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Section 3 – Theory of the Firm

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Title: Section 3 – Theory of the Firm


1
Section 3 Theory of the Firm
  • Thus far we have focused on the individual
    consumers decisions
  • Choosing consumption and leisure to
  • Maximize Utility
  • Minimize Income
  • Section 3 deals with another economic agent, the
    producer, and their decisions
  • Choose inputs, production in order to
  • Minimize Costs (to hopefully maximize profits)

2
Section 3 Theory of the Firm
  • In this section we will cover
  • Chapter 6 Inputs and Production Functions
  • Chapter 7 Costs and Cost Minimization
  • Chapter 8 Cost Curves

3
Chapter 6 Inputs and Production Functions
  • Consumer Theory
  • Theory of the Firm

Goods
Utility
Inputs
Production
Profits
4
Chapter 6 Inputs and Production Functions
  • In this chapter we will cover
  • Inputs and Production
  • Marginal Returns (similar to marginal utility)
  • Average Returns
  • Isoquants (similar to indifference curves)
  • Marginal rate of technical substitution (MRTS,
    similar to MRS)
  • Special production functions (similar to special
    utility functions)

5
Inputs and Production
Definition Productive resources, such as labor
and capital equipment, that firms use to
manufacture goods and services are called
Definition The amount of goods and services
produces by the firm is the firms Definition
transforms a set of inputs into
a set of outputs Definition
determines the quantity of output that is
feasible to attain for a given set of inputs.
inputs or factors of production.
output.
Production
Technology
6
Definitions Continued
Definition The production function tells us the
maximum possible output that can be attained by
the firm for any given quantity of inputs.
Q f(L,K,M) Q f(P,F,L,A) Computer Chips
f1(L,K,M) Econ Mark f2(Intellect, Study, Bribe)
7
Production and Utility Functions
  • In Consumer Theory, consumption of GOODS lead to
    UTILITY
  • Uf(kraft dinner, wieners)
  • In Production Theory, use of INPUTS causes
    PRODUCTION
  • Qf(Labour, Capital, Technology)

8
Notes on the Production Function
  • Definition
  • is attaining the maximum possible output from its
    inputs (using whatever technology is appropriate)
  • Definition A technically inefficient firm is
    attaining less than the maximum possible output
    from its inputs (using whatever technology is
    appropriate)

A technically efficient firm
9
Notes on the Production Function
  • Definition
  • is all points on or below the production function
  • Note Capital refers to physical capital
  • (definition goods that are themselves produced
    goods) and not financial capital (definition the
    money required to start or maintain production).

A production set
10
Q
Example The Production Function and Technical
Efficiency
Production Function
Q f(L)
D

C
Inefficient point


B
Production Set
L
11
  • Definition The feasible but inefficient points
    below the production function make up the firms
    production set
  • Causes of technical inefficiency
  • Shirking
  • Strategic reasons for technical inefficiency
  • Imperfect information on best practices

12
Example
Acme medical equipment faces the production
function QK1/2L1/2 Given labour of 10 and
capital of 20, is Acme producing efficiently by
producing 12 units? What level of production is
technically efficient?
13
Example
Q K1/2L1/2 201/2101/2 14.14 Acme is not
operating efficiently by producing 12 units.
Given labour of 10 and capital of 20, Acme should
be producing 14.14 units in order to be
technically efficient.
14
Returns to Input
  • The production function is also referred to as
    the total product function
  • The increase in production due to an increase in
    input (such as labour) is called returns to the
    input (such as returns to labour)
  • Generally the first few inputs are highly
    productive, but additional units are less
    productive (ie computer programmers working in a
    small room)

15
Q
Example Production as workers increase
Each Additional worker Is less productive
Each Additional worker Decreases Production
Each Additional worker Is equally productive
Each Additional worker Is more productive
Total Product
L
16
Definition of an input is the change
in output that results from a small change in an
input holding the levels of all other inputs
constant.
The marginal product
MPL ?Q/?L (holding constant all other
inputs) MPK ?Q/?K (holding constant all other
inputs)
Example QK1/2L1/2 MPL (1/2)L-1/2K1/2 MPK
(1/2)K-1/2L1/2
17
Marginal Utility and Marginal Product
  • In Consumer Theory, marginal utility was the
    slope of the total utility curve
  • In Production Theory, marginal product is the
    slope of the total product curve

18
Comparison
  • Definition The law of diminishing marginal
    utility states that marginal utility (eventually)
    declines as the quantity consumed of a single
    good increases.
  • Definition The law of diminishing marginal
    returns states that marginal products
    (eventually) decline as the quantity used of a
    single input increases.

