Chapter 7: Medical Care Production and Costs Health Economics

Chapter 7: Medical Care Chapter 7: Medical Care Production and CostsProduction and Costs

Health EconomicsHealth Economics

Assessing the Productivity of Assessing the Productivity of Medical FirmsMedical Firms

Economists often describe production of output Economists often describe production of output as a function of labor and capital :as a function of labor and capital :

q = f(n,k)q = f(n,k)

In the case of health care :In the case of health care :

qq = hospital services = hospital servicesnn = nurses = nursesk k = medical equipment, hospital building = medical equipment, hospital building

Assessing the Productivity of Assessing the Productivity of Medical Firms (cont.)Medical Firms (cont.)

Short run : Short run : kk is fixed, while is fixed, while nn is variable is variable

a) At low level of At low level of n, kn, k is abundant. Each in nurses is abundant. Each in nurses when combined with capital greater in services.when combined with capital greater in services.- potential synergy effect because nurses can - potential synergy effect because nurses can work in teams.work in teams.

b) Further in nurses service, but a decreasing Further in nurses service, but a decreasing rate - law of diminishing marginal productivity. rate - law of diminishing marginal productivity.

c) “Too many “ nurses can cause congestion, com- “Too many “ nurses can cause congestion, communication problems, hospital servicesmunication problems, hospital services

Graphical RepresentationGraphical Representation

Total product = Total product = q q = = f(n,k*)f(n,k*)

hospital hospital servicesservices (q)(q)

Nurses (n)Nurses (n)

marginal marginal productproduct

nursesnurses

MP = MP = qq / / nn

MP is the slope of the TP curveMP is the slope of the TP curve..

n1 n2

TP

n2n1

Graphical RepresentationGraphical Representation

hospital hospital servicesservices

AP = AP = qq // nn

AP is the slope of a ray from the origin to the TP AP is the slope of a ray from the origin to the TP curve.curve.

average average productproduct

B

n3

TPB

C

A

Numerical ExampleNumerical Example

# of nurses

(n)

Amount of k

Total output

(q)

AP of n (q/n)

MP of n (q/n)

0 10 0 --- ---

1 10 10

2 10 30

3 10 60

People living in Boston are hospitalized about 1.5 times as often People living in Boston are hospitalized about 1.5 times as often as those living in New Haven, However, the health outcomes of as those living in New Haven, However, the health outcomes of patients in these 2 cities appear to be identical. Does this mean patients in these 2 cities appear to be identical. Does this mean that hospital care has no ability to improve health?that hospital care has no ability to improve health?

Practice QuestionPractice Question

health health outcomesoutcomes

hospitalizationshospitalizations

Substitutability in Production of Substitutability in Production of Medical CareMedical Care

There may be more than one way to produce a given level of health care.There may be more than one way to produce a given level of health care. Licenced practical nurses (LPNs) vs Registered Nurses (RNs) in hospitals.Licenced practical nurses (LPNs) vs Registered Nurses (RNs) in hospitals.

LPNs have less training.LPNs have less training. Maybe not as productive, but not as costly.Maybe not as productive, but not as costly.

Physician assistants vs physicians at ambulatory Physician assistants vs physicians at ambulatory clinics.clinics. But physician assistants can’t prescribe meds in most statesBut physician assistants can’t prescribe meds in most states. .

Substitutability in Production of Substitutability in Production of Medical Care (cont.)Medical Care (cont.)

= 0 = 0 no substitutabilityno substitutability.. = = perfect substitutability.perfect substitutability.

88

Potential for substitutability If price of 1 input Potential for substitutability If price of 1 input

increases, can minimize impact on total costs by increases, can minimize impact on total costs by

substituting away.substituting away. Elasticity of substitution :Elasticity of substitution :

= [= [(I(I11/I/I22))//II11/I/I22] : [] : [(MP(MP22/MP/MP11))//MPMP22/MP/MP11]]

% change in input ratio, divided by % change in ratio of inputs’ MPs.% change in input ratio, divided by % change in ratio of inputs’ MPs.

Production Function for Hospital Production Function for Hospital AdmissionsAdmissions

Jensen and Morrisey (1986)Jensen and Morrisey (1986) Sample : 3,450 non-teaching hospitals in 1983.Sample : 3,450 non-teaching hospitals in 1983.

qq = hospital admissions = hospital admissions

inputs : physicians, nurses, other staff, hospital bedsphysicians, nurses, other staff, hospital beds.

qq = = 00 + + 11physicians +physicians +22nurses + …. + nurses + …. +

Coefficients in regression are MPs.Coefficients in regression are MPs.

