Final Reminders - Health Care
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Nov 24, 2024
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Final Reminders – Health Care
Atul Gawande, “Cost Conundrum: What a Texas Town Can Teach Us About Health Care,”
Fee-for-Service (FFS) Model
«
Payment system where
providers
are reimbursed (
報銷
) for each service they perform,
such as tests, procedures, or office visits
«
This system can lead to a
higher volume
of care provided, as there is a direct
financial
incentive
to increase the quantity of services
«
However, this
does not necessarily
correlate with improved patient outcomes and can
lead to unnecessary care and higher
overall health care costs
Supply-Induced Demand
«
Supply-induced demand occurs when the availability of medical services increases,
leading to
higher utilization
of those services, regardless of the patient's actual need
«
In health care, this can manifest when there is an abundance of facilities and technology,
which can encourage providers to
recommend more services
to patients, driving up costs
Defensive Medicine
F
Practice of recommending tests or treatments
not
necessarily based on the patient's best
interests but to protect against potential malpractice claims
F
This practice can contribute to
higher health care costs
due to the additional, and possibly
unnecessary
, medical
procedures
being performed
Variation in Practice Patterns
«
There is substantial variation in how medicine is practiced in different regions, which is
often
not associated with
differences in patient populations or health outcomes
«
Gawande's article shows that McAllen has particularly high costs
without corresponding
improvements in patient health, suggesting that
local practice patterns
play a significant
role in driving up spending
Incentives and Profit Motives
«
The economic incentives for health care providers can significantly impact their behaviour
«
Gawande points out that when providers stand to profit from the volume of services they
provide, there can be a
tendency toward overutilization
«
This is especially prevalent in systems where doctors have
ownership interests
in
hospitals or outpatient facilities
Role of Medicare
«
Medicare spending is used as a barometer for health care costs in an area
«
In McAllen, Gawande notes, Medicare spending was among the
highest in the nation
«
The Medicare system largely follows the FFS model, which may unintentionally
encourage providers to
offer more services
, thus driving up costs
Potential Solutions and Alternative Models
P
Gawande discusses alternative care models, such as those employed by the Mayo Clinic,
that prioritize
coordinated, efficient
care over volume
P
These models often use
salaried physicians
and emphasize
team-based care
, which can
lead to lower costs and
better patient outcomes
Quality of Care vs. Cost
P
The relationship between the cost of care and the quality of outcomes is complex
P
Higher spending does not necessarily result in better health outcomes, as seen in McAllen
P
Gawande highlights that more
cost-effective care
can often be provided with a focus on
quality and efficiency
rather than simply increasing the volume of services
Economies of Scale
P
Economies of scale typically suggest that as the
volume of a service increases
, the cost per
unit of that service decreases
P
However, in health care, Gawande finds that this principle does not always apply
P
In McAllen, higher volumes of service led to higher, not lower, per capita costs,
suggesting that the
unique dynamics of health care
economics can defy traditional
economic models
Impact of Health Care Reform
P
While Gawande's article predates the Affordable Care Act (ACA), it contemplates how
health care reforms
could impact costs
P
Reforms that focus on payment models rewarding
value and quality
of care, rather than
volume
P
Could potentially address the issues observed in McAllen and lead to more sustainable
health care economics
Ethical Considerations
Q
The article raises ethical questions about the fee-for-service model, where financial
incentives might lead to care that is
not in the best interest of the patient
Q
This underscores the
conflict between
economic incentives and the ethical responsibility
of health care providers to provide appropriate care
The Role of Government
6
Gawande suggests that government intervention, through policy changes and
adjustments to
reimbursement structures
, could encourage more cost-effective health care
practices
Conclusion
Q
Gawande's examination of McAllen, Texas, demonstrates that the health care cost
conundrum is
multifaceted and deeply rooted
in the economic incentives embedded
within the health care system
Q
The article suggests that a shift towards value-based care models, with a focus on
coordinated care and system-wide efficiency
, is necessary to address the unsustainable
trajectory of health care costs
Michael Specter, “A Deadly Misdiagnosis: Is it possible to save the millions of people who
die from TB?”
