AI at your side: Is Your Health a Choice? Taking Grossman’s Model Apart with AI

Is your health something that happens to you, or something you choose?

Most people answer that it happens to you. You did not choose your genes, the town you grew up in, the driver who ran the red light, or the virus going around the office. Health can feel like weather, something that arrives and has to be dealt with.

In 1972 Michael Grossman, one of the founders of health economics, wrote down a model with a different and slightly uncomfortable answer. To a large degree, he argued, you produce your own health. You begin adult life with a stock of it, it wears down a little each year, and every year you decide how much to spend keeping it up. The checkup you scheduled or skipped, the hour at the gym or on the couch, the sleep you protected or spent, the vaccine you took or did not: all of these are inputs, and health is what they produce. Seen this way, health is closer to capital than to weather. It is a stock you maintain, like a house or a skill, and the interesting question stops being what happened to you and becomes how much of it you choose to hold.

That idea launched the modern economics of health capital and, like most foundational contributions, it has since hardened into a single diagram in most textbooks (a notable exception is Health Economics by Bhattacharya et al.). Students learn to draw it, reproduce it under exam pressure, and move on. Almost none of them can say where it comes from or what it is really made of.

We take that memorized diagram and rebuild it from the decisions underneath, one at a time, so that by the end the finished curve cannot possibly look as though it fell from the sky. You will have watched it assembled out of your own choices, which is the only version of the model worth carrying around.

This is the third piece in a series that reads one classic paper at a time with AI at your side, in the spirit of the book I wrote with Raul A. Sosa, AI at Your Side: The Student’s Guide to Smarter Learning, forthcoming from Oxford University Press. Here the method earns its keep. Ask a chatbot to explain the Grossman model and it will hand you the last page: the diagram, fluent and confident and of no real use for understanding. A summary of a model you cannot yet derive is only the slogan at higher resolution. Used the other way, as something you build alongside and argue with, the same tool becomes the best sparring partner a student has ever had. I will flag the moments where reaching for it pays off.

Health is capital

Everything that follows rests on one reframe. In the model, health is a stock, and Grossman has it doing three jobs at once. You value it directly, because feeling well beats feeling sick, so it enters your utility, the economist’s term for how well off you are. It is also an input, because a healthy body produces something scarce and valuable, namely time that is not lost to illness. And it is a durable asset, one that lasts, wears down, and can be built back up. Most goods do one of these jobs. Health does all three, which is what makes the model powerful and what makes it easy to get lost in. By the end all three will be pressed onto a single curve, the standing bargain economists make with dimensions to keep a diagram on the page.

The central move in the paper is to separate two things that everyday language runs together: health and health care. Nobody enjoys a doctor’s visit. Nobody wants a colonoscopy, a blood draw, or a statin for its own sake. What you want is health, and medical care is one of the inputs you buy to produce it. The demand for care is a derived demand, in the same way the demand for flour is derived from the demand for bread. That is the first screw to come loose. What looked like the good you were buying is only an input, and the thing you actually care about is something you make yourself.

You do not buy health, you produce it

If health is produced, there must be a production function for it, a recipe that turns inputs into output, and the model writes one down. Each period you add to your health, in what the model calls gross investment, by combining medical care and other market goods, call them M, with your own time, Tₕ. Grossman writes this as I = I(M, Tₕ; E). The E at the end is your education, and it sits slightly apart from the other inputs because it governs how efficiently you turn those inputs into health, a point we will come back to.

Time is where the model bites. You have a fixed number of hours in a year, exactly 8,760 of them, which is 365 days times 24 hours. Every hour goes into one of four uses, working for money, doing the things you enjoy, tending to your health, or lying sick. That last use is pure waste. Sick time is taken away from everything else, and the only way to reduce it is to be healthier. So health repays you in a concrete currency, the hours it keeps you from losing.

This is also the point where the money constraint and the time constraint stop being separate. You buy medical care out of income, income comes from the hours you work, and the hours you can work depend on how many of them illness takes from you. Improve your health and the whole system loosens at once.

One feature of that technology does most of the work later, so let me state it plainly now. When you are very sick, one more unit of health buys back many hours. When you are already well, it buys back almost none. So the extra healthy time you get from one more unit of health, a quantity the model calls G, shrinks as your health grows. Hold on to that fact. It is what will make the curve slope downward once we draw it.

The decision, period by period

Every period, then, you face a choice, and it is an optimization like any other. Given the prices in front of you, your wage w, the price of medical care, the interest rate r, you decide how to divide your time and your money. Two separate decisions live inside that choice, and both matter for what comes next.

The first is about cost. To produce any given amount of health, you can lean on medical care or lean on your own time. A busy surgeon buys the trainer and the concierge doctor. A retiree with time to spare and less money walks an hour a day and cooks from scratch. You settle on the mix where the last dollar spent on care and the last dollar’s worth of your own time buy the same amount of health. That mix is the cheapest way to produce a unit of health, and we can call its price π. Notice that π already has your wage and the price of care folded into it, and already reflects a decision you made.

