eco question

Health Economics ECON 5860 PROF. KURT LAVETTI

DEMAND FOR HEALTH: THE GROSSMAN MODEL

The 3 Roles of Health (H)

Health plays three roles in the Grossman model:

1. A consumption good 2. An input into production 3. A form of stock/capital (an

investment)

Health as a consumption good

Health as a direct input into utility

 Health as a consumption good enters directly into utility

 Single-period Utility at time t Ut= U(Ht, Zt)

 Ht = level of health  Zt= “home good”

 Everything non-health that contributes to utility

 E.g. video games, time with friends, movie tickets

**Note: health ≠ health care  Health care is not explicitly in the utility function

 i.e. Getting vaccines does not provide utility but staying healthy does

Time constraints in the Grossman model

 Divide available time between:  Time spent working: TW

 Leisure time: TZ

 Time spent investing in health: TH

 Time lost to sickness: TS

 Example: In each year there are only 365 days that can contribute to utility:

365 = TW + TZ + TH + TS

Health as an input into production

Producing H and Z

Both Health and Home good Z must be produced with time and market inputs

Ht = H (Ht-1, TtH, Mt)

Zt = Z (TtZ, Jt)

 Mt= market inputs for health H  Ex: gym membership, medical care

 Jt= market inputs for home goods Z  Ex: video game, football tickets

 Today’s health Ht also depends on yesterday’s health Ht-1  This is health’s third role as a stock which we discuss later

Production function of “Healthy Days”

TP (“healthy

days”)

H (Health Stock)

365

• The ultimate health outcome in the Grossman model is “healthy days”. It is reasonable that health stock contributes to healthy days in a decreasing fashion

• As with most production functions, the marginal contribution of inputs declines with each additional unit of input

TS

TW + TZ + TH

PPF in the Grossman model  The production

possibilities frontier (PPF) in this model looks unusual—why?

 Which points on the semi-circle A- E are potentially utility-maximizing choices?

A CORRECT PPF

PPF in the Grossman model

 Point A Hmin: no productive time for work, play, or improvement of health

 Point B  “free-lunch zone”  Small improvements in

health yield large increases in productive time; can increase Z without giving up H

A CORRECT PPF

Choosing optimal H* and Z*

 Someone who values both H and Z chooses a point between C and E in order to maximize their utility

 Chooses point F  U2 is unattainable

given PPF constraints  At U0, an individual

can attain more utility  At F: U1 and PPF are

tangent  H* and Z* are optimal

levels of health and home goods

Health as an investment

The three roles of health (H)

Health plays three roles in the Grossman

Model: 1. A consumption good 2. An input into production 3. A form of stock/capital (an investment)

Lifetime of utility

 On any day, an individual considers not only today’s utility U(H0,Z0) but all future utility as well!

 Health is a stock; some of it carries over each new period  Home good Z is a flow (it lasts for only 1 period)

 δ = individual’s discount rate  A person values utility now more than in the future

 Ω = individual’s lifespan (total number of periods)

Health depreciates over time

Some of yesterday’s health lasts to today but not all of it

Ht = H ((1- γ)Ht-1, TtH, Mt )  γ = rate of depreciation  Recall:

 Ht = health at time period t

 Ht-1 = health from previous period

 TtH = time spent on health in period t

 Mt = market inputs for health (like physician visits, prescription drugs)

MEC curve and investments in health

 Marginal Efficiency of Capital (MEC) curve:

 indicates how efficient each unit of health capital is in increasing lifetime utility

 When level of H is low, small investments have high returns to productive time

MEC Curve is Related to Marginal Benefit of Health Capital

H HA HB

• The marginal benefit of additional health capital is high when health capital is low (HA).

• Marginal benefit is low when health capital is high (HB). • Graph 2 traces out the shape of the marginal benefit curve, which

Grossman calls the “Marginal Efficiency of Capital (MEC)”

Marginal Benefit

HA HB

TW + TZ + TH

TS

TP

365

Marginal Cost of Health Capital • Marginal cost has two components:

• Opportunity cost: r • Rather than investing in health, could save money and

earn interest • Foregone interest on savings is an opportunity cost

equal to market interest rate ‘r’

• Depreciation: γ • Health capital depreciates every period • An investment in health capital this year will decline in

value next year due to depreciation • This is a cost of investing in health capital • Rate of depreciation could depend on things like age

• Both γ and r are exogenous assumptions in the Grossman model (they are not affected by the individual’s decisions).

• If γ and r are constant percentages, what will the marginal cost function look like?

Marginal Cost of Health Capital

Marginal Cost

HA HB

γ +r Marginal Cost

If γ and r are constant the marginal cost of health capital does not depend on H!

Optimal Health Capital

Combining these graphs, optimal health capital (H*) occurs where marginal benefit (MEC) = marginal cost.

Rate of Return

HA HB

δ+r

H*

MEC

Marginal Cost

MB>MC

MB=MC

MB<MC

H

Predictions of the Grossman model

The Grossman model helps explain why we observe:

1. Better health among the educated 2. Declining health among the aging

Health and education

 Suppose well-educated individuals are more efficient producers of health

What hypothesis will this model generate about the relationship between health status (H) and education?

