demanded = 36.8
% increase in quantity demanded = 36.8
original demand = 10,000 surgeries
Increase in demand = 10,000 * (36.8/100) = 3,680
So, the quantity demanded will increase by 3,680 surgeries.
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