The Production Process
Learning objectives
• Establish the relationship between inputs and output.
• Distinguish between variable and fixed inputs.
• Define total, average, and marginal product.
• Understand the Law of Diminishing Marginal Returns.
• Investigate the ability of a firm to vary its output in the long run when
all inputs are variable.
• Explore returns to scale: how a firm’s output response is affected by a
proportionate change in all inputs.
• Overview how production relationships can be estimated and some
difference potential functional forms for those relationships.
Production Analysis
• Production Function Q = f(K,L)
• Describes available technology and feasible
means of converting inputs into maximum
level of output, assuming efficient utilization
of inputs:
• ensure firm operates on production function (incentives
for workers to put max effort)
• use cost minimizing input mix
• Short-Run vs. Long-Run Decisions
• Fixed vs. Variable Inputs
Production Analysis
• Factors of production – inputs or ingredients mixed
together by a firm through its technology to produce output
• Production function – a relationship between inputs and
output that identifies the maximum output that can be
produced per time period by each specific combination of
inputs
Q = f(L,K)
• Technologically efficient – a condition in which the firm
produces the maximum output from any given combination
of labor and capital inputs
Short Run and Long Run
•The Short Run: Fixed Plant
•The short run is a time frame in which the quantities of
some resources are fixed.
•In the short run, a firm can usually change the quantity of
labor it uses but not the quantity of capital
•The Long Run: Variable Plant
•The long run is a time frame in which the quantities of
all resources can be changed.
•A sunk cost is irrelevant to the firm’s decisions.
Total Product
• Total product (TP) is the total quantity of a good
produced in a given period.
• Cobb-Douglas Production Function
• Example: Q = f(K,L) = K.5 L.5
• K is fixed at 16 units.
• Short run production function:
Q = (16).5 L.5 = 4 L.5
• Production when 100 units of labor are used?
Q = 4 (100).5 = 4(10) = 40 units
Short Run Production
Marginal Product of Labor
•Measures the output produced by the last worker. Marginal
Product
• Marginal product is the change in total product that
results from a one-unit increase in the quantity of labor
employed.
• It tells us the contribution to total product of adding one
more worker.
• MPL = DQ/DL
• Slope of the production function
Marginal Product
Marginal Product graphed
Observations
• Increasing marginal returns initially
• Increasing marginal returns occur when
the marginal product of an additional worker
exceeds the marginal product of the previous
worker.
• Increasing marginal returns occur when a small
number of workers are employed and arise
from increased specialization and division of
labor in the production process.
Observations
• Decreasing marginal returns
• Decreasing marginal returns occur when the marginal
product of an additional worker is less than the
marginal product of the previous worker.
• Decreasing marginal returns arise from the fact that
more and more workers use the same equipment and
work space.
• As more workers are employed, there is less and less
that is productive for the additional worker to do.
• Negative marginal returns
• Decreasing marginal returns are so pervasive
that they qualify for the status of a law:
• The law of decreasing returns states that:
As a firm uses more of a variable input, with a given quantity
of fixed inputs, the marginal product of the variable input
eventually decreases.
Average Product of Labor
• APL = Q/L, Average product of Labour = Total product 
Quantity of labor
• Measures the output of an “average” worker.
• Slope of the line from origin onto the production function
•Average product is the total product per worker
employed.
•Another name for average product is productivity.
Relationship between MPL and APL
Relationship between MPL and APL
• When marginal product is less than average
product, average product is decreasing.
• When marginal product equals average
product, average product is at its maximum.
• When marginal product is greater than
average product, average product is
increasing.
Law of Diminishing Returns (MPs)
Three significant points are:
Max MPL (TP inflects)
Max APL = MPL
MPL = 0 (Max TP)
25
20
Total Product
TP increases at an increasing
rate (MP > 0 and ) until
inflection , continues to
increase at a diminishing rate
(MP > 0 but ) until max and
then decreases (MP < 0).
15
10
5
04
3
0
2
4
6
8
10
12
8
10
12
Input L
2
1
0
A line from the origin is tangent
to Total Product curve at the
maximum average product.
-1 0
2
4
6
-2
-3
-4
Increasing
MP
Diminishing
MP
Negative
MP
LONG RUN PRODUCTION
Economies of Scale
• Economies of scale exist if when a firm
increases its plant size and labor employed by
the same percentage, its output increases by a
larger percentage and average total cost
decreases.
• The main source of economies of scale is
greater specialization of both labor and capital.
LONG RUN PRODUCTION
Diseconomies of Scale
• Diseconomies of scale exist if when a firm increases its
plant size and labor employed by the same percentage,
its output increases by a smaller percentage and average
total cost increases.
• Diseconomies of scale arise from the difficulty of
coordinating and controlling a large enterprise.
• Eventually, management complexity brings rising
average total cost.
LONG RUN PRODUCTION
Constant Returns to Scale
• Constant returns to scale exist if when a firm
increases its plant size and labor employed by
the same percentage, its output increases by the
same percentage and average total cost remains
constant.
• Constant returns to scale occur when a firm is
able to replicate its existing production facility
including its management system.
Isoquant
• 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.
• Slope or Marginal Rate of Technical Substitution can be
derived using total differential of Q=f(K,L) set equal to
zero (no change in Q along an isoquant)
Cobb-Douglas Production Function
• Q = KaLb
• Inputs are not perfectly
substitutable (slope changes
along the isoquant)
DK
a L
for b  1  a,

