1

Production and Cost

© Allen C. Goodman, 2013

Technology

• A lot of people feel that technology is the “culprit” in the high health care costs.

• Technologies differ widely. Look at different countries.

Table 22-2

Inpatient Beds/1,000

% of U.S.

Practicing Physicians/1,000

% of U.S.

Practicing Nurses/1,000

2008 2009 2009 Canada 03.3 106.5 -- -- 09.4

France 06.9 222.6 -- -- -- Germany 08.2 264.5 3.6 150.0 11.0 Hungary 07.1 229.0 3.1 125.0 06.2 Japan 13.8 445.2 2.2 -- -- S. Korea 07.8 251.6 1.9 079.2 04.5 UK 03.4 109.7 2.6 112.5 09.7 USA 03.1 100.0 2.4 100.0 --

SOURCE: OECD HEALTH DATA 2011, JUNE.

5

Traditional Health Technology Analysis

• Although it would seem obvious from economics that we can substitute inputs for each other, it decidedly unclear that the health professions agree.

• Consider the discussion of need in health care resources.• Most important early work that employed a medical

determination of health manpower needs was a study by Lee and Jones (1933) -- we reference it some in Chapter 16. We discussed it more in earlier editions.

• Their method calculated the # of physicians necessary to perform the needed # of medical procedures. The needed # of medical procedures, in turn, was based on the incidence of a morbidity (illness) in the population.

6

Traditional Health Technology Analysis (2)

Consider Condition A, which strikes 1 percent of the population in a given county.

Suppose further that its treatment requires 6 hours of physician time, and that there are 250,000 residents in the county.

How many physicians are needed, if a physician works 2,000 hours per year.

7

Traditional Health Technology Analysis (3)

a. 250,000 persons x (1 morbidity/100 persons) = 2,500 morbidities.

b. 2,500 morbidities x (6 hours/morbidity) = 15,000 hours

c. 15,000 hours x (1 physician/2,000 hours) = 7.5 physicians.

Suppose that the county currently has 7.5 physicians, and that the county's population is projected to rise from 250,000 to 400,000.

Without any adjustment for the morbidity rate, or for the technology of care, the need would be projected to rise to (400,000/250,000) x 7.5, or 12.0 physicians.

If the projected (actual) total is less than 12.0 then a projected (actual) shortage is said to exist.

8

Severe assumptions.

• Even if we supposed that there are only two factors of production, physicians L and some amount of capital or machinery K, the Lee-Jones approach tends to ignore the possibilities for substitution between inputs.

Presumes:

a. there is no substitution of other inputs for physician inputs, and,

b. there is no projected technological change in the production of health care services.

9

c. there is a single, unique answer to the question of how many medical procedures are appropriate given the illness data for a population,

d. and prices and costs of various inputs are safely ignored.

and additionally:

e. manpower provided to the public will be demanded by the public or otherwise paid for,

f. medical doctors are the appropriate body of people to determine population needs.

Severe assumptions.

10

Reviewing Elasticity of substitution, .

= the % change in the factor input ratio, brought about by a 1% change in the factor price ratio.

K

L

K/L1

K/L2

11

Production FunctionsSeveral different types of production functions. The typical Cobb-

Douglas production function for capital and labor can be written as:

Q = A L K

It turns out that there is a property of the Cobb-Douglas function that

= 1. What does this mean? This gives an interesting result that factor shares stay constant. Why?

s = wL / rK

s = (w/r) (L/K)

Increase in (w/r) means that (L/K) should fall. With matching 1% changes, shares stay constant.

1% 1%

12

Two fundamental problems

Two fundamental problems.

You need measures of factor costs if you want to make it complete.

If you’re looking over time, input price effects may account for large portions of the increasing costs.

Even with static models, however, you have problems. Not including factor prices implies that they do not matter. This is similar to assuming that the substitution elasticity is zero.

GeometricallyLet K be the fixed level

of capital.

Inputs X, output Y.

SR Cost will be higher than LR costs everywhere except at K.

Only at K* will marginal product ratio equal the factor price ratio.

K

X

K

Factor cost ratio

c(Y1) < src(Y1) c(Y2) = src(Y2) c(Y3) < src(Y3)

14

Jensen and Morrissey (1986)

They try to estimate a production function for hospital care. From this production function, they trace isoquants, and calculate substitution elasticities. They have a number of labor inputs, as well as “beds” a measure of capital inputs.

They look at a hospital producing output Q, adjusted for case-mix, using

admitting physicians L and

non-physician labor and capital K.

L is a fraction of S, size of the medical staff, so:

15

Substituting (2) into (1) Q = Q (K, S, N).

They estimate a translog production function for annual cases treated Q:

ln Q = 0 + i ln Xi + i ln Xi2 + ij ln Xi ln Xj.

This leads to:

MPi = i (Q/Xi), where

i = i + 2i (ln Xi) + ij (ln Xj) = output elasticity

Jensen and Morrissey (1986)

16

17

CrossTerms

18

Substitution Elasticities

Substitution Elasticities

Among the substitution elasticities, we have:

- Between medical staff relative to nurses = 0.547

SOME

- Between nurses and residents = 2.127;

CONSIDERABLE

- Even between labor and capital = .124 - .211

A LITTLE BIT

19

Measuring Efficiency

• If we’re right on an isoquant, then we must be efficient.

• If we’re not, then we must be inefficient. How hard could that be?

20

Inputs

Output

White line is best feasible. But we can’t use plain old OLS

Problems

DEA=Data envelopment analysis• Consider 2 inputs.• Collect a lot of data

Capital, K

Labor, L

• Micro theory tells us that some are more efficient than others.

• DEA allows us to use linear programming methods to find the best envelope.

DEA• Those on the frontier are

considered efficient.

Capital, K

Labor, L

• Those off the frontier are considered inefficient.

• There are lots of measures related to lengths of the rays that indicate how inefficient they are.

Variables• Input variables for the analysis are:

1. Total Community Hospitals, 2. Total full time employees, 3. Total part time employees, 4. Total beds

• Output variables are 1. Inpatient days,2. Inpatient surgeries, 3. Births, 4. Emergency outpatient, 5. Other outpatient.

Butler, Goodman, 2011

Thoughts• Higher population, more beds More efficient• More hospitals/county Less efficient• Investor owned More efficient• Not For Profit More efficient but effect is 1/3

that of Investor owned. Gov’t hospitals are other category.

• Major improvement in efficiency from 1994 to 2001; No change from 2001 to 2008. Balanced Budget Act of 1997 may be big explanation