HCMI 3243 - Chapter 7 (Medical Care Production and Costs)

question

Assumptions of short-run production

answer

1. Medical firm produces a single output of medical services, q

2. Only two medical inputs exist: nurse-hours, n, and a composite capital good, k

3. Quantity of capital is fixed at some amount

4. Medical firm faces an incentive to produce as efficiently as possible

5. Medical firm possesses perfect information regarding the demands for its product

question

(Short Run) Production Function

answer

Identifies different ways nurse-hours & capital can be combined

-To produce various levels of medical services

question

(Short Run) Each level of output produced by

answer

Several different combinations of the nurse and capital inputs

-Each combination - assumed to be technically efficient - maximum amount of output that is feasible given the state of technology

q= f(n,k)

q is single output of medical services
n = nurse hours (labor)
k (with a line above) = capital
the line above = fixed

question

(Short Run) Law of diminishing marginal productivity

answer

At first, total output increases at an increasing rate

-after some point, it increases at a decreasing rate

question

(Short Run) Total product curve (TP)

answer

Depicts total output produced by different levels of the variable input, holding all other inputs constant

question

Why does output fail to expand at an increasing rate after n1 (nurse labor) for Figure 7.1

x axis is N
y axis is Q (medical service output)
Actual Product curve is TP

answer

Diminishing marginal productivity

question

Total product curve for Figure 7.1

answer

0 --> N1 : Increases at an increasing rate

N1 --> N2 : Increases at a decreasing rate

N2 --> : Declines

question

Marginal Product

answer

Change in total output associated with a one-unit change in the variable input

MPn= Δ q/Δn

question

What does the magnitude of the marginal product of 1 nurse hour reveal?

answer

Additional quantity of medical services produced by each additional nurse-hour

question

Total Product vs Marginal Product vs

answer

When TP is concave up , Marginal Product is decreasing

When TP is concave down, Marginal Product is decreasing

When TP is concave down AND ALSO negative, Marginal Product is negative

See photo in iPhone notes

question

The Marginal Product Curve

answer

X axis (labor)
Y axis (marginal product)

When MP is negative, it goes below X axis

question

How is Marginal Product calculated?

answer

MP(input)= Δ output/Δinput

question

Average Product APn

answer

Total quantity of medical services divided by the total number of nurse-hours

question

How do you measure Average Product ?

answer

APn = q/n

Average quantity of medical services produced within an hour

Derived from the total product curve

question

What happens to AP when MP increases/decreases

answer

When MP is above AP , AP increases

When MP is below AP , AP decreases

question

GPA example for MP and AP

answer

Marginal Product is your course gpa

Average Product is your whole gpa

question

Course of AP(input)

answer

1. Initially increases
2. Reaches a maximum
3. Then decreases

- Because of law of diminishing marginal productivity

question

Marginal and average product curves

answer

MP curve cuts AP curve at its maximum point

MP is above AP whenever AP is increasing

MP is below AP whenever AP is declining

question

At some point in the production process..

answer

The additional nurse becomes less productive due to the constraint imposed by the fixed input

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Marginal productivity

answer

Influences the average productivity of the team of nurses

question

Realttion between MP And AP curves for figure 7.4

answer

Average productivity rises when marginal productivity exceeds average productivity

Average productivity falls when marginal productivity lies below average productivity

Marginal productivity equals average productivity when average productivity is maximized

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(Elasticity of Input Substitution) More than one variable input

answer

Substitution between any two variable inputs

Degree of substitutability depends on technical and legal considerations

question

Elasticity of substitution

answer

% change in the input ratio / % change in the ratio of the inputs' marginal productivities

-holding constant the level of output

question

Elasticity of substitution, σ

answer

Ii(i=1,2) --> Quantity employed of each input

MP2/MP1 --> ratio of marginal productivities

- Marginal rate of technical substitution

question

Marginal rate of technical substitution

answer

Rate at which one input substitutes for the other in the production process, at the margin

question

Formula for Elasticity of substitution, σ

answer

Change in
(input 1/ input 2)
DIVIDED by
(Input 1/input 2)

THEN divided by

Change in (marginal product 2/ marginal product 1)
DIVIDED by
(marginal product 2/ marginal product 1)

question

Elasticity of substitution, σ

"percentage change....

