Nonprofits

© Allen C. Goodman 2013

Short primer on nonprofit hospitals• Q: How many nonprofit hospitals are there in the United

States?

• A: In 2008, of 5,815 community hospitals (excludes psychiatric and long-term), 2,923 (50.3%) were nonprofit, 1,105 (19.0%) were state/local, so less than 17% (982) were for profit.

• Q: Are Michigan hospitals nonprofit?

• A: Until recently, all of Michigan's 146 acute care facilities are nonprofit. The state has a few private, specialty hospitals for psychiatric and other special services, but they are not general hospitals.

• DMC was bought by Vanguard (now Tenet, which is nominally for-profit) but the concessions they are looking to get (tax relief for example) would make them look like non-profit hospitals.

Public Goods – Why?We go through several discussions. I'll reiterate the Weisbrod

discussion regarding the public good.

It's helpful to derive a public good equilibrium. My favorite way is a simple one where we have a social welfare function in which:

W = W(U1, U2, U3, ...) = Weighted Σ Ui for a community of individuals.

We must decide how much public good G to make. In the pure sense, the public good is nonexcludable and nonrival.

Ui = Ui (xi , G) - Each person gets some xi and all get G.

X = xi = f (G)

f' < 0.

Public Goods

So, optimizeW = wiUi (xi, G) + { xi - f(G)} (1)

w.r.t. xi

W/xi = wiUix + = 0. (2)

W/G = wiUiG - f' = 0 (3)

From (2)wi = -/Ui

x Insert into (3)

W/G = UiG/Ui

X + f' = 0 (3)Factor out , and we get:

UiG/Ui

X + f' = 0 MRSGX = -f' = MRTWell-known Samuelson condition.

w1 = -/U1x

w2 = -/U2x

w3 = -/U3x

Etc.

Optimum

• The condition above tells you the optimum.

• It doesn’t necessarily tell you how to get it.

G

X

1

0

?X*1

?X*2

G*

2

Optimum

• The condition above tells you the optimum.

• It doesn’t necessarily tell you how to get it.

G

X

1

2

0

?X*1

?X*2

G*

Bread and Public Health

• Suppose that we live in a suburb.

• Suppose there are 5 residents. Each one earns $50,000.

• They can spend it on bread, or PH.

50

50

Bread

PH

PrefersBread

PrefersPH

Bread and Public Health (PH)

• They have to pick a tax level that each one of them will pay.

• If they decide on $10,000, each will pay $10,000.

50

50

Bread

PH

PrefersBread

PrefersPH

Bread and PH

• Let’s add a few more “identical” people.

50

50

Bread

PH• We have five

possible levels of “PH”

p1

p2

p3

p4

p5

Bread and PH

• Alternatively, individuals 1-5 are willing to give up different amounts of bread to get PH resources.

50

50

Bread

PH

• We have five different levels of taxes.

p1

p2

p3

p4

p5

• Suppose she promises p5. Person 5 is happy (he didn’t want much). But everyone else wanted more. So politician loses election 4-1.

How do we decide?

• Consider a politician. She has to win an election, and he has to get enough votes by promising the right amount of PH resources

50

50

Bread

PH

1

2

3

4

5

p1

p2

p3

p4

p5

How do we decide?

50

50

Bread

PH

• Suppose she promises p4. 1, 2, and 3 are happier because they’re getting closer to what they want. But he’ll still lose 3-2.

1

2

3

4

5• Suppose she now promises p3.

She’ll win the election because Persons 1 and 2 are happier yet, and Person 3 is happiest, he’s getting exactly what he wants.

p1

p2

p3

p4

p5

This outcome will beat any other in a head-to-head contest.

If you don’t believe me ...

50

50

Bread

PH

• Suppose another politician promises p2. Person 3 won’t be happy anymore because you’re providing MORE PH resources than he wants … so he’ll vote against it.

