UNIVERSIDAD COMPLUTENSE DE MADRID
Departamento de Fundamentos del Análisis Económico I
Microeconomics:
Production
Rafael Salas
2nd term 2014-2015
Objective
Producer theory: to build a model to explain and predict
producer behavior.
Producer face an economic problem: to use inputs to
obtain output, we are interested in how they solve the
problem.
Model
We typically assume firms maximize profits or minimize
costs subject to some constraints
Constraints:
1. Technical constraints: “The state of the arts” are
measurable by the production function
2. Economic constraints: limited resources; prices of
inputs and output. Monetary costs and opportunity costs
3. Institutional constraints: the market the firm is in;
specific legal aspects like taxes, subsidies, etc.
Technical restrictions
1. Production function
Firms transform inputs (or factors) into output or (products).
Production functions represent the technical relationship
between input and outputs. It represent the technology.
It incorporates all production processes (methods) that are
technically efficient (see below)
Inputs and output are physical variables (Tons, etc.) and flows
variable (in a year, in a month)
Technical restrictions
1. Production process (method, technique)
It is a combination of inputs required to attain a certain level
of output.
A production process “A” is technically efficient relative to
another process “B”, if A uses less units of at least one input
and no more from other input as compared with process B to
produce a given level of output.
Production functions only consider technically efficient
production processes.
Examples
• To produce x=1, we have three processes
P1 uses L=2 and K=3
P2 uses L=3 and K=2
P3 uses L=1 and K=4
• To produce x=1, we have two processes
A uses L=2 and K=3
B uses L=3 and K=3
• To produce x=1, we have two processes
C uses L=2 and K=3
D uses L=1 and K=4
Technical restrictions
Assumption: output and inputs are perfect divisible
Production functions are represented by a function of inputs
q=F(L,K,E,…)
It indicates the maximum quantity of output attainable for all
possible combinations of inputs (because it incorporates only
technically efficient processes)
It describes the laws of production (see later on)
Production functions
It can be represented by a map of isoquants
An isoquant includes all the technically efficient
methods (or all the combinations of inputs) for
producing a given level of output
Examples: draw isoquants for q=40 from
q=10L+20K
q=LK
It implies some input substitutability (see below)
Short-run and Long-run production
Different properties according we are in:
The short-run: some input are fixed
Long-run: all inputs are variable
Short-run production
Assume two inputs capital and labor.
Capital is typically fixed
We ask about how output changes as labor varies.
We draw a two-dimensional graph between output and
labor, for a given level of capital.
Average and Marginal Products
Average product (productivity) APL= q/L
Marginal product (productivity) MPL= dq/dL
Graphically:
Average product is the slope of the slope running from
the origin to the corresponding point in the production
function
Marginal product is the slope of the production function
Table 6.1
L
0
1
2
3
4
5
6
7
8
9
10
K
10
10
10
10
10
10
10
10
10
10
10
q
0
10
30
60
80
95
108
112
112
108
100
q/L dq/dL
Graph from Table 6.1
Average and Marginal Products
L
0
1
2
3
4
5
6
7
8
9
10
K
10
10
10
10
10
10
10
10
10
10
10
q
q/L dq/dL
0
10 10
10
30 15
20
60
80
95
108
112
112
108
100
Average and Marginal Products
L
0
1
2
3
4
5
6
7
8
9
10
K
10
10
10
10
10
10
10
10
10
10
10
q
q/L dq/dL
0
10 10
10
30 15
20
60 20
30
80 20
20
95 19
15
108 18
13
112 16
4
112 14
0
108 12
-4
100 10
-8
Graph from Table 6.1
Laws of production in the short-run
Law of diminishing marginal returns states that:
in all productive activities, adding more of the variable
factor, while holding all other constant, will at some point
decrease the marginal productivity
(as in the example above, from x=3 onwards)
Long-run production
Assume two inputs capital and labor.
Capital is also variable
We ask about how output changes when both inputs
vary.
We draw a two-dimensional graph between capital and
labor, and output is drawn as a set of isoquants
(contour lines)
Long-run production
Isoquants are decreasing if they incorporates only
technically efficient production processes
We get different shapes of isoquants (and therefore of
production functions) depending on the degree of
substitutability of factors. The degree of substitutability
is linked with the curvature of the isoquants…
Marginal Rate of Technical
Substitution (MRTS)
One way to describe the degree of substitutability is by
defining the MRTS:
MRTS=-dK/dL=MPL/MPK
MRTS means the number of K needed to be reduced if 1
unit of labor is increased to keep output constant
Apart from the extreme cases (perfect substitutes and
complements), isoquants and downward sloping and
strictly convex. It means decreasing MRTS as labor
increases (capital becomes relatively more productive as
more labor replaces capital to keep output constant)
Different production functions
We get different shapes of isoquants (and therefore of
production functions) depending on the degree of
substitutability of factors:
Linear isoquants (perfect substitutes)
Smooth strictly-convex isoquants
Right-angle isoquants (fixed-proportions production). No
substitutability. Just one process.
They have different properties. Draw them graphically
Laws of production in the long-run
The laws of returns to scale: what would it happen
to output if all factors are changed by the same
proportion. 3 cases:
Increasing Returns to scale (output increases more than
proportionally)
Constant Returns to Scale (output increases proportionally)
Decreasing Returns to Scale scale (output increases less than
proportionally)
Draw them graphically
Exercises
3, 4, 5 of page 219 of the textbook
8, 9 and 10 page 220 of the textbook
UNIVERSIDAD COMPLUTENSE DE MADRID
Departamento de Fundamentos del Análisis Económico I
Microeconomics II:
Production
Rafael Salas
2nd term 2014-2015