ResultsResults

Each additional physician generated 6.05 more Each additional physician generated 6.05 more admits per year.admits per year.

Nurses by far the most productiveNurses by far the most productive

Annual Marginal Products for AdmissionsAnnual Marginal Products for Admissions

Physicians 6.05Physicians 6.05Nurses 20.30Nurses 20.30Other Staff 6.97Other Staff 6.97Beds 3.04Beds 3.04

Input Input MP (at the means)MP (at the means)

Results (cont.)Results (cont.)

Each inputs is a substitute for other in production Each inputs is a substitute for other in production process.process.

If wages of nurses rise, can substitute away by If wages of nurses rise, can substitute away by having more hospital beds.having more hospital beds.

Elasticity of Substitution between InputsElasticity of Substitution between Inputs

Physicians with nurses 0.547Physicians with nurses 0.547Physicians with beds 0.175Physicians with beds 0.175Nurses with beds 0.124Nurses with beds 0.124

Input pairInput pair

Ex. for when Ex. for when = =

8

Medical Care CostMedical Care Cost

Explicit costs of doing business.Explicit costs of doing business. e.g. staff payroll, utility bills, medical supply costs.e.g. staff payroll, utility bills, medical supply costs.

Necessary for :Necessary for : Comparing performance evaluation across Comparing performance evaluation across

providers/depts.providers/depts. TaxesTaxes Government reimbursement/rate settingGovernment reimbursement/rate setting

Accounting CostsAccounting Costs

Medical Care Cost (cost.)Medical Care Cost (cost.)

i.e. opportunity costs.i.e. opportunity costs. e.g. opportunity cost of a facility being used as an e.g. opportunity cost of a facility being used as an

outpatient clinic = rent it could earn otherwise.outpatient clinic = rent it could earn otherwise.

Necessary for :Necessary for : optimal business planning.optimal business planning. allows one to consider highest returns to assets allows one to consider highest returns to assets

anywhere, anywhere, not just vs. direct competitors, or w/in not just vs. direct competitors, or w/in health care industry.health care industry.

Economic Costs Economic Costs = Accounting Costs = Accounting Costs

RecallRecall

Given a production function :Given a production function :

q q = = f (n,k)f (n,k)

q q = = hospital serviceshospital services

n n = = laborlabor = = nursenurse = = n n

k k = c= capitalapital = = medical equipment, hospital medical equipment, hospital buildingbuilding

Short-Run Total CostShort-Run Total Cost

costcost

hospital servicehospital service

STC( STC( q q )) = = w n + r k*w n + r k*

w w = wage rate for nurses = wage rate for nurses r r = rental price of capital= rental price of capitalshort runshort run k fixedk fixed w n = w n = variable costvariable cost

r k = r k = fixed cost . fixed cost .

q0

STCSTC

w n

r k

Short-Run Total Cost Short-Run Total Cost (cont.)(cont.)

STC( STC( q q )) = = w n + r k*w n + r k*

• In the short run, k is fixed.

rk* is the same, regardless of the amount of hospital services (q) produced.

•As q rises, increases in STC are only due to increases in the number of nurses needed (n).

Short-Run Total Cost (cont.)Short-Run Total Cost (cont.)

costcost

hospital servicehospital service

Recall : Production function initially exhibits IRTSRecall : Production function initially exhibits IRTS

Total costs rise at decreasing rate up to qTotal costs rise at decreasing rate up to q00

q0

STCSTC

w n

r k

After qAfter q00, DTRS in production costs rise at , DTRS in production costs rise at

increasing rateincreasing rate

Marginal and Average CostsMarginal and Average Costs

SMC = STC

q

= (wn + rk*)/q

= w(n/q) = w(1/MPn)

= w/MPn

The short run marginal cost of nurses depends on their marginal productivity.

Marginal and Average Costs Marginal and Average Costs (cont).(cont).

SAVC = STVC

q

= (wn)/q

= w(1/APn)

= w/APn

The short average variable cost of nurses depends on their average productivity.