Burden of Disease
F
Tuberculosis is a major global health problem, particularly in low- and middle-income
countries. It poses a significant burden of disease, which can be measured in terms of
mortality, morbidity
, and economic impact
F
This includes direct costs of medical care as well as indirect costs such as
lost productivity
due to illness or death
Cost-Effectiveness of TB Treatment
Q
The treatment of TB is known to be highly cost-effective, especially when compared to the
cost of not treating
the disease.
Early diagnosis and treatment
are key to preventing the
spread of TB and reducing long-term costs associated with the disease
Q
Health economics often considers the cost-effectiveness ratio, which compares the relative
expenses of interventions to their outcomes, measured in quality-adjusted life years
(QALYs) or
disability-adjusted life years
(DALYs)
Funding and Resource Allocation
F
Global funding for TB research, prevention, and treatment is often inadequate. Health
economics examines how
resources are allocated
and how they could be used more
effectively
F
Decisions about
funding allocation
can significantly impact the number of TB cases that
are
successfully diagnosed and treated
Impact of Drug Resistance
Q
Multidrug-resistant TB (MDR-TB) and extensively drug-resistant TB (XDR-TB) pose
significant challenges to TB control and have substantial economic implications
Q
Treatment for drug-resistant TB is
significantly more expensive
and less successful than
treatment for drug-sensitive TB, leading to higher individual and public health costs
Access to Health Services
P
Barriers to accessing health services, including financial barriers, can prevent timely
diagnosis and treatment
of TB, leading to worse health outcomes and higher costs
P
Health economics studies these barriers and potential interventions to improve access to
care
Screening and Prevention
F
Investing in
screening and preventive
measures can be economically beneficial by
reducing the prevalence of the disease and therefore the need for costly treatments
F
Health economics assesses the cost and benefits of different screening methods and
preventive strategies, such as
vaccination where applicable
Economic Impact on Patients and Families
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P
TB can have devastating economic consequences for patients and their families, often
driving them into poverty due to the costs of treatment and loss of income. Health
economics considers both the
direct out-of-pocket expenses
and the
indirect costs
such as
lost earning potential
Global Health Initiatives
Q
International initiative
s, such as the Global Fund to Fight AIDS, Tuberculosis, and
Malaria, play a critical role in financing TB control efforts
Q
Health economics analyses the impact of such initiatives on reducing the burden of TB in
different regions
Health Insurance and TB Care
P
The role of health insurance in covering TB treatment can influence health outcomes and
financial stability
for patients
P
In countries with limited insurance coverage, the economic burden falls heavily on
patients, while
universal health coverage
can alleviate these costs
Public Health vs. Individual Approaches
Q
Health economics evaluates the balance between public health approaches, which focus
on population-level interventions, and
individual patient-centered care
Q
The spread of TB is a public health concern, and strategies that address it at the
community level
can be more cost-effective in the long run
Health Systems Strengthening
P
Strengthening health systems is crucial for effective TB control
P
This includes
investments
in infrastructure, human resources, and health information
systems
P
Health economics helps to identify the most efficient ways to
strengthen health systems
for better TB outcomes
Socioeconomic Determinants of Health
P
The interaction between TB and socioeconomic status is significant
P
Poverty can increase the
risk of contracting TB
and can also result from the costs
associated with the disease
Economic Growth and Health
Ø
Health is a fundamental component of economic development. A healthy workforce is
more productive, which is essential for economic growth
Ø
The article mentions TB's impact on the productive age group (15-45 years), highlighting
the direct connection between
controlling the disease
and the prospects for India's
economic
development
International Collaboration and Knowledge Sharing
Q
Health economics can evaluate how different countries or regions can learn from each
other's successes and failures in TB control, leading to more
cost-effective
global strategies
The Role of Innovation
P
Economic analysis often focuses on the role of innovation in TB treatment and diagnosis,
such as the
development of new drugs
, vaccines, or diagnostic tools
P
Health economics assesses the costs of developing these innovations versus the potential
long-term
savings and health benefits
Conclusion
F
The disease's significant global burden necessitates careful economic consideration to
ensure that limited resources are used in the most effective way to both treat individuals
and prevent the spread of the disease
Q
Addressing TB effectively requires a comprehensive approach that combines medical
treatment with broader
socioeconomic interventions
Q
Health economics provides a framework to evaluate the costs and benefits of various
strategies, aiming to reduce the burden of TB while
making the best use
of available
resources
James R. Chelius and John F. Burton, Jr., (1995), ‘Workers’ Compensation Benefits and
Costs: Who Actually Pays for Workers’ Compensation?’, in Workers’ Compensation
Yearbook
1.
