Econ Dept, UMR
Presents
The Supply Side of the Market
in
Three Parts:
I. An Introduction to Supply and
Producer Surplus
II. The Production Function
III. Cost Functions
Starring
u Supply
v Production
v Cost
u Producer surplus
Featuring
uThe Law of Diminishing Marginal Product
uThe MP/P Rule
uEconomic Cost vs. Accounting Cost
uEconomic Profit vs. Accounting Profit
uThe Unimportance of Sunk Cost
Part III: Cost Functions
Linking Production to Costs
u
Each production relationship has a cost
counterpart
v
v
v
v
v
u
TP:variable input
AP:variable input
MP:variable input
Fixed inputs
MP/P rule
-- variable cost
-- average variable cost
-- marginal cost
-- fixed (or sunk) cost
-- equal MC rule
The production function and the MP/P rule
tells us the minimum cost of producing any
level of output, q: cost = input price times
inputs required = P*R
Short
Run
Costs
First by definition we have Fixed
Costs that do not vary with output
FC = iK ; where i is the price
of the fixed input, capital (K)
FC
q0
q1
q2
q3
q/t
Often fixed costs are also sunk costs. Sunk costs are
costs already incurred and are beyond recovery.
Short
Run
Costs
Second, we have
variable cost.
Adding TVC and FC
gives Total Costs
TC
TVC + FC = TC
TVC
Fixed Costs
TVC = wL where w is
the price of the variable
input, labor (L)
FC
q0
q1
q2
q3
q/t
Notice the vertical distance between TC and TVC is Fixed Cost
TC
Short
Run
Costs
TVC
Notice the curvature of
TC and TVC is the
same. The slope of
both at any output is
marginal cost
Fixed Costs
At q3, slope of TC =
slope of TVC = MC
FC
q0
q1
q2
q3
MC = (ÎTC/ Îq)
q/t = (ÎTVC/ Îq)
The rise over the run is the change in cost, total or
variable, divided by the change in output
Short
Run
Costs
TC
TVC
Tangency’s to show
minimum AVC and
ATC
•q1 min AVC
•q2 min ATC
Note, q2 > q1 as long
as fixed costs are
present. That is the
FC
output at which
AVC is minimized is
q/t
less than the output
q0 q1 q2 q3
at which ATC is
minimized as long
(TVC/q) = AVC; (TC/q) = ATC
as FC > 0
Short
Run
Costs
Inflection Points
TC
TVC
•q0 min MC
At q0, the law of diminishing
marginal returns sets in
FC
q/t
q0 q1 q2 q3
At the Inflection Point, TC and TVC stop increasing at a
decreasing rate and start increasing at an increasing rate.
MC falls up to q0 then starts to increase.
Short
Run
Costs
TC
TVC
Everything
Together
Tangency’s to show
minimum AVC and
ATC
Fixed Costs
Inflection Points
•q0 min MC
•q1 min AVC
FC
•q2 min ATC
q0
q1
q2
q3
TVC + TFC = TC = wL + iK
q/t
•q3 slope of TC
= slope of TVC
= MC at q3
Per Unit Short Run Costs
u Let’s look now at costs on a per unit basis
v Average fixed cost, AFC = FC/q
v Average variable cost, AVC = TVC/q
v Average total cost, ATC = TC/q
v Marginal cost, MC = ÎTC/Îq = ÎTVC/Îq
AFC = FC/q
Short Run
Per Unit
Costs
First, Average Fixed Costs declines
throughout the range of output.
This is because you are dividing a
constant, FC, with an ever
increasing quantity.
