The Production Function

What is the Input-Output Relationship?

The input-output relationship involves the specification of alternative combinations of inputs that yield varying levels of outputs.

Inputs typically consist of:

Labor or workers
Capital
Land and raw materials
Intermediate goods and services
Entrepreneurial abilities

Close up of girl's hand placing the last jigsaw puzzle piece with word Input and Output

Types of Inputs

Amount does not change over time

Amount varies over time

Check your Understanding: Is the Input Fixed or Variable?

Instructions: Choose the correct item in the drop down menu and identify whether the inputs below are fixed or a variable.

The operating room size is increased

A purchase of a new MRI Machine

A shipment of 300,000 face masks received

The increase in the cleaning staff during a pandemic.

Output

Directions: Please select each of the options below to learn more about outputs.

The quantity of whatever good or service that is being produced.

Patient visits
Tests
Procedures

Each unit of output the same quality

Check your Understanding: Input or Output?

Instructions: Choose the correct item in the drop down menu to determine whether the following examples would be considered inputs or outputs in the hospital setting?

The number of flu vaccinations given in November

An increase in nursing staff in over the past year

A purchase of a new mammogram machine

An increase in mammogram testing

What is Happening in This Production Function

Choose each item in the acordion below to learn more.

Variable Output

Labor (L)

ex. The number of nurses used to perform vaccinations.

Number of Nurses (L)	Vaccinations (Q or TP)	Marginal Production of Labor
0	0	-----
1	20	20
2	45	25
3	65	20
4	80	15
5	90	10
6	95	5

Output (Q)

Total Productions (TP)

ex. The number of vaccinations performed

Number of Nurses (L)	Vaccinations (Q or TP)	Marginal Production of Labor
0	0	-----
1	20	20
2	45	25
3	65	20
4	80	15
5	90	10
6	95	5

image of multiple patients getting vaccinations

Fixed Input

A resource or factor of production that cannot be changed

ex. Space available to perform these vaccinations

Number of Nurses (L)	Vaccinations (Q or TP)	Marginal Production of Labor
0	0	-----
1	20	20
2	45	25
3	65	20
4	80	15
5	90	10
6	95	5

Marginal Product of Labor (MPL)

= ∆Q/∆L

Number of Nurses (L)	Vaccinations (Q or TP)	Marginal Production of Labor
0	0	-----
1	20	20
2	45	25
3	65	20
4	80	15
5	90	10
6	95	5

Law of Diminishing Returns

Diminishing marginal returns means at higher levels of labor (L), the marginal productivity begins to decline.

Table: Law of Diminishing Returns

More nurses are used to perform vaccinations, their MLP eventually declines.

Number of Nurses (L)	Vaccinations (Q or TP)	Marginal Production of Labor
0	0	-----
1	20	20
2	45	25
3	65	20
4	80	15
5	90	10
6	95	5

Graph: Law of Diminishing Returns

Note: the production functions gets flatter as the number of variable inputs increases, reflecting diminishing marginal product.

The Factors that Shift the Production Function

The Client Mix

The type and/or severity of the patients seen

Example: If some procedure is being performed and the patient mix is sicker than before, more time will be needed to treat these patients.
Result: This would shift the production function down; fewer patients would he treated.

Check your Understanding

Instructions: Read the following scenarios and choose the correct response.

Which of the following scenarios would produce and shift down in production where fewer patients would be treated?

Change in the Quality of Care

Example: If the quality of care is increased the production function will shift down as more time will be needed to treat each patient.
Result: Fewer patients will be treated.

Check your Understanding

Instructions: Read the following scenarios and choose the correct response.

Which of the following scenarios would produce a shift down in the production function where fewer patients would be treated?

Technology

Example: The effect of technology is ambiguous.
Result:

Some types of new technology can increase the productivity of labor
The production function will shift up which means more patients will be treated.

Check your Understanding

Instructions: Read the following scenarios and choose the correct response.

Which scenario would be a situation where the production function would shift up and more patients would be treated?

The Management Incentive System

Minimize costs → Production function will shift up and more patients will be treated
Fewer resources used per patient → Labor productivity will increase
Use more resources → Production function shifts down and fewer patients will be treated

Check your Understanding

Instructions: Read the following scenarios and choose the correct response.

Which of the following scenarios will cause the production function to shift down and as a result fewer patients will be seen?