The Economic Burden of Workers' Compensation
«
The document begins with a discussion of the financial impact of
workers' compensation
on employers in the United States, highlighting that the costs exceeded $60 billion in 1991
and represented 2.646 percent of payroll
«
This introduces the concept of economic burden, which in health economics refers to the
total cost society bears due to the presence of a health-related issue, in this case,
workplace injuries
and illnesses covered by workers' compensation insurance
2. Incidence of Costs in Health Economics
«
The document raises the question of who ultimately bears the cost of workers'
compensation—employers, consumers, or
workers themselves
«
This touches on the concept of incidence of costs or
cost-shifting
in health economics,
which examines how the financial burden of healthcare (including
insurance
programs) is
distributed among different
entities
in the economy
2.
Employers' Role in Funding Workers' Compensation
A
This aligns with the concept of employer-financed healthcare, where companies either
purchase insurance
for their employees or self-insure, this is part of the broader discussion
on
funding mechanisms
in health economics
4. Pass-Through Economics
O
The document suggests that employers may pass the costs of workers' compensation to
consumers through
higher product prices
O
This is known as pass-through economics and reflects how health-related costs can affect
the pricing strategy in other markets, influencing the general
cost of living
5. Wage Determination and Compensation
Ü
This concept is related to the theory of compensating wage differentials, which in health
economics refers to the idea that workers are willing to accept lower wages for jobs that
offer
better health benefits
or are less risky
6. Economic Theories Underpinning Research
Ü
Economic theory in health economics provides a framework for understanding how
resources are allocated, how individuals
make choices
under constraints, and how these
choices impact health outcomes and financial burdens
7. The Role of Legal Frameworks in Economic Health Outcomes
6
The document refers to the 1917 Supreme Court case, which upheld the constitutionality
of the New York workers' compensation law
6
Frameworks are crucial in shaping health economics as they determine the rules and
regulations under which health-related
financial transactions and insurance
programs
operate
8. Consumer-Borne Costs in Health Economics
6
The notion that consumers ultimately bear the cost of workers' compensation through
higher product prices
ties into the concept of consumer-borne costs in health economics
6
This reflects the endpoint of cost-shifting where the burden falls on the
end-user
or
purchaser of goods and services
9. Taxpayer Subsidization and Public Policy
Q
The document alludes to the idea that taxpayers may
subsidize workers' compensation
programs, which introduces the concept of public goods and
taxpayer-subsidized
healthcare in health economics
Q
The
distribution
of these subsidies and their relationship to public policy is a significant
area of study within the field
10. The Role of Insurance Carriers
Q
Insurance carriers are mentioned as potentially not covering all expenses, which brings up
the concept of
risk pooling and premium setting
in health economics
Q
It also touches on the financial health of insurance carriers, which impacts their ability to
cover long-term risks associated with workers'
compensation claims
11. Impact on Public Policy
«
Finally, the document argues that perceptions of who pays for workers' compensation
influence public policy
«
In health economics, the interplay between public perception, policy-making, and
economic outcomes is critical, as it shapes
healthcare legislation, insurance mandates
,
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and the overall structure of health systems
Malcolm Gladwell, “The Risk Pool: What’s behind Ireland’s Economic Miracle – and
G.M.’s financial Crisis,”
Pension Plans and Economic Security
«
Gladwell discusses the idea of pension plans and their importance in providing economic
security to workers
«
This is a fundamental concept in health economics as pensions are a form of long-term
savings
that ensure
financial security
for individuals when they are no longer able to
work due to old age or disability
Diversification of Risk
P
The proposal for a regional pension plan suggests the diversification of risk. By pooling
resources across
many small employers
, the risk of any single company failing and being
unable to pay out pensions is mitigated
P
This is a key principle in insurance and is widely used in health economics to manage the
financial risk