AFC
q0
q1
q2
q/t
In the short run, the average
curves take on a “U” shape
driven by the law of diminishing
marginal returns
Short Run
Per Unit
Costs
ATC
AVC
AFC = FC/q
q0
q1
AVC = TVC/q
ATC = AFC + AVC = TC/q
q2
Notice the vertical
distance between
ATC and AVC is AFC
AFC
q/t
Also note, q2 > q1 as long as
fixed costs are present
AFC is not very important, so
it is often not drawn with the
other per unit curves
Short Run
Per Unit
Costs
ATC
q0
q1
AVC = TVC/q
ATC = AFC + AVC = TC/q
q2
AVC
Notice the minimum
AVC at q1, occurs when
the average product of
the variable input is
maximized
q/t
Notice MC is “U” shaped too with its
minimum point, at q0, coinciding with
the output where the marginal
product of the variable input is
maximized
ATC
MC
Short Run
Per Unit
Costs
AVC
q0
MC = ÎTC/Îq
= ÎTVC/Îq
q1
q2
q/t
Everything
Together
Short Run
Per Unit
Costs
MC
ATC
AVC
AFC
AFC = TFC/q
q0
q1
AVC = TVC/q
ATC = AFC + AVC = TC/q
q2
q/t
MC = ÎTC/Îq
= ÎTVC/Îq
Before Going to the Long Run
u Review what we mean by “costs”
v Costs are opportunity costs
v Or, costs are benefits foregone-the benefits
of the next best alternative given up
v Market prices are often good measures of
opportunity costs
Opportunity Cost
u In economics, costs are always the value
of the benefits given up--opportunity
cost
u Sometimes these opportunity costs are
monetary, e.g., Wages paid labor
u Sometimes these opportunity costs are
nonmonetary, e.g., Value of time used
Economic Costs
u Total cost (TC) - the total opportunity
cost of all resources used in production
v TC = monetary costs + Nonmonetary costs
Economic vs. Accounting
Concepts of Costs and Profits
u
u
u
In economics costs are opportunity costs
In accounting costs are defined according to
accepted accounting rules designed for tax
and public disclosure purposes
Since the definitions of cost differ so do the
definitions of profits
v
v
Economic profit = total revenue - opportunity
costs
Accounting profit = total revenue - accounting
costs
Illustration of Accounting
Profit vs. Economic Profit
Assume:
Monetary costs (explicit costs) for a month =$15,000
Non-monetary costs for a month
Total costs
= $ 4,000
=$19,000
Economic profit = total revenue (TR) - total costs (TC)
If total revenue for this month is equal to $19,000 then:
there is no economic profit, but there would be a
$4,000 accounting profit. Accounting profit does not
count non-monetary costs as a cost thus profit would
be reported as $4,000
Suppose:
u Monthly costs include:
v
Owner’s time and expertise
$2,000
v
Land already owned but could
be rented
$3,000
v
Payroll expenses
$9,000
v
Utility bills
$1,000
u Total economic costs
$15,000
u Total accounting costs
$10,000
The difference between accounting and economic
costs are non-monetary costs are not included in
the accounting costs
Economic Profit Overview
u TR = TC
the opportunity costs are
covered and there is no economic profit
u TR > TC revenue exceeds opportunity
costs and there is an economic profit
u TR < TC opportunity costs exceed
revenues and there is economic loss
Consider Hooey and Dewie, Who
Opened a Business Selling Turquoise
Belts in the Denver Airport.
Display Cart Costs $10,000 and Is Paid by Withdrawing
Hooey and Dewie’s Savings That Was Earning 5% Per
Year. The Cart Will Last One Year and Has No Salvage
Value.
u Belts Cost $20.00 Each From the Supplier.
u Sales Are Estimated to Be 1,000 Belts Per Year.
u The Price of the Belts Is $60.00.
u The Cart Clerk Is Paid $14,000.
u Hooey and Dewie Will Put in 2000 Hours of Labor
During the Year.
QUESTION: Is This Business Going to Make a Profit, or
Should Hooey and Dewie Move Back in With Uncle
Donald?
u
Hooey and Dewie Have a
Total Revenue of $60,000 for
the Year
u Total revenues.............................$60,000
v P*q = $60*1,000
Hooey and Dewie Have
Accounting Costs of
$44,000 for the Year
Total Revenues. . . . . . . . . . . . . . . . . . . . . . . .$60,000
Total Accounting Costs (Monetary Cost)
Belts From Supplier. . . . . . . .$20,000
Clerk Cost . . . . . . . . . . . . . . . 14,000
Cart Cost. . . . . . . . . . . . . . . . . 10,000
$44,000
Acct’ing Profit = Total Revenue – Acct’ing Costs
= 60,000 - 44,000 = $16,000
(And We Are Ignoring Taxes)
But Hooey and Dewie Have
nonmonetary Costs Too
Total Revenues
$60,000
Total Accounting Costs (Monetary Cost)
Belts From Supplier
$20,000
Clerk Cost
14,000
Cart Cost
10,000
$44,000
Total Nonmonetary Cost
Interest Foregone on $10,000
$ 500
Opportunity Cost of 2000 Hours
X
Economic Costs
$44,500 + X
Economic Profits = Total Revenue - Economic Costs
= 60,000 - 44,500 - X = $15,500 - X
Hooey and Dewie’s Adventure
u
u
Did they make a profit?