MEC and efficiency of health investment

 Better educated are more efficient at each level of health investment

 MECCollege > MECHS  H*College is higher than H*HS

 MECC = college graduate  MECH = high school

dropout

Predictions of the Grossman model

The Grossman model helps explain why we observe:

1. Better health among the educated 2. Declining health among the aging

Depreciation of health  Recall:

Ht = H ( (1- γ)Ht-1, TtH, Mt )  Depreciation γ is not

constant  γ increases with age  As γ increases, costs

(r + γ) increase and it takes more resources to maintain same level of health

As a result of increasing depreciation γ over time, optimal health H* also declines over time!

Optimal death in the Grossman model

 Because of rising depreciation, there are better investments in the market than the individual’s health

 H* eventually reaches Hmin

 Why would anyone choose Hmin?  How is Hmin utility-

maximizing?

Question:

 Does this mean the level of health spending should decrease as people get older?

Age and the derived demand for medical care (or health inputs)

H

Health Inputs (Medical Care)

HYoung HOld

• Not necessarily: suppose the efficiency of investment also falls as people age

• Then the elderly may have a lower stock of H, but a higher demand for medical care • Model can be

easily adapted to fit reality

Health PFOld

Health PFYoung

Conclusion

 Is health something that happens to us or is chosen?  Grossman model says health is a consequence of

our choices

 Indirectly, people choose when to die in the model  While that may seem far-fetched, Grossman model

a useful framework that can be adapted in many ways to help understand the roles and tradeoffs of health

HEALTH BEHAVIOR AND ECONOMIC MODELS OF ADDICTION

Health Behavior • Many factors that affect health and the

demand for healthcare are based on behaviors or choices that people make

• When/why should policies be implemented to intervene in people’s decision-making?

• What types of economic policies can be used to alter behavior?

Rationales for Public Intervention

• To the extent that the government pays for healthcare, they should care about reducing medical costs driven by behaviors • Taxing negative behaviors • Rewarding positive behaviors • Regulatory restrictions (eg banning advertisement of

cigarettes)

• Policymakers may also be concerned about behavioral decisions for paternalistic reasons • Alter behavior if they believe people are making decisions

based on incorrect information • Anti-smoking ads, cigarette label warnings, requiring warnings on

alcohol about risk of drinking while pregnant, 4 loko ban, etc.

• Can make people better off in cases of addiction

Background Motivation

Source: Cawley and Ruhm (2012)

Background Motivation

Source: Cawley and Ruhm (2012)

Economic Models of Addiction

• Whether or not there are paternalistic reasons for intervening in cases of addiction could depend on what causes addiction

• Imperfectly Rational Addiction Models • Myopic Addiction Models • Rational Addiction

• Time-inconsistent preferences that cause short-sightedness • Right now I really want to quit smoking, but my tomorrow-

self doesn’t agree with my today-self • My 1:00 am self thinks that I should set the alarm clock for

7:00 am, but my 7:00 am self thinks I should set it for 9:00

• In behavioral economics, this is called beta- delta discounting (Laibson 1997)

𝑈𝑈𝑡𝑡 = 𝑢𝑢 𝐶𝐶𝑡𝑡 + β � 𝑛𝑛=1

𝑇𝑇−𝑛𝑛

𝛿𝛿𝑡𝑡𝑢𝑢 𝐶𝐶𝑡𝑡+𝑛𝑛

Imperfectly Rational Addiction Models

𝑈𝑈𝑡𝑡 = 𝑢𝑢 𝐶𝐶𝑡𝑡 + β � 𝑛𝑛=1

𝑇𝑇−𝑛𝑛

𝛿𝛿𝑡𝑡𝑢𝑢 𝐶𝐶𝑡𝑡+𝑛𝑛

• Discount utility tomorrow at rate βδ • Discount utility between future period t and period t+1 at the

rate δ • Standard economic models assume β=1, but what if β<1?

• You have a distinct preference for consumption now, even beyond basic time preferences

Imperfectly Rational Addiction Models

• Assumes that people don’t make decisions “correctly” • Wrong information about facts

• Eg Prior to the 1950s many people didn’t know that cigarettes were bad

• Cognitive limits • If the (hypothetical) utility maximization problem is just too

complicated to solve

• Subjective probability biases: people perceive the risk of very rare events to be much higher than they actually are, and the risk of very common events to be lower than they actually are

Myopic Addiction Models

• What if people become addicted for perfectly logical, rational reasons?

• Three general characteristics of addiction: • Reinforcement: the more you’re done something in the past, the

more you want to do it now

• Tolerance: the effect of consuming something now is lower if you’ve had a lot of it in the past

• Withdrawl: there’s a utility cost if you stop right now

Model of Rational Addiction

Characteristics of Addiction

Source: Cawley and Ruhm (2012)

• Based on these 3 characteristics, consider a “stock of addictive capital” S, such that the more addicted you are, the larger S is

• Suppose that whenever S is higher, you want to consume more • Consumers maximize utility over an additive good C, other

consumption goods Y, and addictive capital S U(C(t),Y(t),S(t))

• The stock of addictive capital depreciates over time at the rate δ

S(t)-S(t-1)=C(t)-δS(t)

• The rational addiction model assumes that consumers are forward looking, and anticipate the effect of consumption on their addictive capital S.

Model of Rational Addiction

Equilibrium in the Rational Addiction Model

• Predictions from this model: • Consumption at any point in time is related to current prices and

past prices (because past prices determine current addictive stock)

• Current consumption depends on anticipated future prices

• Permanent price changes have larger effects than temporary ones

• Long-run price elasticity of demand > short-run price elasticity of demand • The size of the difference increases with addictiveness

Rational Addiction Model