Graphing Marginal and Average CostsGraphing Marginal and Average Costs

Costs

q0 q0

SMC

SATC

SAVC

SAVC0

SATC0

SMC0

Graphing Marginal and Average CostsGraphing Marginal and Average Costs

SATC and SAVC are u-shaped curves.Increasing returns to scale followed by

decreasing returns to scale. SMC passes through the minimum of

both SATC and SAVC.If marginal cost is greater than average

cost, then the cost of one additional unit of output must cause the average to rise.

Relating Product and Cost CurvesRelating Product and Cost Curves

n q

MPn

APn

Cost

n1 n30

MPn

APn

SMC

SAVC

q1 q3

Average and Marginal Co (cont.)Average and Marginal Co (cont.)

IRTS followed by DRTS in production leads to U IRTS followed by DRTS in production leads to U shaped AC curve. shaped AC curve.

Hospital Hospital doesn’tdoesn’t necessarily produce at q* (min. necessarily produce at q* (min. cost).cost).

Depends on hospital’s objectives.Depends on hospital’s objectives.

Even so, will attempt to stay Even so, will attempt to stay onon the cost curve the cost curve (not above it).(not above it).

Determinants of Short-run Costs Determinants of Short-run Costs (cont.)(cont.)

5 different measures of q 5 different measures of q inputsinputs

ER careER care nursing labornursing labor medical/surgical caremedical/surgical care auxiliary laborauxiliary labor pediatric carepediatric care professional professional

laborlabor maternity carematernity care administrative administrative

laborlabor other inpatient care other inpatient care general laborgeneral labor materials and suppliesmaterials and supplies

Cowing and Holtmann 1981

FindingsFindings

Found short run economies of scaleFound short run economies of scale Hospitals operate to left of min. on AVC curve.Hospitals operate to left of min. on AVC curve.

i.e Larger hospitals producing at lower costs i.e Larger hospitals producing at lower costs than smaller hospitals. than smaller hospitals.

Best way to reduce aggregate hospital costs?Best way to reduce aggregate hospital costs? Reduce # of hospital beds by a fixed % in all Reduce # of hospital beds by a fixed % in all

hospitals.hospitals.

Close the smallest hospitals in each region.Close the smallest hospitals in each region.

Findings (cont.)Findings (cont.)

Definition : Economies of scopeDefinition : Economies of scope

Cost of producing 2 outputs < sum of cost of Cost of producing 2 outputs < sum of cost of production 2 goods separately. production 2 goods separately.

Found Found DisDiseconomies of scope with respect to economies of scope with respect to ER and other services.ER and other services. Larger ER’s may bring in more complex mix of Larger ER’s may bring in more complex mix of

patients to the hospital. ORpatients to the hospital. OR

Larger ER’s generate operating challenges for Larger ER’s generate operating challenges for other services (e.g. communication, staffing other services (e.g. communication, staffing scheduling).scheduling).

Cost-minimizing input choiceCost-minimizing input choice

Example Example

- - Health care providers’ choice of nursing staff mix. Health care providers’ choice of nursing staff mix.

RN’s care for 6 patients per hour; hourly wage = $20RN’s care for 6 patients per hour; hourly wage = $20

LPN’s care for 4 patients per hour; hourly wage = $10LPN’s care for 4 patients per hour; hourly wage = $10

TC(TC(qq00)=20)=20RNRN + 10 + 10LPNLPN

If a hospital needs to hire nurses to care for If a hospital needs to hire nurses to care for growing patient volume, which should be hired? growing patient volume, which should be hired?

Cost Minimizing Input ChoiceCost Minimizing Input Choice Costs are minimized when:

Suppose that instead:

Then the last dollar spent on an LPN generates more output than the last dollar spent on a registered nurse.

MPRN

wRN

=

MPLPN

wLPN

MPRN

wRN

<

MPLPN

wLPN

Are physicians “costly” to Are physicians “costly” to hospitals? hospitals?

Physicians bill insurers or their patients for care.Physicians bill insurers or their patients for care.

In most cases, physician not paid a wage by a In most cases, physician not paid a wage by a hospital. hospital.

However, physicians generate other hospital However, physicians generate other hospital costs.costs.

Review and process physician’s application.Review and process physician’s application. Monitor physician’s performance.Monitor physician’s performance. Examining rooms and other supplies. Examining rooms and other supplies.

MPMPdocdoc MP MPnn

wwdocdoc wwnn

Are physicians “costly” to Are physicians “costly” to hospitals? (cont.)hospitals? (cont.)

