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# Federally funded dental patients

Q1. The average total cost of operating a clinic is \$800 per patient if the volume is 100 patients, and \$790 per patient if the volume is 110 patients. What is the total cost at each of these two volumes? What is the marginal cost of another case within this range?

Q2. Extended care facilities are paid on a per diem basis, and they have an upward sloping supply curve. What will be the effect on supply or quantity supplied in each of the following cases:

a. A reduction in the real per diem rate paid to the extended care facility?

b. An increase in wages paid to the staff who work in the extended care facility?

c. A new cleaner that allows the extended care facility to hire fewer custodial staff?

d. A greater supply of home care services (a substitute for extended care facilities)?

Q3.

The federal agency responsible for covering the cost of dental care for low-income seniors has set a rate of \$100 for various dental treatments. In addition to these seniors, dentists have patients who pay for their dental services. The demand curve for each dentist is shown below.

Out-of-Pocket Price Quantity of Dental Treatments Demanded
\$160 0
\$145 3
\$130 6
\$115 9
\$100 12
\$85 15
\$70 18

Each dentist also has a cost schedule, as shown below.

Quantity of Dental Treatments Demanded Total Cost
0 \$250
3 \$350
6 \$550
9 \$850
12 \$1250
15 \$1750
18 \$2350

a. If each dentist in this system works on a profit-maximizing basis, how many treatments will be provided to both the paying patients and to the federally funded seniors? (Show your work by tabulating appropriate columns for TR and TC, as well as for MR and MC)

b. What would the number of paying patients and federally funded seniors be if the federal funding agency raised its rate to \$120 per treatment?

Thank you.

#### Solution Preview

Q1. The average total cost of operating a clinic is \$800 per patient if the volume is 100 patients, and \$790 per patient if the volume is 110 patients. What is the total cost at each of these two volumes? What is the marginal cost of another case within this range?

TC (100 or less)= 800Q
MC = 800
TC (110 or more)= 790Q
MC = 790

Remember that MC is the first differential of the total cost function. Thus dTC/dQ = 800 if TC = 800Q. The MC for all cases in both ranges is the same.

Q2. Extended care facilities are paid on a per diem basis, and they have an upward sloping supply curve. What will be the effect on supply or quantity supplied in each of the following cases:

a. A reduction in the real per diem rate paid to the extended care facility?

This would not shift the supply curve but would be represented by a movement along it to a point of lower output. As prices fall ...

#### Solution Summary

How changes in insurance programs would change the the supply of dental services provided.

\$2.19