• KEY POINT !!! The median voter is decisive. Eq’m PH will be at p3. Each voter will pay b3 in taxes and get p3.

1

2

3

4

5

b3

p1

p2

p3

p4

p5

What does median voter model say?

• If you have some number of jurisdictions, one can argue that the levels of public health, schools, fire protection, police protection are broadly consistent with consumer preferences.

• Is it perfect?– No, not all citizens vote.– If there are a lot of issues, the same citizen is not likely to be

the median voter on every issue.

• When you get to the median voter result, there may still be some who would prefer that more be provided. They may choose to give additionally through nonprofit operations.

Non-Profit Institutions

• Why do we have them?– Weisbrod: People who want more public goods,

beneficial externalities, want a means to provide it (e.g. hospitals, charity)

– Hansmann: Contract failure (how do we evaluate hotels v. nursing homes).

• Provide quality and quantity.• What kinds of motivations do they have, if

profit isn’t one of them?

Quality and Quantity

= TR - TC

= p (s, n) n - c (s, n)

s = quality,

n = quantity

Setting = 0:

p (s, n) n = c (s, n)

Quantity n

$p (s1, n)

c (s1, n)

p (s2, n)

c (s2, n)

p (s3, n)

c (s3, n)

n1 n3 n2

Quality and Quantity

Differentiating fully

ps n ds + pn n dn + p dn = cs ds + cn dn

Collecting terms:

(p + pn n - cn) dn = (cs - ps n) ds

[p(1+1/e) - cn] dn = (cs - ps n) ds,

where e is the elasticity of demand.

ds/dn = [p(1+1/e) - cn] / (cs - ps n)

Assume that ps > 0, cs > 0, cn > 0, pn < 0.

If we have linear demand curves then pn is constant.

Quality and Quantity

ds/dn = [p(1+1/e) - cn] / (cs - ps n)

At low n, denominator is positive since psn is small (or 0), and cs > 0. The numerator is positive since it reflects marginal revenue minus marginal costs. So ds/dn > 0.

As n , denominator becomes negative, so we have (+)/ (-) < 0. So ds/dn < 0.

Quantity n

Qua

lity

s

ds/dn > 0ds/dn < 0

Quality and Quantity

ds/dn = [p(1+1/e) - cn] / (cs - ps n)

At low s, cs is small. If we start with both small s and small n, then psn may be small, and we may have a positive denominator. The numerator is positive since it reflect marginal revenue less marginal costs – here ds/dn > 0. If psn is large, the denominator is negative. So ds/dn < 0.

Quantity n

Qua

lity

sds/dn > 0

ds/dn < 0

Where do we end up?

Suppose that nonprofit managers care only about quality (A).

Quantity n

Qua

lity

s

A

Suppose that nonprofit managers care only about quantity (B).

BSuppose they care about both (C).

C

Let’s maximize utility

L = U(N,S) + [P (N,S) N - C (N, S)]L/N = UN + (PNN + P - CN) = 0. (C.1)L/S = US + (PSN - CS) = 0. (C.2)Equating , we get:

UN/US = (PNN + P - CN) / (PSN - CS).or: UN/US = [P(1+1/) – CN]/(PSN - CS).This, of course, gives us our tangency. Let's look at

whereUN = 0. This gives horizontal indifference curves, and

suggests that P [1+(1/ )] = CN.

This is the monopolist's cost mark-up.If US = 0, we have vertical indifference curves, and we

get a different optimum.

A Phelps Observation

UN + (PNN + P - CN) = 0.

If we hold services constant, rearrange C.1 (previous slide) to get a first order condition vis-a-vis pricing, such that:

P = (CN - UN/) [/(1+)]. If UN = 0, then P = CN [/(1+)]. Normal monopoly markup.Generally, we would expect ≤ -1. (Algebraically - Why ???).