associated with
unpredictable health
events
Company vs. Collective Responsibility
P
The tension between company-provided pensions and a more collective approach reflects
differing views on who should
bear the responsibility
for health and retirement benefits
P
This debate is central to health economics, as it pertains to whether healthcare should be
provided by employers, the government, or a mix of both
Private Pension System Crisis:
F
The mention of the private pension system crisis relates to the
sustainability
of health
economics systems
F
The crisis demonstrates what can happen when private entities are unable to fulfil their
financial obligations
for healthcare and pensions, leading to a potential need for
government intervention
Comparative Health Systems
P
Gladwell compares the generosity of the United States' benefits with those of other
industrialized
countries, highlighting the role of government and large groups in
providing insurance
P
This comparison is a key area of study in health economics, focusing on the efficiency,
equity, and performance of different
health system models
Dependency Ratios
P
Dependency ratios, which compare the number of people who are not of working age to
those who are, are important in health economics because they impact the financial
viability
of health systems
P
A high dependency ratio can indicate a greater burden on the working population to
support the young and old, which can
strain public resources
for healthcare and pensions
Demographic Changes and Economic Growth
6
The case of Ireland's economic growth following demographic changes, with a falling
birth rate leading to a lower dependency ratio, showcases the impact of demographics on
health economics
6
The proportion of
working-age individuals relative to dependents
can influence a
country's ability to provide health services and
fund public health
programs
Birth Rates and Economic Policy
°
The lifting of restrictions on contraception in Ireland, which led to a
lower birth rate
,
speaks to the intersection of health policy and economic policy
°
Family planning can have major implications for health economics, affecting workforce
size, dependency ratios, and the
sustainability of health
and social systems
Economic Impact of Health and Pension Benefits
°
The discussion also touches on the economic impact of
health and pension benefits
on
companies, which is a critical issue in health economics
°
The costs associated with providing these benefits can influence
corporate decision-
making
and can have broader implications for the
labor market
and economy
Lecture 5 – Consumer Choice and Demand
Composite good: represents
all other goods
Max U(OG, visits) subject to P
OG
*OG+ P
v
*visits =Y
«
Solution obtained by differentiating: U(OG,visits)+ λ(Y - P
OG
*OG+ P
v
*visits)
Consumer’s equilibrium analysis:
Slope of indifference curve = marginal rate of substitution = price ratio
࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵? =
% ࠵?ℎ࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?
% ࠵?ℎ࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?࠵?࠵?࠵?࠵?
Income elasticity
>0: normal good
Greater than 0 and less than or equal to 1: necessity
>1:
luxury
good
Factor affecting demand of healthcare
Insurance decreases the cost at
time
of purchase
Factors affecting supply of healthcare
Positive: increase in price of related good
Opportunity cost of time makes the demand for healthcare more
elastic
°
If patients have to forego significant income to seek healthcare or if the time commitment
is
substantial
relative to the perceived benefit, they become more sensitive to the time
costs associated with healthcare
°
They might opt to
delay or forgo non-urgent
healthcare services, making the demand
more elastic
°
Small increases in the time cost can lead to relatively larger decreases in the quantity of
healthcare demanded
Graph: effect of a coinsurance rate on healthcare
Lecture 6 – Cost Benefits Analysis for Health Economics
Social
surplus: difference between the maximum consumers are willing to pay and minimum
firms are willing to accept for producing
An allocation of resources is Pareto optimal if it is
impossible to find another allocation
(output level) such that at least one economic agent is made better off and no economic agent
is made worse off
࠵?࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?࠵?࠵?࠵? =
࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?
࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?
External cost: social optimum will have
less output
than perfectly competitive output
External cost diagram:
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Social discount rate is net of inflation (?)