answer

Percentage change in the input ratio that results from a 1 percent change in the marginal rate of technical substitution

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If σ = 0

answer

Variable inputs cannot be substituted

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If σ = ∞

answer

Variable inputs are perfect substitutes in production

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Case-mix-adjusted hospital admissions

answer

f(Physicians, nurses, other non-physician staff, hospital beds, X)

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Marginal product for each input

f(X)

answer

Positive, declined in magnitude with greater usage

- Law of diminishing marginal product

Nurse input = the most productive input

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Each input

answer

A substitute for others

Substitution elasticities between:

1. Physicians and nurses = 0.547
(A 10% increase in the marginal productivity of a doctor causes a 5.47% increase in the ratio of nurses to doctors)

2. Physicians and beds = 0.175

3. Nurses and beds = 0.124

question

How can hospital policy makers avoid some of the price (wage) increase in any one input?

answer

Substitute it with other inputs

question

Total Cost

answer

Explicit + Implicit costs

question

Explicit costs

answer

1. Market transaction

-Wage payments to the hourly medical staff
-Electric utility
-Medical supply expenses

2. Accountants

question

Implicit Costs

answer

Opportunity costs of using any resources the medical firm owns

question

Short run total cost , STC

answer

Variable input nurse hours, n

Fixed input capital, k

Level of medical output, q

Input prices (Assume fixed)
hourly wages for nurse, w
rental/opportunity cost of capital , r

STC (q) = wn + r k(line over k)

question

Short-run total costs of production, STC

answer

Depend on quantities and prices of inputs employed

question

Total variable cost of production, STVC

answer

Wage rate times the number of nurse-hours

-Total wage bill
-Responds to changes in the level of output

question

Total fixed costs of production, STFC

answer

Rental price times the quantity of capital

-Does not respond to changes in output

question

Calculating short-run total cost

answer

Identify necessary number of nurse hours, n
-Or each level of medical output

STVC = w × n

STC = STFC + STVC

question

Relation between STC and TP

answer

When TP is increasing at an increasing rate
- STC - increasing at a decreasing rate

When TP increasing at a decreasing rate
- STC - increasing at an increasing rate

question

The Short Run Total Cost Curve

answer

increases at a decreasing rate

then increases at a increasing rate because of diminishing marginal productivity

question

Fixed costs

answer

Occur in the short-run (operating period)

Levels of some inputs are fixed

question

Variable costs

answer

All inputs are variable during the long run or planning period

question

Short-run marginal costs, SMC

answer

Change in total costs associated with a one-unit change in output

question

Short-run average variable costs, SAVC

answer

Short-run total variable costs, STVC, divided by the quantity of medical output

question

Short-run marginal variable costs.

Inversely related ....

answer

to marginal product of labor

question

Short-run average variable costs

Inversely related.....

answer

to average product of labor

question

Maximum points on marginal product curve

answer

Minimum point on marginal variable cost curves

question

Relation between the Per-Unit Product and Cost Curves

answer

Short-run marginal cost, SMC, equals the change in total costs brought on by a one-unit change in output

Short-run average variable cost, SAVC, equals short-run total variable cost divided by total output

SMC and SAVC are inversely related to marginal and average productivity

question

marginal costs decline as....

answer

marginal productivity increases

question

Short-run average fixed cost, SAFC

answer

Total fixed costs, STFC divided by the level of output, q

SAFC = STFC/q

question

As medical services, q, increases

answer

SAFC declines

question

Short-run average total cost, SATC, equals...

answer

the sum of short-run average variable cost, SAVC, and short-run average fixed cost, SAFC

question

SAFC is reflected in the vertical distance between the...

answer

SATC and SAVC curves at each level of output

question

SMC cuts both of the average cost curves at...

answer

their minimum points

question

SMC lies above the SAVC and SATC curves when they are rising and...

answer

below them when they are falling

question

Prices of the variable inputs increase (decrease)...

answer

Cost curves shift upward (downward)

question

Better quality of care...

answer

Cost curves shift upward

question

More severe patient case-mix...

answer

Cost curves shift upward

question

Excessive amounts of the fixed inputs...