BUT:UN/ = MUN/MU , implying that = -P/(P – CN + UN/)However, if the utility function of the hospital sufficiently emphasizes

quantity of output through UN, then the hospital will willingly operate in the realm of inelastic demand ( approaches 0), and indeed might even willingly charge a negative price (bribe [or subsidize] people to use the service) under some situations.

What if N is really important?

A Phelps Observation

Pauly-Redisch

What if there is a way to maximize profits/person?

NARP = [p Q(M) - other factor costs]/M.

Differentiate w.r.t. M pQ'/M - pQ/M2 = 0.

pQ' = pQ/M

Simply, MP = AP.

In contrast, with open staff, physicians will enter up to level M0.

Number of staff physicians, M

Physician Income

Net Ave. Rev., N

Supply curvefor physiciansS.

S

M*

Ymax

MP

M0

P-R v. Newhouse

How does this relate to the Newhouse model? Go back and simply set up the optimization, where rather than 0 profits, the constraint is now:

= p (s, n) n - c (s, n), where can be positive, if there is profit maximizing behavior. First order conditions are the same, because we've just put in a constant.

Quantity n

Qua

lity

s

= 0

= 1

2

3

max

So, Pauly-Reddisch hospital produces less.

With competition!

Demand at any hospital will decrease

At previous output they can’t cover costs.

Hence output must fall

Leads to 0 profits for all.

Quantity n

Qua

lity

s

= neg

= neg

neg

neg

0!

Think of this as ahill on an island. Ifthe water level rises, at some point,only the peak willbe safe

Frech on Nonprofits

• Are they inefficient?• If you put constraints on the

amount of wealth managers can take out of ownership, you may lead to less efficient use of resources.

• Simple Model

Nonpecuniary benefits n

Wea

lth w

U (w, n)

ww

n0 n1

Frech on Nonprofits

1 + (Un/Uw) (n/w) - /Uw = 0.

-(Un/Uw) = (w/n) (1 - /Uw).

-(Un/Uw)/ (w/n) = (1 - /Uw).

Nonpecuniary benefits n

Wea

lth w

U (w, n)

ww

n0 n1

[ , ( )] ( )U w n w w w

0

w

nUU

w nw

How do non-π and for-π co-exist?

• Look first at the “traditional” market model.

D S

Q

$$

qmktfirm

p*p*

AC

• In the LR, the “marginal” firm will produce output q*.

q*

Lakdawalla-Philipson, 2006

How do non-π and for-π co-exist?

• Here, the for-π firm faces constraint, π ≥ 0

D S

Q

$$

qmktfirm

p*p*

AC

q*

• Non-π firm faces constraint π + D ≥ 0. D = donations. Entry for non π

Lakdawalla-Philipson, 2006

How do non-π and for-π co-exist?

D S

Q

$$

qmktfirm

p*p*

AC

q*

Entry for non π

• For-π firms enter or leave as we move up and down industry supply curve.

• With enough non-π firms, the industry average cost minimizes at a low cost, driving out for-π firms.

• Capital to non-π provided at negative interest rates, since they do not require interest or principal payments.

Lakdawalla-Philipson, 2006

Non ’s

How do non-π and for-π co-exist?

D S

Q

$$

qmktfirm

p*p*

AC

q*

Entry for non π

• So, in the LR, the for-profits are the marginal firms, and their cost structure determines the market equilibrium price.

Lakdawalla-Philipson, 2006

• If there is regulation of hospital cost structures, the hospital effects are determined by the for-profit hospitals that enter and leave.

Feature: Why are RNs' Wages Higher in Nonprofit Nursing Homes?

Holtmann and Idson (1993) explain why Registered Nurses (RNs) are paid higher wages by non-π than by for-π nursing homes. As described above, nonprofits are formed in response to patients' informational limitations in assessing quality. Specifically, because of patients' difficulties in distinguishing among nursing homes of varying quality, the market may fail to produce high quality nursing homes.