19
Q
L
MPL increasing
MPL becomes negative
MPL
MPL decreasing
L
20
Definition The average product of an input is
equal to the total output that is to be produced
divided by the quantity of the input that is used
in its production APL Q/L
APK Q/K
Example QK1/2L1/2 APL K1/2L1/2/L
K1/2L-1/2 APK K1/2L1/2/K L1/2K-1/2
21
Marginal, and Average Product
  • When Marginal Product is greater than average
    product, average product is increasing
  • -ie When you get an assignment mark higher than
    your average, your average increases
  • When Marginal Product is less than average
    product, average product is decreasing
  • -ie When you get an assignment mark lower than
    your average, your average decreases
  • Therefore Average Product is maximized when it
    equals marginal product

22
Q
L
APL increasing
APL decreasing
APL MPL
APL maximized
APL
L
MPL
23
Isoquants
Definition An isoquant traces out all the
combinations of inputs (labor and capital) that
allow that firm to produce the same quantity of
output. Example Q 4K1/2L1/2   What is the
equation of the isoquant for Q 40?  
40 4K1/2L1/2   gt 100 KL
gt K 100/L
24
and the isoquant for Q Q?   Q
4K1/2L1/2   Q2 16KL K Q2/16L
25
K
Example Isoquants
All combinations of (L,K) along the isoquant
produce 40 units of output.
Q 40
Q 20
Slope?K/?L
L
0
26
Indifference and Isoquant Curves
  • In Consumer Theory, the indifference curve showed
    combinations of goods giving the same utility
  • The slope of the indifference curve was the
    marginal rate of substitution
  • In Production Theory, the isoquant curve shows
    combinations of inputs giving the same product
  • The slope of the isoquant curve is the marginal
    rate of technical substitution

27
Definition The marginal rate of technical
substitution (labor for capital) measures the
amount of an input, K, the firm the firm could
give up in exchange for a little more of another
input, L, in order to just be able to produce the
same output as before.
Marginal products and the MRTS are
related MPL/MPK -?K/?L MRTSL,K
28
Marginal Rate of Technical Substitution (MRS)
29
  • The marginal rate of technical substitution,
    MRTSL,K tells us
  • The amount capital can be decreased for every
    increase in labour, holding output constant
  • OR
  • The amount capital must be increased for every
    decrease in labour, holding output constant
  • -as we move down the isoquant, the slope
    decreases, decreasing the MRTSL,K
  • -this is diminishing marginal rate of technical
    substitution
  • -IE as you focus more on one input, the other
    input becomes more productive

30
MRTS Example
Let Q4LK MPL4K MPK4L Find MRTSL,K MRTSL,K
MPL/MPK MRTSL,K 4K/4L MRTSL,K K/L
31
Isoquants Regions of Production
  • Due to the law of diminishing marginal returns,
    increasing one input will eventually decrease
    total output (ie 50 workers in a small room)
  • When this occurs, in order to maintain a level of
    output (stay on the same isoquant), the other
    input will have to increase
  • This type of production is not economical, and
    results in backward-bending and upward sloping
    sections of the isoquant

32
K
Example The Economic and the Uneconomic Regions
of Production
Isoquants
MPK lt 0
Uneconomic region
Q 20
MPL lt 0
Economic region
Q 10
L
0
33
Isoquants and Substitution
  • Different industries have different production
    functions resulting in different substitution
    possibilities
  • Ie In mowing lawns, hard to substitute away from
    lawn mowers
  • In general, it is easier to substitute away from
    an input when it is abundant
  • This is shown on the isoquant curve

34
MRTSL,K is high labour is scarce so a little
more labour frees up a lot of capital
K
MRTSL,K is low labour is abundant so a little
more labour barely affects the need for capital


