Teaching programmes:
Master of Public Health, University of Tromsø, Norway
HEL-3007 Health Economics and Policy
Master of Public Health, Monash University, Australia
ECC-5979 Health Economics
Master of Health Administration, Monash University
ECC-5970 Introduction to Health Economics
Main text:
Olsen JA (2009): Principles in Health Economics and Policy,
Oxford University Press, Oxford
Lecture 14:
Estimating costs
Discounting future health gains
Jan Abel Olsen
University of Tromsø, Norway
www.janabelolsen.org
Key costs concepts
• Marginal costs
– As opposed to average costs
• Societal costs
– The value to society of all resources used
• Opportunity costs = benefits forgone
– The benefits produced had the same resources been
spent on the best alternative programme
1
Fixed and variable costs
The simplest cost function: TC = C0 + c*X
Fixed costs:
Average fixed costs:
Variable costs:
Average variable costs:
C0
C0 / X
c*X
c*X /X = c
Average total costs, AC =
TC / X
Costs reflect productivity
• Remember: Costs reflect expenditures on
input factors
• If constant marginal productivity
 Constant costs per unit of production
• If diminishing marginal productivity
 Increasing costs per unit of production
2
Total costs
C
TC
c*X
C0
X
Average costs
if constant average variable costs
C
AC = c + C0 / X
c
C0 / X
X
3
Marginal costs
The simplest cost function:
A more general cost function:
TC = C0 + c*X
TC = C0 + c(X)
Marginal costs = the additional costs of producing one
additional unit of X
MC = C0 + c(X+1) – [C0 + c(X)] = c(X+1) – c(X),
– i.e. the additional variable costs only
Marginal costs
C
MC
AC
c(X) / X
C0 / X
X
4
The relationships between average and marginal costs,
and between productivity and costs
Fill in these columns
L
0
X
FC
VC
(L*200)
TC
0
1000
0
1000
1
4
1000
200
1200
2
10
1000
400
1400
3
20
1000
600
1600
4
28
1000
800
1800
5
35
1000
1000
2000
6
40
1000
1200
2200
7
42
1000
1400
2400
FC
X
VC
X
TC
X
MC=
VC/X
∆X
∆L
On the importance of looking at the
margin
• Instead of ‘all or nothing’, take
‘one step at a time’!
• Compare incremental costs with
incremental gains!
5
What do we gain from the sixth stool guaiac?
Neuhauser, Lewicki, NEJM, 1975
No of
tests
No of
cases
1
65.9469
77,511
1,175
2
71.4424
107,690
1,507
3
71.9004
130,199
1,810
4
71.9385
148,116
2,059
5
71.9417
163,141
2,268
6
71.9420
176,331
2,451
Total
costs
Average
cost/case
What do we gain from the sixth stool guaiac?
Neuhauser, Lewicki, NEJM, 1975
No of
tests
No of
cases
1
65.9469
65.9469
77,511
77,511
1,175
1,175
2
71.4424
5.4956
107,690
30,179
1,507
5,492
3
71.9004
0.4580
130,199
22,509
1,810
49,150
4
71.9385
0.0382
148,116
17,987
2,059
469,534
5
71.9417
0.0032
163,141
15,024
2,268
4,724,695
6
71.9420
0.0003
176,331
13,190
2,451 47,107,214
Incremen
-tal gain
Total
costs
Incremen Average
-tal costs cost/case
Marginal
cost/case
6
Which costing perspective?
• The particular health care institution
• The health service
• The public sector
• All sectors of the economy, i.e. society
Societal costs
• Health care costs
– Direct treatment costs
– Follow-up costs (primary care / rehabilitation)
• Costs to the patient/family
– Travel time
• Production loss
– The value of reduced production because patients (and
caregivers) are away from work during treatment
7
Measuring costs
• Health care costs
– Average treatment costs (hospital DRGs)
– More than 70% of costs are labour costs
• Costs to the patient/family
– Travel costs
– Time costs I; forgone leisure = net income
• Production loss
– Time costs II; lost production = gross income
• when patients are away from work during treatment
A complicating issue regarding
societal costs vs equity
• Which types of costs (resource use ) involve
opportunity costs to other patients, in terms of
health benefits forgone?
– Health care costs (primarily)
• Which types of costs involve opportunity costs to
other people (‘the rest of society’), in terms of
wider benefits forgone?
– Public sector costs (primarily)
8
Discounting health
Should QALYs gained count the
same no matter how far into the
future they occur?
Discounting – preference for the present!
The stronger the preference for immediate effects, the
higher the discount rate (‘time weight’)
The stronger the time preferences and the further into
the future, the lower weight is put on the future health
gains as compared to immediate gains
 A controversial issue
9
Costs and effects occur parallel in time
Effects
t
Costs
Costs now, effects later
Effects
t
Costs
10
The present value of a future event
Present value of Z,
with a value of 1,
with a discount rate r,
taking place in time t:
1
ZPVt =
(1 + r)t
Annuity
– the present value of a future stream
1
1
1
1
1 – (1+r)–t
A = ———— + ———— + ———— +…+ ———— = —————
(1 + r)
(1 + r)2
(1 + r)3
(1 + r)t
r
11
Discounting at 3%, 5%, 10%
ZPVt
A
r
t=5
t = 20
t=5
t = 20
0%
1
1
5
20
3%
0.86
0.55
4.6
14.9
5%
0.78
0.38
4.3
12.5
10 %
0.62
0.15
3.8
8.5
Why positive time preferences?
• Impatience
• Diminishing marginal utility
• Uncertainty; risk aversion
12
Discounting at 3%, 5%, 10%
1,00
0,90
0,80
0,70
0,60
0,50
0,40
0,30
0,20
0,10
0,00
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
Discounting a life with an expected
75 years of remaining lifetime
Q: How much is left with a discount rate of 3%?
A: Life is ‘discounted’ from 75 to 29.9 ‘present valued years’
100,00
90,00
80,00
70,00
60,00
50,00
40,00
30,00
20,00
10,00
0,00
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
13
Intergenerational choice: A or B?
• Programme A saves
1,000 lives this year
• Programme B saves
1,000 lives in 20 years
• If you chose Programme A, how many lives N
would Programme B have to save for you to
consider the two programmes equally good?
• N = 2,500: 5% annual rate
• N = 7,000: 10% annual rate
Intragenerational choice: A or B?
• Programme A
4,000 people will gain
5 life years each
• Programme B
1,000 people will gain
20 life years each
• If you chose Programme A, how many people N would
Programme B be able to treat for you to consider the two
programmes equally good?
• N = 1,400: 5% annual rate
• N = 1,800: 10% annual rate
14
Discounting and equity
• Intergenerational equity (across generations)
– use low discount rate
• Intragenerational equity (same generations)
– use high discount rate
Different value bases on discounting
• Pragmatic economist
– The same rate as elsewhere in the economy
• Consumer sovereignty economist
– The rate that best reflects peoples’ time preferences
for health
• Ethicist
– Zero rate or close to zero
15