DL
1 a K
• Diminishing MRTS: slope
becomes flatter
K
Q3
Q2
Q1
Increasing
Output
-DK1
||
-DK2
• Most production processes
have isoquants of this shape
• Output requires both inputs
DL1 < DL2
L
Linear Production Function
• Q = aK + bL
• Capital and labor are
perfect substitutes
(slope of isoquant is
constant)
y = ax + b
K = Q/a - (b/a)L
• Output can be
produced using only
one input
K
Increasing
Output
Q1
Q2
Q3
L
Leontief Production Function
• Q = min{aK, bL}
• Capital and labor are
perfect complements and
cannot be substituted (no
MRTS <=> no slope)
• Capital and labor are
used in fixed-proportions
• Both inputs needed to
produce output
Q3
K
Q2
Q1
Increasing
Output
• The combinations of
Isocost
inputs that cost the same
amount of money
C = K*PK + L*PL
K
New Isocost for
an increase in the
budget (total cost).
• For given input prices,
isocosts farther from the
origin are associated with
higher costs.
• Changes in input prices
change the slope (Market
Rate of Substitution) of the
isocost line
K = C/PK - (PL/PK)L
C0
K
C1
L
New Isocost for
a decrease in the
wage (labor price).
L
Long Run Cost Minimization
Min cost where isocost
is tangent to isoquant
(slopes are the same)
MRS KL  
PL
MPL

 MRTS KL
PK
MPK
Expressed differently:
MP (benefit) per dollar
spent (cost) must be
equal for all inputs
MPL MPK

PL
PK
K
-PL/PK < -MPL/MPK
MPK/PK< MPL/PL
Point of Cost
Minimization
-PL/PK = -MPL/MPK
MPK/PK= MPL/PL
-PL/PK > -MPL/MPK
MPK/PK> MPL/PL
Q
L
K
E
KE
Q3
TC
LE
Q1
L
Q2
Returns to Scale
• Return (MP): How TP changes when one input increases
• RTS: How TP changes when all inputs increase by the
same multiple  > 0
• Q = f(K, L)

Increasing
• If f(K, L)  Q  Constant Returns to Scale

Decreasing
• Q = 50K½L½
Q = 100,000 + 500L + 100K
Q = 0.01K3 + 4K2L + L2K + 0.0001L3