L
35
MRTS Example
Let Q4LK MPL4K MPK4L MRTSL,K K/L Show
diminishing MRTS when Q16. When Q16,
(L,K)(1,4), (2,2), (4,1) MRTS(1,4)4/14 MRTS(2,
2)2/21 MRTS(4,1)1/4
36
K
MRTSL,K 4

4
MRTSL,K 1
MRTSL,K 1/4

2

1
Q16
L
1
2
4
37
When input substitution is easy, isoquants are
nearly straight lines
K
When input substitution is hard when inputs are
scarce, isoquants are more L-shaped
170
130
100
L
55
100
38
Returns To Scale
How much will output increase when ALL inputs
increase by a particular amount? RTS
?Q/?(all inputs)
1 increase in inputs gt more than 1 increase
in output, increasing returns to scale. 1
increase in inputs gt 1 increase in
output constant returns to scale. 1 increase in
inputs gt a less than 1 increase in output,
decreasing returns to scale.
39
Example 1 Q1 500L1400K1 Q1
500(?L1)400(?K1) Q1 ?500L1?400K1 Q1
?(500L1400K1) Q1 ?Q1 So this production
function exhibits CONSTANT returns to scale. Ie
if inputs double (?2), outputs double.
40
Example 2 Q1 AL1?K?1 Q2
A(?L1)?(?K1)? ??? AL1?K?1
???Q1 so returns to scale
will depend on the value of ??. ?? 1
CRS ?? lt1 DRS ?? gt1 IRS
41
Returns To Scale
  • Why are returns to scale important?
  • If an industry faces DECREASING returns to scale,
    small factories make sense
  • -It is easier to have small firms in this
    industry
  • If an industry faces INCREASING returns to scale,
    large factories make sense
  • -Large firms have an advantage natural
    monopolies

42
Notes
  • The marginal product of a single factor may
    diminish while the returns to scale do not
  • Marginal product deals with a SINGLE input
    increasing, while returns to scale deals with
    MULTIPLE inputs increasing
  • Returns to scale need not be the same at
    different levels of production

43
Special Production Functions
  • 1. Linear Production Function
  • Q aL bK
  • MRTS constant
  • Constant returns to scale
  • Inputs are PERFECT SUBSTITUTES
  • -Ie 10 CDs are a perfect substitute for 1 DVD
    for storing data.

44
K
Example Linear Production Function
Q Q1
Q Q0
L
0
45
Special Production Functions
-ie 2 pieces of bread and 1 piece of cheese
make a grilled cheese sandwich Qmin (c, 1/2b)
46
Cheese
Example Fixed Proportion Production Function
Q 2
2
Q 1
1
0
Bread
2 4
47
Special Production Functions
  • Cobb-Douglas Production Function
  • Q aL?K?
  • if ? ? gt 1 then IRTS
  • if ? ? 1 then CRTS
  • if ? ? lt 1 then DRTS
  • smooth isoquants
  • MRTS varies along isoquants

48
K
Example Cobb-Douglas Production Function
Q Q1
Q Q0
0
L
49
  • Constant Elasticity of Substitution Production
    Function
  • Q aL?bK?1/?
  • Where ? (?-1)/?
  • if ? 0, we get Leontief case
  • if ? ?, we get linear case
  • if ? 1, we get the Cobb-Douglas case
  • General form of other functions

50
Technological Progress
Definition Technological progress shifts the
production function inward by allowing the firm
to achieve more output from a given combination
of inputs (or the same output with fewer inputs).
Neutral technological progress shifts the
isoquant corresponding to a given level of output
inwards, but leaves the MRTSL,K unchanged along
any ray from the origin
51
Technological Progress Ctd...
Labor saving technological progress results in a
fall in the MRTSL,K along any ray from the
origin Capital saving technological progress
results in a rise in the MRTSL,K along any ray
from the origin.
52
Example neutral technological progress
K
Q 100 before
Q 100 after
MRTS remains same
K/L
L
53
Example Labor Saving Technological Progress
K
Q 100 before
MRTS gets smaller
Q 100 after
K/L
L
54
Example capital saving technological progress
K
Q 100 before
Q 100 after
MRTS gets larger
K/L
L
55
Technological Progress
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