The second is about quantity. How much health should you hold? To answer it you set what a unit of health gives you against what it costs to produce. A unit of health returns the value of the extra healthy time it creates, which is your wage times the extra hours G, so the benefit is w·G. Set that against π, the cost of the unit, and the whole model is about to fold into a single line. For now we price only this investment payoff, the healthy time a unit of health reclaims, and set aside the direct pleasure of feeling well that was the first of its three jobs. Economists call this the pure investment version of the model, and Exercise 4 puts the missing piece back.

The curve is the compression

Divide the benefit by the cost, and you have the rate of return on a unit of health:

rate of return = (w · G(H)) / π

Economists give this rate a name, the marginal efficiency of health capital, or MEC. Read the pieces slowly. w is the value of an hour of your time. G(H) is the extra healthy time one more unit of health provides. π is what it costs to produce that unit. Plot this rate against your health stock H, and you get the curve in Figure 1.

Figure 1. The MEC curve. At each level of health H, it gives the return on one more unit of health.

Now look closely at what sits inside that fraction, because this is where the argument lives. Every term in it has a history. w is what your labor market already pays for an hour of your time. π is the cost-minimized price of health, which came out of the first decision in the previous section. G(H) is the marginal product of your health stock, the extra healthy time one more unit of it buys back at the level of health you are holding. π is the output of the optimization you just ran, w is the price that optimization takes as given, and G(H) is the technology they act on. So every point on the curve answers a conditional question. If your health stock were H, what would one more unit of it return, given that you had already chosen your medical care, your own time, your hours of work, and everything else as well as you could at today’s prices? Ask that question at every level of H, and the answers, taken together, are the curve you are looking at.

So the curve is no primitive. It is the compressed record of your own optimizing, one height for every possible level of health, each height already assuming you got everything else right.

Why the curve slopes down? Of them, w and π do not depend on your health stock at all. Only G(H) does, and G shrinks as H grows. The entire downward tilt of the curve comes from one plain fact: the sicker you are, the more a unit of health gives back, and the healthier you are, the less. That is all “diminishing returns” has ever meant here.

Where your health settles

That was the demand side. The cost side is shorter.

Holding health is not free, and two things charge you rent on it. First, the money you sink into producing health could have earned the market interest rate r somewhere else, so every unit you hold carries an opportunity cost of r. Second, health depreciates. It wears out at a rate we call δ, and faster as you age, so you have to keep investing simply to stay level. Add the two and the cost of holding a unit of health for a period is r + δ. That is a flat line, the same at every level of health, because it is only the price of tying your wealth up in your own body rather than somewhere else.

Set the return equal to that cost, and the model is finished:

(w · G(H)) / π = r + δ

In plain terms, you invest in health until the return on the last unit equals the cost of holding it. Below that level, health pays more than it charges, so you buy more. Above it, health charges more than it pays, so you let it slide. The level of health where the two are equal is the one you choose, and it finally has a name you understand from the inside: H*.

Only now does the diagram earn its place. The downward curve is your own optimizing, compressed. The flat line is the cost of capital. Where they cross is the amount of health that a person with this wage, this efficiency, and this rate of decay will rationally decide to hold.

Figure 2. The optimal health stock. The downward curve is the MEC from Figure 1. The flat line, r + δ, is the cost of holding health. You hold H*, the level where the two cross.

This is the first natural place to bring in AI, and how you do it decides whether it helps at all. Asking it what the MEC curve is returns a paragraph you could have found anywhere. Handing it your own derivation and telling it to find the leak is a different exercise.

Here is my attempt to get from the two first-order conditions to the condition w·G/π = r + δ. Check each step. Tell me the first place my algebra or my economics goes wrong, and why it matters.

What comes back is not a lecture on Grossman but a finger on the exact line where you confused a stock with a flow or dropped a term, and that is the only kind of correction that teaches you anything.

Reading the world with the curve

The reward for all this machinery is that real patterns become easy to read. Once the diagram is two curves that can move, every fact about health becomes a question of which curve moved and why.

Start with education, the model’s most famous prediction. Educated people, Grossman argues, are more efficient producers of health. The same hour of exercise, the same prescription, the same piece of advice about what actually helps all convert into more health in the hands of someone who knows more. That makes each unit of health cheaper to produce, so π falls and the return w·G/π rises at every level of health. The curve shifts up and out, and the optimal stock rises with it. The educated hold more health, which is intuitive enough. The surprising part is what the model then says about medical care. Because they produce health more efficiently, the educated can reach that higher health with fewer inputs rather than more. The model’s headline prediction is that they are both healthier and spend less on medicine, and it holds unless that added efficiency leads them to want so much more health that they buy more inputs after all. The health half of that prediction is among the most robust findings in all of health economics. A result that looks like a paradox falls straight out of a curve that shifted.

