Totals,
Averages, &
Marginals
Part 2:
Production
Example:
Pizza Production
You’re in the pizza business.
. .
.
You rent a building, pay
for utilities, employ the
workers, and buy the
ovens, other appliances,
and furniture.
You purchase the flour,
tomatoes, cheese, etc.
You calculate all your costs.
You have determined that the total cost (TC)
of producing a quantity (Q) of 1000 pizzas
is $6000.
To produce 1010 pizzas cost $6050.
To produce 1020 pizzas cost $6150.
factor of production
•
•
•
Something that is used to create a product
or service.
Also called an input or productive resource.
Examples: buildings, machinery, land,
labor, and raw materials.
fixed inputs
These are inputs the quantity of which can
not be changed in a short amount of time.
Therefore, in the short run, the quantities of
these inputs do not vary with the amount of
output you produce.
example: the building space
Pizza House
Total Fixed Cost (TFC)
the total amount of money spent on fixed inputs
example: your monthly rent, the amount paid
for the building space, is a fixed cost
Note that the building space is the fixed input
and the rent is fixed cost.
variable inputs
These are inputs the quantity of which can
be changed in a short amount of time.
The quantities of these inputs vary with the
amount of output you produce.
examples: time worked by employees, flour,
tomatoes, and cheese
.
.
.
Total Variable Cost (TVC)
the total money spent on variable inputs
example: wages paid to employees
Note that the labor is the variable input and
the wages are variable cost.
The relationship between TFC, TVC, and TC
TFC + TVC = TC
Equivalently,
TVC = TC - TFC
TFC = TC - TVC
A Brief Digression on Distinguishing
Fixed & Variable Inputs
Suppose business is extremely good and you
would like to dramatically increase your output.
If you were starting from scratch, you would
probably lease a bigger building and operate
with more heavy equipment, as well as more of
your other inputs (for example, labor, small
tools, and raw materials).
However, you have a one-year lease on your
building space and it takes a while to special
order the heavy equipment.
So, for the time being, you just hire some
more workers, get more tools and raw
materials, and do the best you can.
If things continue to go well, you plan to
look into leasing a larger property and
ordering the heavy equipment.
So in the short run, some inputs are fixed
(such as building space and heavy equipment)
and some inputs are variable
(such as labor, small tools, and raw materials).
In the long run, everything can be changed.
Now, back to our example.
Suppose TFC = $ 2000.
Recall: for Q = 1000, TC = 6000
Q = 1010, TC = 6050
Q = 1020, TC = 6150
What are total variable costs for these output
levels?
Q = 1000: TVC = TC -TFC = 6000-2000 = 4000
Q = 1010: TVC = TC -TFC = 6050-2000 = 4050
Q = 1020: TVC = TC -TFC = 6150-2000 = 4150
Average Total Cost (ATC)
total cost per unit of output
(total cost per pizza)
ATC = TC / Q
Q = 1000
Q = 1010
Q = 1020
TC = 6000
TC = 6050
TC = 6150
What is ATC at the given output levels?
ATC = TC / Q
Q = 1000: ATC = 6000/1000 = $6.00
Q = 1010: ATC = 6050/1010 = $5.99
Q = 1020: ATC = 6150/1020 = $6.03
Average Variable Cost (AVC)
variable cost per unit of output
(variable cost per pizza)
AVC = TVC / Q
Q = 1000
Q = 1010
Q = 1020
TVC = 4000
TVC = 4050
TVC = 4150
What is AVC at the given output levels?
AVC = TVC/Q
Q = 1000: AVC = 4000/1000 = $4.00
Q = 1010: AVC = 4050/1010 = $4.01
Q = 1020: AVC = 4150/1020 = $4.07
Average Fixed Cost (AFC)
fixed cost per unit of output
(fixed cost per pizza)
AFC = TFC / Q
TFC = 2000
What is AFC at output levels 1000, 1010, and
1020?
AFC = TFC/Q
Q = 1000: AFC = 2000/1000 = $2.00
Q = 1010: AFC = 2000/1010 = $1.98
Q = 1020: AFC = 2000/1020 = $1.96
Note: AFC always declines as output increases.
Marginal Cost (MC)
the additional cost associated with the
production of another unit of output
MC = DTC / DQ
Q = 1000 TC = 6000
Q = 1010 TC = 6050
Q = 1020 TC = 6150
What is MC for pizza 1010 and for pizza 1020?