answer

Cost curves shift upward

question

STVC =

answer

f(output level, input prices, quality of care, patient case-mix, quantity of the fixed inputs)

-These factors can explain cost differentials among medical firms in the same industry

-Output - where the medical firm operates along the cost curve

-The other factors affect the location of the curve

question

Studies by Cowing and Holtmann (1983) revealed:

STVC = f(q1,q2,q3,q4,q5,w1,w2,w3,w4,w5,w6,K,A)

**The Q's

answer

qi(i=1,5) - quantity of one of five different patient services

i.e Emergency room care, medical-surgical care, pediatric care, maternity care, and other inpatient care - measured in total patient days

question

Studies by Cowing and Holtmann (1983) revealed:

STVC = f(q1,q2,q3,q4,q5,w1,w2,w3,w4,w5,w6,K,A)

** The W's

answer

wj(j=1,6) - one of six different variable input prices

i.e Nursing labor, auxiliary labor, professional labor, administrative labor, general labor, and material and supplies

question

wj(j=1,6) - one of six different variable input prices
Nursing labor, auxiliary labor, professional labor, administrative labor, general labor, and material and supplies

*K and A

answer

K - single measure of the capital stock (measured by the market value of a hospital)

A - fixed number of admitting physicians in the hospital

question

Economies of scope

answer

Result from the joint sharing among related outputs of resources

Exist if the joint cost of producing two outputs is less than the sum of the costs of producing the two outputs separately

question

Minimize TC(q0)=wR × RN + wL × LPN
subject to:

answer

q0=f(RN, LPN)

question

answer

amount of medical services

question

answer

total cost

question

answer

registered nurses

- variale input

question

LPN

answer

licensed practical nurse

-variable input

question

answer

hourly wage for RNs

-input price

question

answer

hourly wage for LPNs

-input price

question

In the long run, all...

answer

inputs, including capital, can be changed

question

Long-run average total cost curve, LATC

answer

Derived from a series of short-run cost curves

-Different sizes

Choose the SATC or size that minimizes the average cost

Envelope curve

question

The U shape of the LATC reflects...

answer

economies and diseconomies of scale

question

Long-run average total cost curve, LATC is...

**Characteristics

answer

U-shaped

Initially declines, reaches a minimum, and eventually increases

Long-run economies and diseconomies of scale

question

Long-run economies of scale

Average costs ....

answer

fall as a medical firm gets physically larger due to specialization of labor and capital

question

[Long-Run Cost Curves]

Increasing returns to scale

answer

An increase in all inputs results in a more than proportionate increase in output

question

[Long-Run Cost Curves]

Constant returns to scale

answer

Horizontal LATC curve

question

[Long-Run Cost Curves]

Diseconomies of scale

answer

Result when the medical firm becomes too large

Average costs increase as a medical firm gets physically larger

question

[Long-Run Cost Curves]

Decreasing returns to scale

answer

An increase in all inputs results in a less than proportionate increase in output

question

[Shifts in Long-Run Average Cost Curve]
Increase in prices of medical inputs

answer

LATC shifts upward

question

[Shifts in Long-Run Average Cost Curve]

Quality

answer

Cost-saving technology: LATC shifts downward

Higher quality of care: LATC shifts upward

question

[Shifts in Long-Run Average Cost Curve]

Patient case-mix

answer

More severe patient case-mix: LATC shifts upward

question

[Long-Run Cost Minimization and the Indivisibility of Fixed Inputs]

Assumption

answer

All inputs can be costlessly adjusted upward or downward

question

[Long-Run Cost Minimization and the Indivisibility of Fixed Inputs]

Capital inputs

answer

Not easily changed

question

[Long-Run Cost Minimization and the Indivisibility of Fixed Inputs]

Medical firms may adjust slowly

answer

Not produce in long-run equilibrium

Operate with excess capital relative to a long-run equilibrium point

question

[Figure 7.9 - Long-Run Disequilibrium of the Medical Firm]

A firm may not operate in long-run equilibrium because....

answer

of the sizeable costs of adjusting to a sharp change in demand

question

Long-run total cost, LTC

LTC = STVC(q, w ,k)+ r × k

answer

LTC = sum of (minimum) short-run total variable costs, STVC and capital costs

STVC - depends on: quantity of output, q, the wage rate, w, and the quantity of capital, k

question

Necessary condition for long-run cost minimization

ΔSTVC/Δk = -r

answer

Variable cost savings realized from substituting one more unit of capital
(Must equal the rental price of capital in long-run equilibrium)