The wage works through the same curve but in its own way. A raise makes an hour of your time more valuable, so a day lost to illness costs you more and health is worth more to you. A raise also lifts π, since your own time is one of the inputs into producing health, but the value of the healthy time you gain rises faster, so the return still climbs and you hold more health. The one contrast with education is on the spending side. Because your time has become expensive, you produce that extra health by buying more medical care and using less of your own time. Education and higher wages both raise health, yet they likely push medical spending in opposite directions, and the model tells you exactly why.

Age is the last of the three. As the years pass the depreciation rate δ climbs, health wears out faster, the flat cost line rises, and the optimal stock falls year after year. The model even writes its own ending. Once the health you would rationally choose to hold falls below the minimum a body needs to keep functioning, a level the model calls Hₘᵢₙ, life stops. Death here is not bolted on from the outside but a consequence of the very same optimization that governed everything before it.

Figure 3. The same picture under two shifts. Left: education makes you a more efficient producer of health, pushing the MEC curve outward, so the optimal stock rises from a lower H* to a higher one. Right: as you age your health depreciates faster, lifting the cost line r + δ, so the optimal stock walks down toward Hₘᵢₙ.

The life cycle is a good place for a second round with AI, because it is exactly where intuition tends to fail. Ask what happens to medical spending as a person ages, and then make the model argue against your first guess. The obvious one is that spending falls, since the optimal stock is falling too. The model says the opposite can hold. As depreciation accelerates, people often spend more on their health even as the stock itself declines, because they are fighting a stronger current just to slow the fall. A good prompt makes AI defend that counterintuitive result and lay out the condition under which it holds, so that you come away with the mechanism instead of the wrong hunch.

The right and wrong way to do this with AI

Look back at what just happened. We took a diagram that students memorize, pulled it back into the decisions it stands for, and somewhere along the way it stopped being a picture to reproduce and became something you could reason with.

It could easily have gone the other way. Ask a chatbot to explain the Grossman model and you get the finished diagram and three neat bullet points about what shifts what, correct and fluent and hollow, the last page again with nothing behind it. What made the difference was using the tool in the opposite spirit. You derived the equilibrium condition and had it catch the step you botched. You asked why the curve slopes down and refused to accept “diminishing returns” as a magic phrase until you could say why one more unit of health does less and less as you grow healthier. You predicted a pattern over the life cycle and let it prove you wrong. The model did not become clear because AI explained it to you. It became clear because AI was the thing you argued with while you explained it to yourself.

That is the whole argument of the book I wrote, and health capital may be the perfect case for it, precisely because the payoff is a single, memorable diagram. A memorable diagram is the easiest thing in economics to carry around without understanding. Taking it apart is the difference between having seen the Grossman model and being able to think with it.

So, back to the question we started with. Is health something that happens to you, or something you choose? The honest answer is both, and the model is unusually precise about the split. You do not choose your genes, your accidents, or the rate at which you depreciate. But given all of that, at every age, you are choosing how much health to hold, and the famous curve is nothing more than the running ledger of those choices. Health is not quite weather. It is a decision made under constraints you did not pick, which is true of almost everything worth understanding.

Final comment

Every great model leaves something out. Grossman’s does too. It largely treats individuals as isolated decision makers, paying relatively little attention to social interactions, behavioral biases, or uncertainty. Later work expanded the model in all of these directions. But none of those extensions make sense until you first understand the original.

Exercises

1. Derive the condition w·G/π = r + δ yourself, starting from the idea that the return on a unit of health should equal the return on any other investment. Then hand your derivation to an AI and ask it to find the first step that is wrong or hand-wavy, and why that step matters. Do not ask it to derive the condition for you.

2. The model predicts that more educated people hold more health but buy less medical care. Ask an AI to construct the assumption under which that prediction reverses. Then decide for yourself whether that assumption is realistic.

3. Take a real decision you made this month: skipping sleep in exam week, buying or skipping the gym membership, walking instead of driving. Name the health stock, the investment, the depreciation, and the return in healthy time. Where on your own MEC curve were you sitting?

4. In the version we built we priced health only through the useful time it produces, setting aside the direct pleasure of feeling well that we opened with. Ask an AI to put that consumption value back in, and have it show you which conclusions survive and which ones, like the clean predictions for education and the wage, get muddied once feeling well is something you value directly.

References:

Bhattacharya, J., Hyde, T., & Tu, P. (2014). Health Economics. Palgrave Macmillan.

Grossman, M. (1972). On the Concept of Health Capital and the Demand for Health. Journal of Political Economy, 80(2), 223–255.

Galiani, S., & Sosa, R. A. AI at Your Side: The Student’s Guide to Smarter Learning. Forthcoming. Oxford University Press.

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*** Disclaimer: I used ChatGPT-5.5. as an editorial and language-refinement tool. The ideas and arguments are entirely my own, and I take full responsibility for them.