RNs seem to receive higher wages in the non-π nursing home sector. Earlier studies (for example, Borjas, Frech and Ginsburg, 1983) attributed these differentials to the premise that since non-π do not distribute the residuals (the revenues less the costs), that they are less interested in minimizing the costs. Holtmann and Idson compare the earlier “property rights” hypothesis an alternative hypothesis, that non-π nursing pay higher wages to get higher quality.

wj

Decomposing Differences

• Suppose we are looking at the impact of experience. We get two regressions. How do we analyze it.

Experience

WageRate

Sector j

Sector k

• Mean for Sector j is Ej. Mean for Sector k is Ek.

• Key -- Evaluate at mean.

EjEk

wk

E

Coefficient effect

Useful Technique For Health Econ … and other things!

Some Math

Mathematically, proceed as follows. Begin with sector j and sector k samples:

ln Wk = i ik zik (1a)

ln Wj = i ij zij (1b)

Define ik = ij + i; and zik = zij + zi. Then,

ln Wk - ln Wj = i ik zik - ijzij = i (ij + i) (zij + zi) - ijzij (2)

Gathering terms:

ln Wk - ln Wj = i i zij + ij zi+ i zi. (3)

The first term is a coefficient effect, holding z constant; the second is a attribute effect, holding constant; the third is an interaction.

Note + sign

Watch Subscripts

However, if formulated alternatively, the decomposition leads to different component parts.

Defining instead ij = ik - i; and zij = zik - zi, then,

ln Wk - ln Wj = i ik zik - ijzij = i ik zik - (ik - i) (zik - zi)(2)

Gathering terms:

ln Wk - ln Wj = i i zik + ik zi - i zi. (3)

Although (3) and (3) are formally the same, the component parts differ due to the weights (zik and ik, rather than zij and ij). To avoid weighting problems, add (3) and (3), and divide by 2.

Some Math

Note - sign

ln Wk - ln Wj = i i zij + ij zi+ i zi. (3)

This yields:

ln Wk - ln Wj = i i + zi, (4)

or

ln (Wk/ Wj) = i i + zi, and

Wk/ Wj = exp ( i i ) exp ( i zi)

where:

= (ik + ij)/2, and (5a)

= (zik + zij)/2. (5b)

Term i i is the coefficient effect (where ik varies between sectors); term i zi is the attribute effect (where zi varies between sectors).

Some Math

iz i

iz i

i

iz

izi

iz i

Back to Holtmann and Idson

They want to look at the differences in wages, and see how they vary between non-profit and for-profit nursing homes. If this is the case, then paying more for higher quality does not mean waste.Mean wage in non-profit homes = $9.95Mean wage in for-profit homes = $9.72 2% difference.

Table 1 –Seems that non-profit homes have nurses w/ more nursing experience, more degrees.

Table 2 –Run some wage regressionsColumns 2, 3 – Separate w/ a selection adjustmentSelection seems to affect coefficients on for-profit homes. But not

much on non-profit.Selection – 1 = for profit; 0 = non-profit. Experience and education

seemed to select nurses into non-profit.

Wage Regressions

Wage regressions

Return to education and experience seems higher in non-profit setting. Non-profit homes value, and hence reward, both general and specific training and experience investments more than for-profit homes. On the other hand, returns to a Nursing M.A., and in general, to educational factors, are higher in the for-profit sector.

Table 3

Experience and tenure effects help to explain higher observed wages in the nonprofit sector. Sectoral valuation, particularly facility size, tends to offset.

Comparisons

• The authors then compare the “quality” and the “property rights” hypotheses.

• According to the property rights hypothesis employees in nonprofit homes are paid higher wages than they could command in for-profit homes; this implies a higher return to their productivity related attributes than in for-profit homes.

• However, the authors’ methods show that workers in nonprofit facilities are generally compensated at a lower rate for their productivity-related attributes, and it is the fact that they have more of these attributes that leads to the wage differences.

• They view these distinctions as “strong evidence against the property-rights hypothesis that nonprofits are paying wasteful, inefficient wage premiums.”