Impacts that result in
redistribution
of income should be ignored, as they are indirect
Lecture 7 – Asymmetric Information and Agency
Adverse selection, a phenomenon in which insurance attracts patients who are likely to use
services at a
higher-than-average
rate, results from asymmetric information because potential
beneficiaries have
better information than the insurer
about their health status and their
expected demand for health care
Akerlof’s
Lemon Principle
Q
Due to the potential consequences of receiving poor-quality care (which can be as severe
as life-threatening complications or death), patients are often risk-averse
Q
As a result, they may be willing to pay a premium for services that they perceive as being
of higher quality or that come with better reputations, even if they can't directly assess the
quality
Q
Leaving
only the lemons behind
Lecture 8 – Imperfect Information
Supplier induced demand as an example of an agency problem
°
Patient (principal) relies on the healthcare provider (agent) for information and
recommendations
on treatments
°
If the healthcare provider stands to benefit financially from more treatments (e.g., through
fee-for-service
payment structures), they may have an incentive to
overprescribe
treatments, tests, or procedures,
inducing
demand that may not be medically necessary
Small area variation:
historical
practices and institutional behaviors shape current decision-
making and operational modes
Capitation: receives payment per patient per unit of time
Q
Healthcare providers receive a
set amount of money per patient
for a defined period of
time, regardless of
how many times the patient
is seen or how extensive the services
provided are
Target Income Hypothesis
6
Desired income level they aim to achieve, which influences their behavior in terms of the
volume and type
of services they provide
6
Once this income target is reached, the hypothesis posits that physicians may be less
motivated to increase their workload or patient throughput because the
marginal utility
of additional income decreases after their target is met
Evans/Benchmark/
Disutility
of Inducements Model: physicians’ problem is to max U=U(p,l)
Q
Subject to physician’s profit line: mQ
0
+ml
Q
Q
0
: This is the
quantity
of services provided without any inducement
Equilibrium will occur
marginal rate of substitution
equals the profit rate
Graph: physician’s response to reduced profit rate
Ø
Flatter profit line indicates a lower profit rate
per additional unit
of service (lower m).
Ø
When the profit rate per service decreases, the physician must provide more services to
achieve the same level of income as before (assuming costs remain constant), which
means that the additional income gained from
each additional service
(ml) is now less
Ø
Mathematically, if the profit rate (m) is reduced, for any given quantity of inducement-
driven services (l), the increase in income (ml) will be smaller
Income effect
Decreased Income: If the profit rate per induced service decreases,
and physicians do not increase the volume of services to
compensate, their overall income from inducements will drop.
This loss in income makes
each dollar more valuable
to the
physician.
Inducement Becomes More Desirable: Despite the lower profit
rate, the physician might be inclined to provide more induced
services in an effort to
maintain their previous income
level. From
this perspective, even though each additional service is less
profitable, the need to
sustain income
might lead the physician to
increase the service volume.
Substitution effect
Profitability of inducements decreases; suppliers have
less
incentive to offer inducement-driven services. Their influence over
their own net income through inducements is
weakened
because
the financial return from inducements is reduced.
Lower Inducement Quantity at Tangency Point: The new tangency
point has a lower inducement quantity because, at the lower profit
rate, the
balance
between net income and disutility has shifted.
Providers will choose to provide fewer inducements since the
additional income earned from each unit of inducement is now
lower
and does not justify the increasing disutility.
Monopoly power: MC=MR
Graph: monopoly model profit maximizing point: increase in advertising
6
Increase in MC, MC curve shifts
upwards
6
If the physician responds to this increased demand by seeing more patients or performing
more procedures, the costs associated with these
additional services
(like staff time,
equipment use, and supplies) will increase the marginal cost of
providing care
Graph:
inefficiency
of misinformation about the MB of healthcare
Horizontal MC curve: cost of providing an
additional unit
of service does not increase with
the quantity of services provided
Lecture 9 – Organization of Health Insurance
US: there is only private insurance provided
by an employer
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Payroll tax:
increase in cost
of using labor inputs
à
decrease in labor demand
Supply Curve Shifts Down
«
Compensation Package Increase: Health insurance effectively increases the total
compensation package for the workers
«
While it adds a cost $z for the employer, for the employees, it's a part of their salary
package
«
Higher Net Wage Equivalent: The provision of health insurance can be seen as increasing
the
net wage
equivalent that workers receive. If workers value the health insurance at its
cost $z, then the supply of labor at any given monetary wage rate increases because the
total compensation (wage plus the value of health insurance) is higher
