Unit 6

Firm Production Processes (SR, LR)

Key Topics

1. Productiona. Definition

b. Relationship to profit

c. Short-run vs long-run

2. Short-run production conceptsa. Total product (or production function)

b. Marginal product (& diminishing returns)

c. Average product

d. Stages of production

Key Topics

3. Long-run production conceptsa. Isoquants

b. Labor vs. capital intensive

c. Marginal rate of technical substitution

d. Technological progress

Common goal of business firms

= profit

= total revenue (TR) – total costs (TC)

Questions

1. What business firm decisions affect profits of the firm?

2. How can a firm increase its profits?

Firm decisions that impact TR

1. Products to produce

2. Product prices

3. Quantity of products

4. How to market/promote products

Firm decisions that impact TC

1. Quantity of products produced

2. What inputs to use to produce products

3. What quantity and combinations of inputs to use

4. How to acquire inputs

5. How to make inputs more productive

Examples of corn producer ‘input’ decisions:

Seed brand Seeds per acre to plant When to plant Calibrate planter Nitrogen fertilizer per acre to apply When and how to spray weeds

Examples of restaurant ‘input’ decisions:

Number of cooks Number of waiters/waitresses Number of receptionists What supplies (food, other) Quantity of supplies (food, other) Hours of operation Cooking equipment

Production

= the process by which inputs are combined and transformed into outputs

Question

What’s the difference between short-run and long-run production to an economist?

Types (or lengths) of production periods

1. Short run (SR) period of time for which a firm is stuck with a fixed or given quantity of at least one input

2. Long run (LR) period of time for which a firm can vary or alter the quantities of all inputs

Production Function

= a numerical, tabular, or graphical expression showing the maximum units (quantities) of a product that can be produced as a function of units (quantities) of inputs

Q. What do the following have in common?

The owner of a restaurant who is deciding how many cooks to hire for a given day.

A corn farmer who is deciding how many pounds of nitrogen fertilizer to apply.

Management of a manufacturing firm who is deciding how many workers to employ at various points in an assembly line.

A. They all need some knowledge as to what the relevant ‘production function’ looks like (i.e. the relationship between physical units of input and physical units of output for their operation).

General equation of a typical SR production function

q f k L where

q physica l un its o f ou tpu t

k fixed num ber o f physica l un its o f cap ita l

L physica l un its o f labor tha t are iab le

( , )

" "

" var "

SR Production Concepts

1. TP = total product

= total physical units of output

= total quantity of output

= q = f ( , )k L

2. AP = average product

= output per unit of input

= output of ‘average’ input

= slope of line from origin to TP curve

= q/L

SR Production Concepts

3. MP = marginal product

= additional output per unit of additional input

= slope of TP curve

= output of last input unit

= Δq/ΔL

Production Function Example

Labor Units (Employees)

Total Product (Sandwiches/hr)

Marginal Product of

Labor

Average Product of Labor (Total product ÷ Labor Units)

0 0 -- --

1 10 10 10.0

2 25 15 12.5

3 35 10 11.7

4 40 5 10.0

5 42 2 8.4

6 42 0 7.0

Q. Can you graph the TP, MP, AP curves?

‘Linear’ SR Production Function

TP

L

L

a

AP, MP

MP=AP=a

q=aL

Types of SR production functions

Nonlinear

Linear

“Stages” of production

Stage Characteristic

I AP is ing

II* AP is ing and MP > 0

III MP < 0

*Firms will be maximizing profits only if they are operating in Stage II.

Questions

How does your cumulative GPA and your last-term GPA relate to production concepts?

What happens to your cumulative GPA if your last-term GPA is greater?

Nonlinear Production AP and MP relationship

If MP > AP, AP is ingIf MP < AP, AP is ingIf MP = AP, AP is either at a max

or is a constant

The law of diminishing returns

As additional units of a variable input are combined with fixed inputs, there will come a point where the marginal product of the variable input will start to decline.

General equation of a LR production function

q = f (K,L)

q = physical units of output

k = physical units of capital that are variable

L = physical units of labor that are variable

Isoquant

A graph of the combinations of inputs (K, L) that yield the producer the same level of output.

The shape of an isoquant reflects the ease with which a producer can substitute among inputs while maintaining the same level of output.

Pt ‘a’ = ‘capital’ intensive production process

Pt ‘b’ = ‘labor’ intensive production process

K

La

Ka

Kb

Lb L

a

bq1

isoquant

LR Production Example: Alternative Combinations of Capital (K) and labor (L) Required to Produce 50 and 100, Units of Output

QX = 50 QX = 100

K L K L

1 8 2 10

2 5 3 6

3 3 4 4

5 2 6 3

8 1 10 2

Q. Can you graph the Q = 50 and Q = 100 isoquants?

SR Production in LR Diagram

K

L1LL2

q1

q2

K

- Slope of Isoquant

From 1 pt on an isoquant to another

Δq = MPK (ΔK) + MPL (ΔL) = 0

MPK (ΔK) + MPL (-ΔL) = 0

K

L

MP

MPL

K

= Rate K can be exchanged for 1 unit of L holding output constant (= marginal rate of technical substitution)

SR Technological Progress

q

L

TP2

TP1

LR Technological Progress

K

K1

b a

c

L1 L

q1 (old)

q1 (new)