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ECO 7550 More Health Capital

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.

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ECO 7550 More Health Capital

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  1. ECO 7550 More Health Capital

  2. 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.

  3. 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. Rate of Return (%) Size of I (in $)

  4. Marginal Efficiency of Investment (MEI) and 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. Rate of Return (%) Size of I (in $)

  5. 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. Cost of capital = interest rate + depreciation rate Rate of Return (%) Size of I (in $)

  6. 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.

  7. 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 + ). Cost of capital = interest rate (r) + depreciation rate (d) Rate of Return (%) Size of I (in $)

  8. ↓ I may NOT mean ↓ Expenditures Optimum amount of capital MEI Curve • The optimum amount of capital demanded is thus Ko, 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. Cost of capital = interest rate (r) + depreciation rate (d) Rate of Return (%) Expenditures I* Size of I (in $)

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

  10. Equilibria MEI Curve • 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 + ). Increased depreciation rate Cost of capital = interest rate (r) + depreciation rate (d) Rate of Return (%) I** I* Size of I (in $)

  11. 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. Pure investment eq’m Health PP curve Bread

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

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

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

  15. Comparative Statics – Wage MEI Curve • 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. Cost of capital = interest rate (r) + depreciation rate (d) Rate of Return (%) I* Size of I (in $)

  16. One More Example of MEI – Uncertainty MEI • 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. Cost of Capital I* Investment

  17. Uncertainty MEI MEI' • Depends! • An ↑ in I this year will increase health capital next year. If this ↑ productivity, MEI shifts right  Do it (i.e. Invest)! Cost of Capital • 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.) I* Investment

  18. One More Example – Uncertainty • 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.

  19. 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: = Marginal Benefits Marginal Costs Sick time [1] [2] [3] [4]

  20. What does it mean? = Marginal Benefits Marginal Costs [1] [2] [3] [4] [3] Increased health must reduce sick time (-). If not, I = 0. [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.

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

  22. 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?

  23. Rybczynski - A little calculus Let: agIand atIdenote the goods and leisure per unit of Health Investment, I agcand atc 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: agII + agcC = G atII + atcC = T

  24. Solving these equations for I/T and C/T yields: I/T = [atc (G/T) - agc] / [agIatc -atIagc] C/T = [agI - atI(G/T)] / [agIatc -atIagc] We can then solve for: I/C = [atc (G/T) - agc]/[agI - atI(G/T)] x Factor the Denominators x 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) = (agIatc - atIagc) / (agI - atI (G/T))2 Then: d (I/C) / d (G/T)0, as (agI/atI) (agc/atc). d (I/C) / d (G/T) 0, as (agI/atI) (agc/atc). agI/atI = (goods/leisure ratio)I agc/atc = (goods/leisure ratio)C.

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

  26. 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.

  27. BMI Health analysts usually measure obesity in terms of Body Mass Index, or BMI, with the formula . BMI BMI Calculator

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

  29. http://www.cdc.gov/nchs/data/databriefs/db82.pdf

  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.

  31. 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.

  32. 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.

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

  34. 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

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

  36. 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

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