5.3 Consumer Surplus
Difference between maximum amount a consumer is willing to pay for a good (reservation price) and
the amount he must actually pay to purchase the good in the market place.
10.2 The Invisible Hand
Will always guide the supply and demand
curve back to equilibrium
10.9 Import Quotas and Tariffs
Pg 390 Impact of quotas and tariffs
Chapter 6
Inputs and Production Functions
Intro to Inputs and Production
Functions
• Inputs – Resources such as labor, capital equipment, and raw
materials that are combined to produce finished goods
• Factors of Production – resources that are used to produce a good
• Output – The amount of a good or service produced by a firm
• Production function – A mathematical representation that shows the
maximum quantity of output a firm can produce given the quantities
of inputs that it might employ
– Q is the quantity of output Q= f(L,K)
– L is the quantity of labor used
– K is the quantity of capital employed
• Production set – The set of technically feasible combinations of
inputs and outputs
•
•
•
Technically Inefficient – The set of points in
the productions set at which the firm is
getting less output from its labor than it
could
Technically Efficient – The set of points in
the production set at which the firm is
producing as much output as it possibly
can given the amount of labor it employs
Labor requirements functions – A function
that indicates the minimum amount of labor
required to product a given amount of
output
–
L=g(Q) the minimum amount of labor L
required to produce a given amount of output
Q
Total Product Functions
•
•
•
•
•
A total product function with a single
input shows how total output depends
on the level of the input
Increasingly marginal returns to labor –
the region along the total product
function where output rises with
additional labor at an increasing rate
(sometimes not always = to slope)
Diminishing marginal returns to labor –
the region along the total product
function in which output rises with
additional labor but at a decreasing rate
Diminishing total returns to labor – the
region along the total product function
where output decreases with additional
labor
Stages
–
–
–
1 Increasing Marginal Returns
2 Diminishing Marginal Returns
3 Diminishing Total Returns
Marginal and Average Product of
Labor
• Average product of
labor is the average
output per unit of labor
– APL= total
product/quantity of
labor = Q/L
• Marginal product of
labor is the rate at which
total output changes as
the quantity of labor the
firm uses is changed.
– MPL = Δ in total
product/ Δ in total
quantity of labor =
ΔQ/ΔL
Law of diminishing marginal
returns- principle
The principle that as the usage of one input
increases, the quantities of other inputs
being held fixed, a point will be reached
beyond which the marginal product of the
variable input will decrease
Relationship between Marginal and
Average Product
• When average product is
increasing in labor,
marginal product is
greater than average
product. That is if APL
increases in L, then MPL >
APL
• When average product is
decreasing in labor, the
marginal product is less
than average product.
That is, if APL is at
maximum, then marginal
product is equal to
average product.
Production Functions with
more than one output
Total Product Hill
A three-dimensional graph of
production function
Isoquants
• “Means same quantity”:
any combination of labor
and capital among a given
isoquant allows the firm to
produce the same
quantity of output
• Isoquant is a curve that
shows all of the
combinations of labor and
capital that can produce
given levels of output.
Economic and Uneconomic
Regions of Production
• Uneconomic region of
production - the region
of upward-sloping or
backward-bending
isoquants. In the
uneconomic region, at
least one input has a
negative marginal
product
• Economic region of
production – The
region where the
isoquants are
downward sloping
Marginal Rate of Technical
Substitution
•
•
MRTSL,K-The rate at which the quantity of capital can be reduced for every one unit
increase in the quantity of labor, holding the quantity output constant.
MRTSL,K tells us:
–
–
The rate at which the quantity of capital can be decreased for every one unit increase in the
quantity of labor, holding the quantity of the output constant
The rate at which the quantity of capital must be increased for every one unit decrease in the
quantity of labor, holding the quantity of output constant
Diminishing Marginal Rate of
Substitution
A feature of a production function in which the marginal rate
of technical substitution of labor for capital diminishes as
the quantity of labor increases along an isoquant
Substitutability Among Inputs
Elasticity of Substitution
• A measure of how easy
it is for a firm to
substitute labor for
capital. It is equal to the
percentage change in
the capital-labor ratio for
every one percent
change in the marginal
rate of technical
substitution of capital for
labor as we move along
the isoquant
• Capital-labor ratio – The
ratio of the quantity of
capital to the quantity of
labor (used as labor is
substituted by capital)
Special Production Functions
Linear Production Function
• Perfect Substitutes – (in production) Inputs in a
production function with a constant marginal rate
of technical substitution
• A production function of the form Q=aL+bK,
where a and b are positive constants
The Fixed-Proportions Production
Function
• Fixed-proportions production function – a production
function where the inputs must be combined in a
constant ration to one another
• Perfect complements – (in production) Inputs in a fixedproportions production function.