Marginal benefits and costs of capital substitution should be equal

question

Cowing and Holtmann (1983), results:

"Average" hospital in their New York sample
Too much capital and too many physicians

answer

Hospitals could reduce their costs by limiting the amount of capital and controlling the number of physicians.

question

Neoclassical cost theory

Assumptions

answer

Perfect certainty

Firms produce as efficiently as possible

Perfect information

question

Short-run or long-run costs of producing a given level of output can be determined by ...

answer

observing the relevant point on the appropriate cost curve

question

Misleading when applied to medical firms because

Some medical firms....

answer

Are not-for-profit entities or are reimbursed on a cost-plus basis or both

No incentive to minimize costs

May operate above a given cost curve

question

Medical firms - uncertain demand for their services

answer

May produce with some amount of reserve capacity just in case an unexpected large increase in demand occurs

1 of 97

question

Assumptions of short-run production

answer

question

(Short Run) Production Function

answer

Identifies different ways nurse-hours & capital can be combined

-To produce various levels of medical services

question

(Short Run) Each level of output produced by

answer

question

(Short Run) Law of diminishing marginal productivity

answer

At first, total output increases at an increasing rate

-after some point, it increases at a decreasing rate

question

(Short Run) Total product curve (TP)

answer

Depicts total output produced by different levels of the variable input, holding all other inputs constant

question

Why does output fail to expand at an increasing rate after n1 (nurse labor) for Figure 7.1

x axis is N
y axis is Q (medical service output)
Actual Product curve is TP

answer

Diminishing marginal productivity

question

Total product curve for Figure 7.1

answer

0 --> N1 : Increases at an increasing rate

N1 --> N2 : Increases at a decreasing rate

N2 --> : Declines

question

Marginal Product

answer

Change in total output associated with a one-unit change in the variable input

MPn= Δ q/Δn

question

What does the magnitude of the marginal product of 1 nurse hour reveal?

answer

Additional quantity of medical services produced by each additional nurse-hour

question

Total Product vs Marginal Product vs

answer

question

The Marginal Product Curve

answer

X axis (labor)
Y axis (marginal product)

When MP is negative, it goes below X axis

question

How is Marginal Product calculated?

answer

MP(input)= Δ output/Δinput

question

Average Product APn

answer

Total quantity of medical services divided by the total number of nurse-hours

question

How do you measure Average Product ?

answer

APn = q/n

Average quantity of medical services produced within an hour

Derived from the total product curve

question

What happens to AP when MP increases/decreases

answer

When MP is above AP , AP increases

When MP is below AP , AP decreases

question

GPA example for MP and AP

answer

Marginal Product is your course gpa

Average Product is your whole gpa

question

Course of AP(input)

answer

1. Initially increases
2. Reaches a maximum
3. Then decreases

- Because of law of diminishing marginal productivity

question

Marginal and average product curves

answer

MP curve cuts AP curve at its maximum point

MP is above AP whenever AP is increasing

MP is below AP whenever AP is declining

question

At some point in the production process..

answer

The additional nurse becomes less productive due to the constraint imposed by the fixed input

question

Marginal productivity

answer

Influences the average productivity of the team of nurses

question

Realttion between MP And AP curves for figure 7.4

answer

question

(Elasticity of Input Substitution) More than one variable input

answer

Substitution between any two variable inputs

Degree of substitutability depends on technical and legal considerations

question

Elasticity of substitution

answer

% change in the input ratio / % change in the ratio of the inputs' marginal productivities

-holding constant the level of output

question

Elasticity of substitution, σ

answer

Ii(i=1,2) --> Quantity employed of each input

MP2/MP1 --> ratio of marginal productivities

- Marginal rate of technical substitution

question

Marginal rate of technical substitution

answer

Rate at which one input substitutes for the other in the production process, at the margin

question

Formula for Elasticity of substitution, σ

answer

Change in
(input 1/ input 2)
DIVIDED by
(Input 1/input 2)

