Calculation of Present Value of Benefits under Alternative Discount Rates

 Calculation of Present Value of Benefits under Alternative Discount Rates

Part A: Discounting Factors

Discount Rate (1 + r) (1 + r)2 (1 + r)3 (1 + r)4 (1 + r)5
.04 1.04 1.08 1.12 1.17 1.22
.08 1.08 1.16 1.25 1.36 1.41
.12 1.12 1.25 1.41 1.57 1.63
Part B: Discounted Present Value
of Benefits ($10,000)

Discount Rate B1/(1 + r) B2/(1 + r)2 B3/(1 + r)3 (B4/(1 + r)4 B5/(1 + r)5 Present Value (row sum)
.04 8,615 9,233 8,896 8,554 8,196 44,494
.08 9,259 8,620 8,000 7,353 7,092 40,324
.12 8,928 8,000 7,029 6,275 5,602 35,834


Siegal has two alternative activities to help relieve her backache. In the
first, she can visit a physiotherapist. The total time for a physiotherapist
visit, including travel and waiting, is two hours. Mrs. Siegal earns a wage of
$20 an hour. Physiotherapists charge $50 per visit, and Mrs. Siegal does not
have any health insurance. As a second alternative, Mrs. Siegal can take pain
killers. Each pill costs 50 cents, and Mrs. Siegal needs to take 30 pills per
month. The two treatments are not equally effective. The physiotherapy visits
yield 10 additional healthy days per month, while the pills yield 6 healthy

  • a.If Mrs. Siegal can only
    choose one alternative, and if she wants to maximize the most healthy days
    per dollar that she gets, which option will she choose?
  • b.If the price of a pill
    increases to $3, which option will she choose?

this and answer exercise #2
5.7.4Hospital Economies of Scale

A large number of studies have investigated the possible existence of
economies of scale in hospitals, with very mixed results (Berki 1972;
Frech and Mobley 1995).
Early studies identified economies of scale but subsequent studies have
uncovered no evidence (Lave and Lave 1984)
or conflicting evidence (Frech and Mobley 1995).
There is an explanation for the differences in findings.

As discussed earlier, the typical hospital is an organization with a complex
case mix and a large number of different services. Each service has its own
cost-output relation, which may exhibit economies of scale. The scope of
services is greater for larger hospitals (Berry 1973),
but these hospitals may have more varied case types, so some services (e.g.,
cobalt therapy) that are devoted to specific case types may be operated at low
capacity and high cost. A multiproduct hospital can be quite large yet have a
number of services with considerable excess capacity (Finkler 1979b).
As a result, it might exhibit a higher average cost than many smaller

One study (Hornbrook and Monheit 1985)
that incorporated both case mix and service scope variables to investigate
economies of scale found no such economies at the hospital level. But a number
of studies of individual services, such as open-heart surgery facilities, CT
scanner units, therapeutic radiology facilities, and hospital laundries, have
found evidence of economies of scale (Finkler 1979a;
Gregory 1976–1977;
McGregor and Pelletier 1978;
Okunade 1993;
Schwartz and Joskow 1980).
This suggests that the economies of scale that do occur in some hospital
departments are offset by diseconomies of scale in others.

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