ECO 7550 More Health Capital

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ECO 7550 More Health Capital
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The Demand for Health Capital

• Conventional economic analysis provides a
  powerful conceptual apparatus by which to analyze
  the demand for a capital good.
• The cost of capital, in terms of foregone
  resources (for health capital, both time and
  money) is a supply concept.
• The 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.

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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 )
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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 10,000.
• We can also calculate the rate of return, which
  would be 10,000/50,000 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 )
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Marginal Efficiency of Investment (MEI) and Rate
of Return

• In terms of rates, 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 )
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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.
• To understand this, consider 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 were to add a second
  X-ray machine, then logically it could only be
  assigned to lesser priority uses (and might be
  idle on occasion). Thus it would have a lower
  rate of return than the first.
• The clinic would then purchase the second X-ray
  machine as well, only if its rate of return was
  still higher than interest plus depreciation.

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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 )
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Optimum amount of capital
? I may Not mean ? Expenditures
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 )
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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
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Equilibria

• The cost of capital for health would similarly
  reflect the interest rate plus the rate of
  depreciation in health.
• A 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 ?).

MEI Curve
Increased depreciation rate
Cost of capital interest rate (r)
depreciation rate (d)
Rate of Return ()
I
I
Size of I (in )
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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 eqm
Health
PP curve
Bread
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Pure Investment and Consumption Models

• If all we also care about health, we get more
  conventional indifference curves.

Pure investment eqm
Health

• Less bread -- more health

PPP
Bread
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One More Example Uncertainty
MEI

• Some models say I ?. Others say I ?.
• Lets look ex ante.
• Youre 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
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One More Example Uncertainty

• Depends!
• An ? in I this year will increase health capital
  next year. If this ? productivity, MEI shifts
  right ? Do it!

MEI
MEI'
Cost of Capital

• An ? in I will increase health capital next year.
  If this does NOT ? productivity, you move down
  MEI curve ? Dont do it.

I
Investment
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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.

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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
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What does it mean?

Marginal Benefits
Marginal Costs
1
2
3
4
3 Increased health must reduce sick time (-)
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.
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Edgeworth Boxes and Constant Returns
Leisure
Health

• An a ? in goods and leisure
• an a ? in health and home good

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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?

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Rybczynski - A little calculus
Let agI and atI denote the goods and leisure per
unit of Health Investment, I agc and 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.
Denoting the total amounts of goods and leisure
available as G and T respectively   agII agcC
G   atII atcC T
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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
x
This is the ratio of commodity outputs as a
function of the goods/time ratio.   Differentiatin
g (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.
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Income Effects
As drawn, I is more mkt.-intensive.
An ? in G leads to relatively large ? in I.
Invest.

Bread
Time