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ECO 7550 - Lecture 4
Grossman Model
Chapter 7
Grossman Model• Labor-Leisure Choice
– Labor Leisure Trade-off– Optimization in a Single Time Period– What is Impact of Health? (A> Shifts out Budget Constraint)
• Investment Decision– Book example– Cost of Capital– Optimal Investment Rule
• Grossman's Model– How do we allocate resources to health and non-health activities in a
given period?– How do we allocate resources to health and non-health activities over
time?
There are lots of examples,but the “teeth” story (9/4/2009)is a good one.
How to Manage Dental Costs, With or Without Insurance
By WALECIA KONRAD
Published: September 4, 2009
http://www.nytimes.com/2009/09/05/health/05patient.html?hpw
100 million without dental coverage
• Much has been said and written about the tens of millions of Americans without health insurance. But often overlooked in these discussions is another vital medical statistic: more than 100 million Americans go without dental coverage.
• Many employer-sponsored health care plans do not include dental insurance, and those that do will typically offer only limited benefits. Individual private insurance is often too costly to be feasible. And Medicaid and Medicare offer only limited safety nets.
35% have not visited a dentist in last 12 months
• For most of people, a toothache that turns into an expensive procedure like a crown or implant means thousands of dollars out of pocket. Routine checkups, cleanings and fillings can set you back hundreds. No wonder 35% of Americans have not visited a dentist in the last 12 months, according to a recent Gallup report.
• Even if you’re fortunate enough to have some kind of coverage, you have probably discovered just how little it pays if you have big problems. Most dental policies pay for preventive care like twice-a-year checkups, but cover only a fraction of higher-cost procedures like root canals.
• Even fillings can get short-changed, if the insurer decides the tooth-colored filler the dentist used was too “cosmetic” for the pothole being patched.
Without Dental Insurance
• DISCOUNT NETWORKS If you do not have group dental insurance through your employer, there are very few viable insurance alternatives, unfortunately. Paying the premiums for individual dental insurance, Dr. Wolff said, is almost always unaffordable. “In most cases, you’ll end up paying as much or more as you would if you pay for treatment out of pocket,” he said.
• Some discount networks have formed to fill the void. Consumers pay roughly $100 to $200 a year in exchange for 15 to 50 percent discounts on service and treatments from participating dentists. “Be sure to compare plans carefully,” said Ms. Rogers of Oral Health America. And, she added, make sure the discounts you are likely to use will be enough to cover the annual fee — and look carefully for any limits and restrictions.
The Economics – Health Capital
• Your body is like a truck (!?)
• You invest!• MEI – mgl efficiency
of investment• User cost of capital.• Deferred Maintenance?
MEI = Mgl Efficiency of Investment
Health Investment
Cost,Returnin %
User Cost
I*
Health CareDietExerciseEnvironmentIncomeTime
Health Outcomes Healthy days: Physical Health Mental Health Activity Health Limitations
Health Inputs
Health Capital Stock Over Time
Health OutputsEach Year
0
5
10
15
20
25
30
1 2 3 4 5 6 7 8 9
Time Period
Investing in Health Capital
Change in healthstock implies differinglevels of investment.
Demand for Health Care as Derived from Demand for Health
Early work found that some of the things that we might have expected, did not necessarily occur. If we look at the demand for medical care inputs, we might expect that some fairly normal types of things would occur. If we do:
QD = QD (p, y, Educ, Age, ...)- + + ?
we would expect some usual signs.
In fact, often the income effects were small, and the age and education effects were ambiguous. This suggested that we should look at some more sophisticated models of what was going on. Lots of people who were working with Gary Becker were looking into the various allocations of labor and leisure time, as well as with market goods. Grossman was one of them.
Labor-Leisure Tradeoff
• Let's start first with some review of the labor-leisure trade-off.
• In the simplest case, we can speak of an individual with 365 days/year. However, the individual is typically sick 10 days per year, so there is only 355 days available.
Leisure
Inco
me
355
slope related to (after-tax) wage rate
wageincome
Work
0
Comparative Statics
• Increase in dividend income.
Leisure
Inco
me
355
slope related to wage rate
Work
wageincome• Unambiguous decrease
in work. Increase in leisure. Why?