The Cobb-Douglas Production
Function
•
•
•
A production function of the form Q ALα Kβ, where Q is the quantity of output
from L units of labor and Kunits of capital and where A, α, and β are positive
constants.
The elasticity of substitution for a Cobb–Douglas production function falls
somewhere between 0 and ∞. In fact, it turns out that the elasticity of
substitution along a Cobb–Douglas production function is always equal to 1.
Capital and Labor can be substituted for each other
The Constant Elasticity of
Substitution Production Function
A type of production function that
includes linear production functions,
fixed-proportions production
functions, and Cobb-Douglas
production functions as special
cases.
Returns to Scale
The concept that tells us the percentage by which output
will increase when all inputs are increased by a given
percentage
Let φ represent the resulting proportionate increase in the quantity of
output Q (i.e., the quantity of output increases from Q to φQ).
• increasing returns to scale - A proportionate increase in all input
quantities resulting in a greater than proportionate increase in
output.
– If φ > λ
• constant returns to scale - A proportionate increase in all input
quantities simultaneously that results in the same percentage
increase in output.
– If φ = λ
• decreasing returns to scale - A proportionate increase in all input
quantities resulting in a less than proportionate increase in output.
– φ<λ
Returns to Scale vs Diminishing
Marginal Returns
Returns to scale pertains to the impact of an increase in all
input quantities simultaneously, while marginal returns
(i.e., marginal product) pertains to the impact of an
increase in the quantity of a single input, such as labor,
holding the quantities of all other inputs fixed.
Technological Progress
Technological Progress – a change in
production process that enables a firm to
achieve more output from a given
combination of inputs or, equivalently, the
same amount of output from less inputs
Neutral Technological Progress
• progress that decreases the amounts of labor and capital needed to
produce a given output, without affecting the marginal rate of
technical substitution of labor for capital
– or… Isoquant shifts inward indicating that lesser amounts of labor and
capital are needed to produce a given output, but the shift leaves
MRTSL,K, the marginal rate of technical substitution of labor or capital,
unchanged along any ray (e.g., 0A) from the origin.
Labor-saving Technical Progress
• progress that causes the marginal product of capital to
increase relative to the marginal product of labor
– Isoquant shifts inward, but the isoquant becomes flatter
Capital-Savings Technological
Progress
Progress that causes the marginal product of labor to
increase relative to the marginal product of capital
Chapter Summary
•
•
•
•
•
•
The production function tells us the maximum
quantity of output a firm can get as a function of the
quantities of various inputs that it might employ.
Single-input production functions are total product
functions. A total product function typically has three
regions: a region of increasing marginal returns, a
region of diminishing marginal returns, and a region
of diminishing total returns.
The average product of labor is the average amount
of output per unit of labor. The marginal product of
labor is the rate at which total output changes as
the quantity of labor a firm uses changes.
The law of diminishing marginal returns says that as
the usage of one input (e.g., labor) increases—the
quantities of other inputs, such as capital or land,
being held fixed—then at some point the marginal
product of that input will decrease.
Isoquants depict multiple-input production function
in a two-dimensional graph. An isoquant shows all
combinations of labor and capital that produce the
same quantity of output.
For some production functions, the isoquants have
an upward-sloping and backward-bending region.
This region is called the uneconomic region of
production.
•
•
•
•
•
Here, one of the inputs has a negative marginal
product. The economic region of production is the
region of downward-sloping isoquants.
The marginal rate of technical substitution of labor
for capital tells us the rate at which the quantity of
capital can be reduced for every one unit increase
in the quantity of labor, holding the quantity of
output constant. Mathematically, the marginal rate
of technical substitution of labor for capital is equal
to the ratio of the marginal product of labor to the
marginal product of capital.
Isoquants that are bowed in toward the origin
exhibit diminishing marginal rate of technical
substitution. When the marginal rate of technical
substitution of labor for capital diminishes, fewer
and fewer units of capital can be sacrificed as each
additional unit of labor is added along an isoquant.
The elasticity of substitution measures the
percentage rate of change of K/L for each 1 percent
change in MRTSL,K.
Three important special production functions are the
linear production function (perfect substitutes), the
fixed-proportions production function (perfect
complements), and the Cobb–Douglas production
function. Each of these is a member of a class of
production functions known as constant elasticity of
substitution production functions.