«
Shift of Supply Curve: In the labor supply curve, which shows the relationship between
the wage rate and the quantity of labor supplied, the addition of health insurance at cost
$z effectively
reduces the wage rate
that workers are willing to accept. This is because part
of their compensation is now coming in the form of health insurance benefits rather than
cash wages. Therefore, the labor
supply curve shifts downward
by the amount $z
Demand for Labor Curve Shifts Left
P
Increased Cost of Hiring: From the employer's perspective, providing health insurance
increases the total cost of hiring an employee. Even if the cash wages do not change, the
total cost now includes the additional cost $z for the health insurance
P
Reduced Marginal Product Value: Employers hire workers up to the point where the
value of the
marginal product of labor equals the marginal cost
of hiring (wage rate plus
any additional costs like health insurance). With the extra cost $z, the marginal cost of
hiring increases, which means the value of the marginal product of labor must increase for
additional hiring to occur
P
Leftward Shift of Demand Curve: Since the value of the marginal product of labor is
unlikely to change just because health insurance is provided, the demand curve for labor
shifts to the left. This is because, at any given wage rate, the
cost of hiring an additional
worker is now higher by $z
Supply Curve Shifts Upward by an Amount Less Than $z
Q
Workers may value the insurance provided at less than its cost $z$. If workers do not fully
appreciate the value of the insurance or if it
doesn't meet their specific
needs, they might
not be willing to reduce their cash wage demands by the full amount of $z$. This
misalignment in valuation can cause the supply curve to shift up slightly
Lecture 10 – Managed Care
Overconsumption: beyond MB=MC
Organized delivery system: association with an
insurance product
MCO steering: send enrollees to providers
in the network
Prospective
à
Concurrent
à
Retrospective
Gatekeeper
NOT Gatekeeper
Provider network
Health maintenance organization
Preferred provider organization
NOT Provider Network
Point-of-service
Fee-for-service
PPO contracts with physicians rarely involve capitation
Benefits of managed care: decrease in prices,
decrease in price discrimination
Supply curve is horizontal: MC=AC
Graph a market with elastic demand:
Each firm will supply whatever quantity is demanded at the market price—provided that this
price covers the marginal cost of production. Since the price
does not change with the quantity
(the firms
cannot influence
the price and will continue to sell at the market price), the market
supply curve appears horizontal
Perfect price discrimination: physician will extract
all the consumer surplus
Graph the differences between managed care and fee-for-service:
Changed incentives in managed care: constrain utilization of services and prices of services
°
Healthcare provider
shares risks with the insurer
, reduces the volume of services they can
provide
Additional Lecture
Weighted social opportunity cost of capital: weights based on contributions of different
sources of resources
࠵?࠵?࠵?࠵? = ࠵?࠵?
!
+ ࠵?࠵? + (1 − ࠵? − ࠵?)࠵?
!
a: proportion of the project resources that displaces
private investment
b: proportion of the resources that are financed by borrowing from
foreigners
(1-a-b): proportion of the resources displacing domestic consumption
i: government’s real long-term
borrowing rate
where p<i<r
rz tends to produce large discount rate estimates, computations are based on
corporate bonds
,
which have risk premium
«
Rate of return that could have been earned had these funds been used in the next best
alternative public sector
project. It accounts for the fact that when government allocates
money to one project, it is foregoing the opportunity to invest that money elsewhere for
potentially beneficial public
services like education, healthcare, or infrastructure.
pz produces discount rates that are too low,
individuals cannot properly account
for long-run
effects of infrastructure on future generations
?
Proxies for a
rate of time preferences
after correcting for inflation and taxes
Social discount rate: postpone small amount of consumption for future consumption
Saving schedule
not sensitive
to interest rate
à
inelastic
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Estimate of social discount rate:
࠵? = ࠵?࠵?
!
+ (1 − ࠵?)࠵?
!
where a= (change in I)/(change in C+I) and (1-a)=(change in C)/(change in C+I)
Highly
investment-oriented
economy: change in C is close to 0, a is close to 1
F
s=r
z
Market equilibrium with distortions
S: supply of funds
Increase in taxes: decrease investment demand and supply of
funds
r
z
: marginal return on investment before taxes = opportunity
cost of forgone investment
p
z
: marginal return on savings
after taxes
i: government’s real long-term borrowing rate
࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?
"
࠵? ࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵? − ࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵? =
࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵? − ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?
࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?
Project financed only by tax:
࠵? =
࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?
࠵?࠵?࠵?࠵? ࠵?࠵?࠵?
Interest payment and transfers between borrowers and lenders:
NOT in calculation
of project
valuation
Depreciation allowances:
tax purposes
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