Comparative Statics
• Increase in wage rate
Leisure
Inco
me
355
slope related to wage rate
Work
wageincome• Income effect is positive.
Why? Substitution effect is negative. Why?
How health comes in
• Even within this simple diagram, we might consider the impacts of improved health. What are they?– A.1> More healthy time (shifts out LL curve)– A.2> Increased productivity (increases wage)
• This kind of analysis suggests that we want to consider a whole set of individual decisions about allocating resources. Within a given period, we want to ask:– amount of labor, leisure, income– division of leisure into health and non-health activities– division of income into medical and non-medical goods– combination of time and goods into health and “bread”– how these vary over time
Discounting and the Evaluation of Health Care Investments
• Since the investment aspect to health expenditure is critical to the model of demand for health capital, it is appropriate to discuss the evaluation of investments. Economists are often asked to compare investments that provide different streams of income over a number of periods.
• Why, for example, should George pay for a physical check-up (Investment H), when instead he can have his car serviced (Investment S) for the same cost.
Evaluating Investments
• Compare Investment H, which provides $20 at the end of Year 1, and $20 at the end of Year 2, with Investment S, which provides $28 at the end of Year 1, and $11 at the end of Year 2.
a. Interest rate = 5%
Health (H) Return Car (S) Return
Period 1 20 Period 1 28
Period 2 20 Period 2 11
PDV 37.19 PDV 36.64
Health has a higher PDV!
DIS
Evaluating Investments
• Compare Investment H, which provides $20 at the end of Year 1, and $20 at the end of Year 2, with Investment S, which provides $28 at the end of Year 1, and $11 at the end of Year 2.
b. Interest rate = 15%
Health Return Car Return
Period 1 20 Period 1 28
Period 2 20 Period 2 11
PDV 32.51 PDV 32.66
Car has a higher PDV!
Investment Over Time - (Cost of Capital)
Since health is a capital good, it is necessary to understand the cost of capital as well as the capital good demand process. A health clinic, for example, purchases hundreds of thousands of dollars of X-ray equipment. The return to the X-ray equipment is in the future earnings that ownership of the equipment can provide.
Suppose that an X-ray machine costs $500,000, and that its price does not change over time. Suppose that the annual income attributable to the use of the X-ray machine is $100,000. Is this a good investment?
What did the capital cost (e.g. what did we GIVE UP because we purchased the capital?)
How to consider: Suppose that instead of purchasing the X-ray machine the clinic could have put the $500,000 in a savings account, at 5 percent interest, yielding:
Cost of Capital
500,000 * 1.05 = 525,000 , at the end of Year 1.
525,000 * 1.05 = 551,250 , at the end of Year 2.
551,250 * 1.05 = 578,810, at the end of Year 3.
578,810 * 1.05 = 607,750, at the end of Year 4.
607,750 * 1.05 = 638,140, at the end of Year 5.
For the investment in an X-ray machine to be desirable by these criteria, it should provide at least $138,140 in incremental revenue over the five years.
Cost of Capital
The problem is more complicated, however, because most capital goods depreciate over time. Suppose that the clinic knows that the X-ray machine will wear out (or depreciate), so that after five years, it will be worth only half its original value.
The clinic must earn enough not only to cover the opportunity cost from the bank, but also to maintain the value of the machine. For the investment to be worthwhile, then, it must not only earn the competitive 5 percent return each year, but it must also provide enough return to cover depreciation of the machine.
Depreciation
• We usually tell silly stories, “the one hoss shay”• Applies of course to other goods, and the
depreciation may be economic, not necessarily physical.
• Consider desktop computers or printers. What is a 5 year old computer worth? Why?
• If we do not put aside funds to replace it, it will be economically useless after 5 years.
• Why?
Cost of capital
This suggests that the cost of holding this capital good for any one year, as well as over time, will equal the opportunity cost of the capital (interest foregone) plus the depreciation (deterioration of value). Had the price of the asset changed, leading to capital losses or gains, this feature too would have to be considered. How do we consider this?<A> If there is an expected capital gain, we expect a lower cost of holding the capital.