It depends on the value they place on their
time, the 2000 hours
v
v
u
u
They cleared $16,000 according to the accountant
and would be asked to pay taxes on this amount
(after figuring loopholes)
But the opportunity cost of their savings and time
were not taken into account
$500 for foregone interest lowers profit by $500
If they value their time less than $7.50 per hour
(= $15,500/2000) they made a profit otherwise,
they didn’t and should move back in with uncle
Donald
Before Moving to the Long
Run, Let’s Review
u Total cost concepts
u Per unit cost concepts
u The shape of cost curves
v Due to the law of diminishing marginal
returns
u The relationship between marginal and
average
u Efficiency in getting what we want
Total Cost Concepts
u
Total fixed cost (FC) - costs which do not vary
with output
v
u
Total variable costs (TVC) - any cost that
varies with the quantity of output produced
v
u
The costs of fixed inputs, e.g., Capital
The costs of variable inputs, e.g., Labor
Total cost (TC) - sum of all costs of
production
v
TC = fixed costs + total variable costs
Per Unit Cost Concepts
u Marginal cost (MC) - the additional cost
of producing one more unit of output
v MC = ∆TC / ∆q
u Average variable cost (AVC) = TVC/q
u Average fixed cost (AFC) = FC/q
u Average total cost (ATC) = TC/q
Shape of Cost Curves
u
Total cost and total variable cost
v
u
Marginal cost
v
u
Eventually upward sloping due to law of
diminishing marginal returns
Average fixed cost
v
u
Eventually steeper due to law of diminishing
marginal returns
Downward sloping always: a fixed number (FC) is
divided by increasing q as output rises
Average total cost and average variable cost
v
“U” shaped but eventually upward sloping due to
law of diminishing marginal returns
Law of Diminishing Marginal
Returns and Cost Curves
u
If each unit of labor produces less additional
output eventually, then in order to produce
each additional unit of output we need to hire
increasing amounts of inputs (labor)
eventually (law of diminishing marginal
returns)
v
v
Tells us total product eventually gets flatter and
marginal product eventually declines
Tells us total costs eventually gets steeper and
marginal costs eventually rise
Average-marginal Rule
u
u
u
u
The marginal cost and average cost curves
have to obey the average-marginal rule
The average-marginal rule says that if
marginal is above average, then average must
be rising
If marginal is below average, then average
falling
This implies the MC curve crosses the ATC
and AVC curves at the bottom of both, and
that the MP curve must cross the AP curve at
the top of AP
Average-marginal Rule
u For example, your grade point average
(GPA) is an average. The marginal
grade is the next grade you get
u If your next grade (marginal grade) is
above your average (GPA), then your
GPA rises
u If your next grade (marginal grade) is
below your average (GPA), then your
GPA falls
Minimum Cost Condition
u
u
We saw earlier the rationale of the MP/P rule:
to minimize cost of any level of activity, a
supplier must mix variable inputs in such a
way their marginal product divided by their
price are equal
If input and output prices are taken as given,
and suppliers are profit maximizers, the
marginal costs of suppliers will be equal
(MC1 = MC2 = … = MCj for all j suppliers).
This is a necessary condition for insuring
industry output is produced at minimum cost
Now We Move to Costs in the
Long Run
u Long run - period of time in which all
inputs are variable
u Capital and labor, all inputs, can change
u Think of the long run as a planning
period
v Firm can estimate costs based on various
plant sizes, number of machines, etc
v Once it makes a decision and builds the
plant, buys the machines, etc., It moves into
the short run and are stuck with their
decision for a while
Costs in the Long Run
u Long run average total cost (LRATC) -
ATC of producing a given level of
output when all inputs can vary
u LRATC curve is constructed as an
envelope of all possible short run cost
curves
u NOTE - no AFC in long-run
v In long run all inputs are variable, so no
fixed costs
v LRATC is equal to long run AVC since all
costs are variable
Long Run and Short Run ATC
u Consider what happens to the short run
ATC curve when we increase fixed
costs:
v The average cost of making a small amount
of product rises
v The average cost of making a large amount
goes down
v For instance, we increase the size of an
assembly line - the ATC of making 1000
cars is now higher, but the ATC of 250,000
cars is less
Long Run ATC Curve
SRATC1
$
Higher
ATC with
higher
Fixed Cost
SRATC2
(Higher Fixed
Costs)
Lower ATC with higher Fixed Cost
0
q/t
The Shape of the LRATC
u We draw the LRATC as “U” shaped
similar to the “U” shape of the short run
average cost curves
u But the AVC and ATC were “U” shaped
due to the law of diminishing marginal
returns which doesn’t apply in the long
run (all inputs are variable)
u What gives? A:
returns to scale
Returns to Scale
u
u
Changing all inputs in the same proportion is
a “scale” change, e.g., increase all by 10%,
decrease all by 5%
The “U” shape of the LRATC is due to the
possibility of three types of returns to scale:
v
v
v
u
Increasing returns to scale: %Îq>%Îr
Constant returns to scale: % Îq=%Îr
Decreasing returns to scale: %Îq<%Îr (where R is
all resources)
Cost curves in the long run are based on the
underlying production technology, i.e.,
Returns to scale
Returns to Scale, Examples
u IRTS:
doubling all inputs leads to an
increase of 125% in q (LRATC falls)
u DRTS: an increase in all inputs by 5%
leads to a 3% increase in q (LRATC rises)
u CRTS: a decrease in all inputs by 10%
lead to a 10% fall in q (LRATC is
constant)
u If all inputs are decreased by 5% and
output falls by 7%, %Îq>%Îr, therefore
IRTS
What If All Inputs Change but
Not in the Same Proportion?
