3. (7 points) An insurance company is considering raising the health insurance copayment that its customers must pay when they go to the doctor. Currently, a patient must pay 20% of the doctor's fee, while the remaining 80% is covered by the insurance company. Suppose that, at this copayment level, the price elasticity of demand for doctor visits/year is 0.25. a. By what percentage will the quantity demanded for doctor visits per year decrease if the copayment is raised from 20 percent to 25 percent? Hint: Think carefully about what the percentage change in price is for this problem! b. As you might imagine, the frequency that patients see their doctor directly impacts the rate at which they are hospitalized. Patients who go to the doctor more frequently are less likely to be hospitalized, since the doctor engages in preventative care. Suppose that when patients have a 20% copayment, they go to the doctor at a frequency such that the following holds: %doctorsvisits/year%hospitalvisits/year=3 (Note that this measure is also considered an elasticity, as it measures the percentage change in one variable over the percentage change in another.) If copayment increases from 20% to 25%, how will the rate of hospital visits per year change? c. Suppose hospital visits are twenty times more costly than doctors' visits, and that the insurance company covers a patient's entire hospital bill. Also suppose that under the current copayment structure ( 20% copayment), patients go to the doctor twenty times more frequently than they go to the hospital. Will raising the copayment from 20% to 25% be profitable for the insurance company, once hospital costs are factored in? Please show your work. 3. (7 points) An insurance company is considering raising the health insurance copayment that its customers must pay when they go to the doctor. Currently, a patient must pay 20% of the doctor's fee, while the remaining 80% is covered by the insurance company. Suppose that, at this copayment level, the price elasticity of demand for doctor visits/year is 0.25. a. By what percentage will the quantity demanded for doctor visits per year decrease if the copayment is raised from 20 percent to 25 percent? Hint: Think carefully about what the percentage change in price is for this problem! b. As you might imagine, the frequency that patients see their doctor directly impacts the rate at which they are hospitalized. Patients who go to the doctor more frequently are less likely to be hospitalized, since the doctor engages in preventative care. Suppose that when patients have a 20% copayment, they go to the doctor at a frequency such that the following holds: %doctorsvisits/year%hospitalvisits/year=3 (Note that this measure is also considered an elasticity, as it measures the percentage change in one variable over the percentage change in another.) If copayment increases from 20% to 25%, how will the rate of hospital visits per year change? c. Suppose hospital visits are twenty times more costly than doctors' visits, and that the insurance company covers a patient's entire hospital bill. Also suppose that under the current copayment structure ( 20% copayment), patients go to the doctor twenty times more frequently than they go to the hospital. Will raising the copayment from 20% to 25% be profitable for the insurance company, once hospital costs are factored in? Please show your work
