ECO 7550 More Health Capital

The Demand for Health Capital Cost of capital, in terms of foregone resources (for health capital, both time and money) is a supply concept. Other needed tool is the concept of the marginal efficiency of investment, the MEI, a demand concept which relates the return to investment to the amount of resources invested.

Marginal Efficiency of Investment (MEI) and Rate of Return The MEI can be described in terms of the X-ray machine example. A clinic which does considerable business may wish to own more than one such X-ray machine. How many? The clinic management may logically consider them in sequence. Size of I (in $) Rate of Return (%)

The first X-ray machine purchased (if they were to buy only one) would yield a return. Suppose that return each year was $100,000. We can also calculate the rate of return, which would be $100,000/$500,000 or 20% per year. They would buy this X- ray machine if it covered its opportunity cost of capital and the depreciation. Size of I (in $) Rate of Return (%) Marginal Efficiency of Investment (MEI) and Rate of Return

Management would choose to own the first X-ray machine as long as the rate of return, 20%, was greater than the –interest rate (the opportunity cost of capital) –plus the depreciation rate. Size of I (in $) Rate of Return (%) Marginal Efficiency of Investment (MEI) and Rate of Return Cost of capital = interest rate + depreciation rate

Marginal Efficiency of Investment If they considered owning two X-ray machines, they would discover that the rate of return to the second X-ray machine was probably less than the first. Suppose that a clinic buying only one X-ray machine would assign it to the highest priority uses, those with the highest rate of return. If they add a second X-ray machine, then logically it could only be assigned to lesser priority uses (and might be idle on occasion)  lower rate of return than the first. Clinic would also purchase the second X-ray machine only if its rate of return was still higher than interest plus depreciation.

Decreasing MEI Let the marginal efficiency of investment curve, MEI, describe the pattern of rates of return, declining as the amount of investment (measured on the horizontal axis) increases. The cost of capital, that is, the interest rate plus the depreciation rate, is shown as the horizontal line labeled (r +  ). Size of I (in $) Rate of Return (%) Cost of capital = interest rate (r) + depreciation rate (  )

Optimum amount of capital The optimum amount of capital demanded is thus K o, which represents the amount of capital at which the marginal efficiency of investment just equals the cost of capital. Like the mgl efficiency of investment curve in this example, the MEI curve for investments in health would also be downward sloping. Size of I (in $) Rate of Return (%) I* MEI Curve Expenditures ↓ I may NOT mean ↓ Expenditures Cost of capital = interest rate (r) + depreciation rate (  )

Diminishing Marginal Returns This occurs because the production function for healthy days (Figure 7.4) exhibits diminishing marginal returns. Health Inputs Healthy Days 365 Total Product

Equilibria Cost of capital for health would similarly reflect the interest rate plus the rate of depreciation in health. Person’s health, like any capital good, will also depreciate over time. Thus the optimal demand for health is likewise given at the intersection of the MEI curve and the cost of capital curve, (r +  ). Size of I (in $) Rate of Return (%) Cost of capital = interest rate (r) + depreciation rate (  ) I* MEI Curve Increased depreciation rate I**

Pure Investment and Pure Consumption Models Do we invest in health because it makes us feel good, or do we invest in health because it makes us more productive? If all we care about is the money we can earn, then all we care about is bread. We have vertical indifference curves. We want only the amount that will allow us to earn as much as we can. Health Bread PP curve Pure investment eq’m

Pure Investment and Consumption Models If all we also care about health, we get more conventional indifference curves. Health Bread PPP Less bread -- more health Pure investment eq’m

Comparative Statics – Age Age  What happens to MEI? Why? Size of I (in $) Rate of Return (%) Cost of capital = interest rate (r) + depreciation rate (  ) I* MEI Curve

Comparative Statics – Education Higher Education  What happens to MEI? Why? Size of I (in $) Rate of Return (%) Cost of capital = interest rate (r) + depreciation rate (  ) I* MEI Curve

Comparative Statics – Wage Wage  What happens to MEI? Why? But what if investment has a large wage component? As drawn the impact is positive, but mathematically it is ambiguous. Size of I (in $) Rate of Return (%) Cost of capital = interest rate (r) + depreciation rate (  ) I* MEI Curve

One More Example of MEI – Uncertainty What is impact of increased uncertainty. Some models say I ↑. Others say I ↓. Let’s look ex ante. You’re uncertain about the future. You can invest in I, or in F (non-health financial asset), which by assumption is less risky. What do we do this year. Investment Cost of Capital MEI I*

Uncertainty Depends! An ↑ in I this year will increase health capital next year. If this ↑ productivity, MEI shifts right  Do it (i.e. Invest)! Investment MEI I* MEI' An ↑ in I will increase health capital next year. If this does NOT ↑ productivity, you move down MEI curve  Don’t do it (i.e. Don’t Invest.) Cost of Capital

If on net, sum of the impacts is positive, uncertainty increases health investment. If on net, sum of impacts is negative, uncertainty decreases health investment. One More Example – Uncertainty

So, what does Grossman tell us? How resources are allocated over time. How resources are allocated in any given period. Grossman focuses on the first. Ultimately the math is complex but it comes to the equation: [1][2][3][4] Marginal BenefitsMarginal Costs = Sick time

What does it mean? [3] Increased health must reduce sick time (-). If not, I = 0. [1][2][3][4] Marginal BenefitsMarginal Costs = [1] Valuation of health as a consumption good. Numerator (-) refers to increased utility that health buys. Denominator (+) tells about the increased income from financial assets (nonwage income), and what you can buy with it. [2] Increased labor income (-)  pure investment effect [4] Cost of capital * amount of capital.