THEN divided by

Change in (marginal product 2/ marginal product 1)
DIVIDED by
(marginal product 2/ marginal product 1)

question

Elasticity of substitution, σ

"percentage change....

answer

Percentage change in the input ratio that results from a 1 percent change in the marginal rate of technical substitution

question

If σ = 0

answer

Variable inputs cannot be substituted

question

If σ = ∞

answer

Variable inputs are perfect substitutes in production

question

Case-mix-adjusted hospital admissions

answer

f(Physicians, nurses, other non-physician staff, hospital beds, X)

question

Marginal product for each input

f(X)

answer

Positive, declined in magnitude with greater usage

- Law of diminishing marginal product

Nurse input = the most productive input

question

Each input

answer

question

How can hospital policy makers avoid some of the price (wage) increase in any one input?

answer

Substitute it with other inputs

question

Total Cost

answer

Explicit + Implicit costs

question

Explicit costs

answer

1. Market transaction

-Wage payments to the hourly medical staff
-Electric utility
-Medical supply expenses

2. Accountants

question

Implicit Costs

answer

Opportunity costs of using any resources the medical firm owns

question

Short run total cost , STC

answer

question

Short-run total costs of production, STC

answer

Depend on quantities and prices of inputs employed

question

Total variable cost of production, STVC

answer

Wage rate times the number of nurse-hours

-Total wage bill
-Responds to changes in the level of output

question

Total fixed costs of production, STFC

answer

Rental price times the quantity of capital

-Does not respond to changes in output

question

Calculating short-run total cost

answer

Identify necessary number of nurse hours, n
-Or each level of medical output

STVC = w × n

STC = STFC + STVC

question

Relation between STC and TP

answer

When TP is increasing at an increasing rate
- STC - increasing at a decreasing rate

When TP increasing at a decreasing rate
- STC - increasing at an increasing rate

question

The Short Run Total Cost Curve

answer

increases at a decreasing rate

then increases at a increasing rate because of diminishing marginal productivity

question

Fixed costs

answer

Occur in the short-run (operating period)

Levels of some inputs are fixed

question

Variable costs

answer

All inputs are variable during the long run or planning period

question

Short-run marginal costs, SMC

answer

Change in total costs associated with a one-unit change in output

question

Short-run average variable costs, SAVC

answer

Short-run total variable costs, STVC, divided by the quantity of medical output

question

Short-run marginal variable costs.

Inversely related ....

answer

to marginal product of labor

question

Short-run average variable costs

Inversely related.....

answer

to average product of labor

question

Maximum points on marginal product curve

answer

Minimum point on marginal variable cost curves

question

Relation between the Per-Unit Product and Cost Curves

answer

question

marginal costs decline as....

answer

marginal productivity increases

question

Short-run average fixed cost, SAFC

answer

Total fixed costs, STFC divided by the level of output, q

SAFC = STFC/q

question

As medical services, q, increases

answer

SAFC declines

question

Short-run average total cost, SATC, equals...

answer

the sum of short-run average variable cost, SAVC, and short-run average fixed cost, SAFC

question

SAFC is reflected in the vertical distance between the...

answer

SATC and SAVC curves at each level of output

question

SMC cuts both of the average cost curves at...

answer

their minimum points

question

SMC lies above the SAVC and SATC curves when they are rising and...

answer

below them when they are falling

question

Prices of the variable inputs increase (decrease)...

answer

Cost curves shift upward (downward)

question

Better quality of care...

answer

Cost curves shift upward

question

More severe patient case-mix...

answer

Cost curves shift upward

question

Excessive amounts of the fixed inputs...

answer

Cost curves shift upward

question

STVC =

answer

question

Studies by Cowing and Holtmann (1983) revealed:

STVC = f(q1,q2,q3,q4,q5,w1,w2,w3,w4,w5,w6,K,A)

**The Q's

answer

question

Studies by Cowing and Holtmann (1983) revealed:

STVC = f(q1,q2,q3,q4,q5,w1,w2,w3,w4,w5,w6,K,A)

** The W's

answer

wj(j=1,6) - one of six different variable input prices

i.e Nursing labor, auxiliary labor, professional labor, administrative labor, general labor, and material and supplies

question

wj(j=1,6) - one of six different variable input prices
Nursing labor, auxiliary labor, professional labor, administrative labor, general labor, and material and supplies