Can solve for “shadow price” of doctors, if other Can solve for “shadow price” of doctors, if other variables known.variables known.

wwdocdoc = $7,012 per year. = $7,012 per year.

Does Higher Quality Higher Costs?Does Higher Quality Higher Costs?

Reducing costs without sacrificing quality. Reducing costs without sacrificing quality.

Improved production line.Improved production line.

bedside access to computerized treatment bedside access to computerized treatment guidelines.guidelines.

computerized patient charts.computerized patient charts.

Motivated work force.Motivated work force.

involving nurses in case managementinvolving nurses in case management

reimburse physicians based on performance reimburse physicians based on performance evaluationsevaluations

Does Higher Quality Higher Costs?Does Higher Quality Higher Costs?

“ “ In an increasingly competitive environment, In an increasingly competitive environment, hospitals must take a critical look at their hospitals must take a critical look at their product lines… Many institutions must decide product lines… Many institutions must decide between eliminating or investing in unprofitable between eliminating or investing in unprofitable product lines” product lines”

Juran ReportJuran Report e.g. Hospital may have unprofitable, high quality e.g. Hospital may have unprofitable, high quality

heart surgery, but kidney surgery may be losing $, heart surgery, but kidney surgery may be losing $, lower quality.lower quality.

Business opportunities in costsBusiness opportunities in costs

Companies which can synthesize complex data Companies which can synthesize complex data to improve quality and restrain cost will survive.to improve quality and restrain cost will survive.

Express Scripts - Express Scripts - Pharmacy Benefit Manager (PBM) Pharmacy Benefit Manager (PBM)

Manages prescription claims on behalf of Manages prescription claims on behalf of HMO’s, insurance companies, unions, etc.HMO’s, insurance companies, unions, etc.

Obtains drug cost savings through drug Obtains drug cost savings through drug utilization review, generic substitution, mail-utilization review, generic substitution, mail-order pharmacy, volume discounts from retail order pharmacy, volume discounts from retail pharmacy.pharmacy.


Express ScriptsExpress Scripts-- Practice Pattern Science (PPS) Practice Pattern Science (PPS)

An information service company.An information service company. Offers practice variation analysis and disease Offers practice variation analysis and disease

management support service linking healthcare data management support service linking healthcare data from all points of care.from all points of care.

Complements PBM servicesComplements PBM services Be a leader in the development of disease Be a leader in the development of disease

management, provider profiling and outcomes management, provider profiling and outcomes assessment technologies.assessment technologies.


Express ScriptsExpress Scripts-- Practice Pattern Science (PPS) (cont.)Practice Pattern Science (PPS) (cont.)

Diagnostic ClusterDiagnostic ClusterSMSM Methodology : Methodology : links to a “global” pattern treatment through its patient links to a “global” pattern treatment through its patient treatment episodes (PTEtreatment episodes (PTETMTM))

Provider Profiling :Provider Profiling : reduce providers practice pattern variationreduce providers practice pattern variation

Diseases Management Support Service :Diseases Management Support Service : Gatekeeper of patient case mix.Gatekeeper of patient case mix. Scorekeeper for patterns of treatment.Scorekeeper for patterns of treatment.

Pharmaceutical Information :Pharmaceutical Information : Benchmark prescription drug patternsBenchmark prescription drug patterns Track the composition of prescription drugsTrack the composition of prescription drugs Report the mean and median global treatment costReport the mean and median global treatment cost

Business opportunities in costs Business opportunities in costs (cont.)(cont.)

Practice Pattern Science (PPS) subsidiary. Practice Pattern Science (PPS) subsidiary. Computerized patient profile database.Computerized patient profile database. Bars claims if potential dangerous interactions Bars claims if potential dangerous interactions

identified.identified. Identifies people over-utilizing drugs by visiting Identifies people over-utilizing drugs by visiting

multiple doctors.multiple doctors.

Long Run Costs of ProductionLong Run Costs of Production

In the long run, all inputs are variable. k is no longer fixed. e.g. A hospital can build a new facility or

add extra floors to increase bedsize in the long run.

If all inputs are variable, what does the long run average cost curve look like?

The Long Run Average Cost CurveThe Long Run Average Cost Curve

Average Cost of Hospital Services

# of patients

LATC

q0 q1 q2


Just like the short run cost curve, the long run cost curve for a firm is also u-shaped.However, the short run cost curve is due to

IRTS, then DRTS relative to a fixed input.e.g. In the short run, the only way to

increase the number of patients treated was to hire more nurses; but the # of beds (k) was fixed.