Edgeworth Boxes and Constant Returns An a%  in goods and leisure  an a%  in health and home good Health Leisure Expansion path for health Expansion path for home good Think about CRTS? What does the length of the ray mean?

Edgeworth Boxes and Increases in 1 Factor An a% increase in goods  an  in goods-intensive output (here, health), but a  in home good. Why?

Rybczynski - A little calculus Let: a gI and a tI denote the goods and leisure per unit of Health Investment, I a gc and a tc denote the goods and leisure per unit of Home Good, C These coefficients will vary with the relative factor prices {Leisure - wage rate; Home good - out-of-pocket price}, but since a given commodity price ratio (e.g. Health Investment/Home Good) uniquely determines a factor price ratio, these coefficients will be constants at the given commodity price-ratio (why?). Denoting the total amounts of goods and leisure available as G and T respectively: a gI I + a gc C = G a tI I + a tc C = T

Solving these equations for I/T and C/T yields: I/T = [a tc (G/T) - a gc ] / [a gI a tc -a tI a gc ] C/T = [a gI - a tI (G/T)] / [a gI a tc -a tI a gc ] We can then solve for: I/C = [a tc (G/T) - a gc ]/[a gI - a tI (G/T)] This is the ratio of commodity outputs as a function of the goods/time ratio. Differentiating (I/C) with respect to (G/T) yields: d (I/C) / d (G/T) = (a gI a tc - a tI a gc ) / (a gI - a tI (G/T)) 2 Then: d (I/C) / d (G/T)  0, as (a gI /a tI )  (a gc /a tc ). d (I/C) / d (G/T)  0, as (a gI /a tI )  (a gc /a tc ). a gI /a tI = (goods/leisure ratio) I a gc /a tc = (goods/leisure ratio) C. x x Factor the Denominators

Income Effects As drawn, I is more mkt.-intensive. An  in G leads to relatively large  in I. Bread Invest. Time $

Obesity – An Application of Human Capital A leading risk factor for heart disease, hypertension (high blood pressure), certain cancers, and type-2 diabetes. According to reports from the CDC in 2012, over one third of U.S. adults (more than 72 million) people and 17% of U.S. children are obese. From 1980 through 2008, obesity rates for adults doubled and rates for children tripled. Obesity describes health capital: –may make the body less productive, –more susceptible to disease, and –possibly cause it to depreciate more quickly.

BMI Health analysts usually measure obesity in terms of Body Mass Index, or BMI, with the formula. CategoryBMI range Severely underweightless than 16 Underweight16 to 18.5 Normal18.5 to 25 Overweight25 to 30 Obese Class I30 to 35 Obese Class II35 to 40 Obese Class III40 and above BMI BMI Calculator

2000 Obesity Trends* Among U.S. Adults BRFSS, 1990, 2000, 2010 (*BMI 30, or about 30 lbs. overweight for 5’4” person) No Data <10% 10%–14% 15%–19% 20%–24% 25%–29% ≥30%

Yaniv, Rosin, and Tobol Calories are expended in both in physical activity and when the body is at rest. The rest component, known as Basal Metabolic Rate (BMR), is the largest source of energy expenditure, reflecting blood circulation, respiration and daily maintenance of body temperature. Differing BMRs among individuals indicate why one person can “eat like a horse” and gain little weight, while another may gain weight with far less intake of food.

Obesity – Economic Theory Weight gain as the outcome of rational choice that reflects a willingness to trade off some future health for the present pleasures of less restrained eating and lower physical activity. “Diets” reverse this.

Model Overweight individuals can determine consumption of junk-food meals, F, and healthy meals, H. They may also choose their level of exercise, x. The model defines the weight gain during a period, or obesity, S, as: S = δF + εH − μx − BMR YRT develop the model showing that taxes on junk food (reducing consumption), or subsidies to healthy food (increasing its consumption) could have important impacts on formation of health capital.

Why has obesity increased. Cutler, Glaeser, and Shapiro (2003)

Changes in the time costs of food production Vacuum packing, improved preservatives. Mass preparation –French fries are a pain to make at home –Quick and easy at the restaurants –Food professionals and economies of scale

Time Costs by Group Cutler, Glaeser, and Shapiro (2003) 104.4

References Cutler, David M., Edward L. Glaeser and Jesse M. Shapiro, “Why Have Americans Become More Obese?” Journal of Economic Perspectives 17 (3): 93–118 Yaniv, Gideon, Odelia Rosin, and Yossef Tobel, “Junk-food, Home Cooking, Physical Activity and Obesity: The Effect of the Fat Tax and the Thin Subsidy,” Journal of Public Economics 93 (2009): 823–830