*K and A

answer

K - single measure of the capital stock (measured by the market value of a hospital)

A - fixed number of admitting physicians in the hospital

question

Economies of scope

answer

Result from the joint sharing among related outputs of resources

Exist if the joint cost of producing two outputs is less than the sum of the costs of producing the two outputs separately

question

Minimize TC(q0)=wR × RN + wL × LPN
subject to:

answer

q0=f(RN, LPN)

question

answer

amount of medical services

question

answer

total cost

question

answer

registered nurses

- variale input

question

LPN

answer

licensed practical nurse

-variable input

question

answer

hourly wage for RNs

-input price

question

answer

hourly wage for LPNs

-input price

question

In the long run, all...

answer

inputs, including capital, can be changed

question

Long-run average total cost curve, LATC

answer

Derived from a series of short-run cost curves

-Different sizes

Choose the SATC or size that minimizes the average cost

Envelope curve

question

The U shape of the LATC reflects...

answer

economies and diseconomies of scale

question

Long-run average total cost curve, LATC is...

**Characteristics

answer

U-shaped

Initially declines, reaches a minimum, and eventually increases

Long-run economies and diseconomies of scale

question

Long-run economies of scale

Average costs ....

answer

fall as a medical firm gets physically larger due to specialization of labor and capital

question

[Long-Run Cost Curves]

Increasing returns to scale

answer

An increase in all inputs results in a more than proportionate increase in output

question

[Long-Run Cost Curves]

Constant returns to scale

answer

Horizontal LATC curve

question

[Long-Run Cost Curves]

Diseconomies of scale

answer

Result when the medical firm becomes too large

Average costs increase as a medical firm gets physically larger

question

[Long-Run Cost Curves]

Decreasing returns to scale

answer

An increase in all inputs results in a less than proportionate increase in output

question

[Shifts in Long-Run Average Cost Curve]
Increase in prices of medical inputs

answer

LATC shifts upward

question

[Shifts in Long-Run Average Cost Curve]

Quality

answer

Cost-saving technology: LATC shifts downward

Higher quality of care: LATC shifts upward

question

[Shifts in Long-Run Average Cost Curve]

Patient case-mix

answer

More severe patient case-mix: LATC shifts upward

question

[Long-Run Cost Minimization and the Indivisibility of Fixed Inputs]

Assumption

answer

All inputs can be costlessly adjusted upward or downward

question

[Long-Run Cost Minimization and the Indivisibility of Fixed Inputs]

Capital inputs

answer

Not easily changed

question

[Long-Run Cost Minimization and the Indivisibility of Fixed Inputs]

Medical firms may adjust slowly

answer

Not produce in long-run equilibrium

Operate with excess capital relative to a long-run equilibrium point

question

[Figure 7.9 - Long-Run Disequilibrium of the Medical Firm]

A firm may not operate in long-run equilibrium because....

answer

of the sizeable costs of adjusting to a sharp change in demand

question

Long-run total cost, LTC

LTC = STVC(q, w ,k)+ r × k

answer

LTC = sum of (minimum) short-run total variable costs, STVC and capital costs

STVC - depends on: quantity of output, q, the wage rate, w, and the quantity of capital, k

question

Necessary condition for long-run cost minimization

ΔSTVC/Δk = -r

answer

question

Cowing and Holtmann (1983), results:

"Average" hospital in their New York sample
Too much capital and too many physicians

answer

Hospitals could reduce their costs by limiting the amount of capital and controlling the number of physicians.

question

Neoclassical cost theory

Assumptions

answer

Perfect certainty

Firms produce as efficiently as possible

Perfect information

question

Short-run or long-run costs of producing a given level of output can be determined by ...

answer

observing the relevant point on the appropriate cost curve

question

Misleading when applied to medical firms because

Some medical firms....

answer

Are not-for-profit entities or are reimbursed on a cost-plus basis or both

No incentive to minimize costs

May operate above a given cost curve

question

Medical firms - uncertain demand for their services

answer

May produce with some amount of reserve capacity just in case an unexpected large increase in demand occurs

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HCMI 3243 – Chapter 7 (Medical Care Production and Costs)

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