But in the long run, there are no fixed inputs.


The u-shaped long run average cost curve is due to economies of scale and diseconomies of scale.

Economies of scale Average cost per unit of output falls as the

firm increases output.Due to specialization of labor and capital.


Example of specialization and the resulting economies of scale.A large hospital can purchase a

sophisticated computer system to manage its inpatient pharmaceutical needs.

Although the total cost of this system is more than a small hospital could afford, these costs can be spread over a larger number of patients.

The average cost per patient of dispensing drugs can be lower for the larger facility.


Economies of scale arise due to specialization of labor and/or capital.That is, the long run relationship between

average costs and output reflects the nature of the production process.

This is why economies of scale (in costs) are can also be referred to as increasing returns to scale (in production).


Increasing returns to scaleAn increase in all inputs results in a more

than proportionate increase in output.e.g. If a hospital doubles its number of

nurses and beds, it may be able to triple the number of patients it cares for.

However, most economists believe that economies of scale are exhausted, and diseconomies of scale set in at some point.


Diseconomies of scale arise when a firm becomes too large.e.g. bureaucratic red tape, or breakdown in

communication flows.At this point, the average cost per unit of

output rises, and the LATC takes on an upward slope.

Diseconomies of scale (in costs) imply decreasing returns to scale in production.

The Long Run Average Cost CurveThe Long Run Average Cost Curve


# of patients

LATC

q0 q1 q2

Economies of scale Diseconomies of scale


Decreasing returns to scaleAn increase in all inputs results in a less

than proportionate increase in output.e.g. Doubling the number of patients cared

for in a hospital may require 3 times as many beds and nurses.

In some cases, the production process exhibits constant returns to scale.A doubling of inputs results in a doubling of

output.

The Long Run Average Cost Curve The Long Run Average Cost Curve under Constant Returns to Scaleunder Constant Returns to Scale


# of patients


Like the short run cost curve, a number of factors can cause the short run cost curve to shift up or down.Input prices.Quality.Patient casemix.

e.g. If the hourly wage of nurses increases, the average cost of caring for each patient will also rise.The average cost curve will shift _____


Empirical evidence on HMOs and costs. See handout.

Computing ProfitsComputing Profits

Recall that the total costs of production for a firm are:

TC(q) = wn + rk Sum of each input price times the # of

inputs used.

We can express total revenues derived from producing and selling a given level of output (q) as:

TR(q) = output price x q

Computing Profits (cont.)Computing Profits (cont.)

Thus, we can express profits for the firm as:

(q) = TR(q) – TC(q)

= Profits

TR = Total revenue

TC = Total costs

We assume that firms choose a level of output (q) to maximize profits.


Assume that as output increases, total revenue rises at a diminishing rate.

Also, recall the shape of short run total cost curve derived previously.

Then we can graph the total revenue curve and the total cost curve, and use them to visualize profits.Profits will be the vertical distance between

total revenues and total costs at any given quantity of output.

Graphing ProfitsGraphing ProfitsTotal dollars

Quantity of output (q)

TC

TR

q0

TR0

TC0

(q0) = TR0 – TC0



TC

TR

At what output level(s) does the firm make profits equal to 0? At what output levels could the firm make negative profits ?



TC

TR

q0

TR0

TC0

Notice that I have plotted q0 where the TR curve is above the TC curve, and the 2 curves are the furthest apart (in vertical distance).


I have plotted q0 at the point where the firm maximizes profits.At this point the difference between total

revenues and total costs is the greatest, and TR>TC.

Note that this is also the point where the slopes of the TR curve and the TC curve are equal.


Recall that the slope of the total cost curve represents marginal costs.

MC = TC/q

The slope of the total revenue curve represents marginal revenue.

MR = TR/q

A firm maximizes profits where:MR=MC


A firm maximizes profits where MR=MC. Why?

Suppose the firm was instead producing at a point where MR>MC. Then additional units of output would

generate more marginal revenues than marginal costs, and profits could be higher.

Suppose the firm was instead producing at a point where MC>MR.Then the last unit of output generates

economic losses.



TC

TR

At q1, the firm should raise output to increase profits.

At q2, the firm should lower output to increase profits.

MC>MR

MR>MC

q1 q2

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Chapter 7: Medical Care Production and Costs Health Economics