u If the %Îq>%Îcosts we use the term
economies of scale
u If the %Îq<%Îcosts we use the term
diseconomies of scale
u IRTS implies economies of scale but
economies of scale do not imply IRTS
u The same is true for the relationship
between diseconomies of scale and DRTS
u Reasons for economies and diseconomies
of scale are given in Part II
Linking the Short Run to the
Long Run
u Suppose you have four choices for a stock
of fixed inputs, e.g., 4 different sizes of
office buildings to build or lease
u There are tradeoffs apparent:
v Smaller fixed costs are associated with higher
variable costs
v Economies and diseconomies of scale are
apparent
u The output you expect to sell is
paramount, but that depends on demand
conditions we will consider next chapter
Four Short Run ATC Curve
Choices
SRATC1
$
SRATC4
SRATC2
SRATC3
0
q1
q2
q3
q4
q/t
Selection of Fixed Input Stock
u If you expect business to support
output q1 you select the input stock
associated with SRATC1
u And so on, e.g., If you expect to sell q3
then you will select the input stock
associated with SRATC3
u With only 4 possible input stock sizes,
the LRATC is the heavy sections of the
short run curves outlined in blue on the
next slide
Four Short Run ATC Curve
Choices and Their LRATC
SRATC1
$
SRATC4
SRATC2
SRATC3
0
q1
q2
q3
q4
q/t
LRATC Curve When There Are
Many Input Stocks to Select From
SRATC1
$
SRATC2
SRATC4
SRATC3
LRATC
: Minimum SRATC
: Tangency of SRATC
and LRATC
0
q1
q2
q3
q/t
q4
Reviewing the Shape of LRATC
u Explained by economies and
diseconomies of scale
u Typically firms will make efforts to
expand to take advantage of economies
of scale and take caution not to get too
big so as to experience diseconomies of
scale
u We find for most industries, firms
operating at constant ATC over a
considerable range of output
$
Long Run ATC Curve
(Economies of Scale)
Economies of Scale
0
q/t
$
Long Run ATC Curve
(Diseconomies of Scale)
Diseconomies of Scale
0
q/t
$
Long Run ATC Curve
(Constant Average Costs)
Constant Average Costs
0
q/t
Typical LRATC
$
Sort of like a Frying Pan
Constant Average Total Costs
0
q/t
What If a Mistake Is Made?
u You select SRATC1, expecting to sell q1
per period, but things are better than
expected, you sell q2
u Your ATC are higher than they need have
been (represented by a level rather
than shown on a couple of slides back)
u But your decision has been made and you
have to live with it for now
u It is important to learn that sunk costs are
not important (if your fixed inputs can be
sold their costs are not sunk)
Sunk Cost
u Sunk costs are fixed costs, but FC may
not be sunk if there are valuable
alternatives. If the capital equipment
may be sold then the capital cost is not
sunk
u Economics has an important message
about sunk cost--they don’t matter
u The proverb to remember is “let bygones
be bygones”
Sunk Costs
u A good poker player “knows when to
hold’em, knows when to fold’ em”--the
money in the pot is not important
u You ought not stay in a major because
you have almost completed the degree-the decision must be based on expected
benefits and costs of the change, not
costs already experienced
The End