MC = DTC /DQ
pizza 1010:
MC = (6050 - 6000) / (1010 - 1000) = 50/10 = 5
pizza 1020:
MC= (6150 - 6050)/(1020 - 1010) = 100/10 = 10
Relation between
Marginal Cost
and Average Total Cost
MC > ATC:
ATC
MC < ATC:
ATC
MC = ATC: ATC stays the same
Relation between
Marginal Cost
and Average Variable Cost
MC > AVC:
AVC
MC < AVC:
AVC
MC = AVC: AVC stays the same
Q = 1000: ATC = 6
Q = 1010: MC = 5, ATC = 5.99
How does the Marginal Cost of pizza 1010
compare to the Average Total Cost of
producing 1000 pizzas?
MC is less than the old ATC (5 < 6).
What happens to the Average Total Cost?
It falls from 6 to 5.99, because the MC is
pulling it down.
Q = 1010: ATC = 5.99
Q = 1020: MC = 10, ATC = 6.03
How does the Marginal Cost of pizza 1020
compare to the Average Total Cost of
producing 1010 pizzas?
MC is greater than the old ATC (10 > 5.99).
What happens to the Average Total Cost?
It rises (from 5.99 to 6.03), because the MC is
pulling it up.
Note: The next two questions are
about Average Variable Cost.
The preceding questions were
about Average Total Cost.
Q = 1000: AVC = 4
Q = 1010: MC = 5, AVC = 4.01
How does the Marginal Cost of pizza 1010
compare to the Average Variable Cost of
producing 1000 pizzas?
MC > old AVC (5 > 4).
What happens to the Average Variable Cost?
It rises (from 4 to 4.01), because the MC is
pulling it up.
Q = 1010: AVC = 4.01
Q = 1020: MC = 10, AVC = 4.07
How does the Marginal Cost of pizza 1020
compare to the Average Variable Cost of
producing 1010 pizzas?
MC is greater than the old AVC (10 > 4.01) .
What happens to the Average Variable Cost?
It rises (from 4.01 to 4.07), because the MC is
pulling it up.
Note
The marginal and average relationship works
for ATC and AVC.
This relationship does not hold for AFC, since
total fixed costs are unaffected by increases
in output level.
Graphing Cost Curves
Total Fixed Cost
$
TFC is constant,
so the curve is a
horizontal line.
TFC
Quantity
Average Fixed Cost
$
The AFC curve slopes
downward and gets
closer and closer to the
horizontal axis.
AFC
Quantity
Total Variable Cost
$
TVC
Quantity
The TVC curve is
upward sloping.
It is often drawn
so it looks like a
flipped over S;
the curve at first
gets flatter &
flatter, and then it
gets steeper &
steeper.
Average Variable Cost
$
AVC
AVC is
U-shaped.
Quantity
Total Cost
$
TC
TFC
Quantity
The TC
curve
looks like
the TVC
curve, but
it is
shifted up,
by the
amount of
TFC.
Average Total Cost
$
ATC
ATC is
U-shaped.
Quantity
Marginal Cost
$
MC
MC is
U-shaped,
but it is
often
drawn so
it extends
up higher
on the
right side.
Quantity
When ATC, AVC, and MC
are drawn on the same graph:
the MC must intersect the ATC at its
minimum and the AVC curve at its
minimum.
ATC, AVC, & MC
$
MC
ATC
AVC
Quantity
Suppose that the price (P) of a pizza in your
region is $8.00.
As a small firm, you take that going price as a
given. (You are a “price-taker.”)
Total Revenue
Total Revenue = Price x Quantity
TR = P Q
Price is $8. What is your Total Revenue (TR)
from pizza sales, if you sold 1000, 1010, and
1020 pizzas?
TR = P Q
Q = 1000: TR = (8)(1000) = $8000
Q = 1010: TR = (8)(1010) = $8080
Q = 1020: TR = (8)(1020) = $8160
Average Revenue (AR)
AR is the revenue per pizza.
AR = TR / Q
= PQ / Q
=P
Q = 1000: TR = 8000
Q = 1010: TR = 8080
Q = 1020: TR = 8160
What is AR at these output levels?
AR = TR / Q
Q = 1000: AR = 8000 / 1000 = $8 = price
Q = 1010: AR = 8080 / 1010 = $8 = price
Q = 1020: AR = 8160 / 1020 = $8 = price
Marginal Revenue (MR)
Marginal Revenue is the additional revenue
earned from selling an additional unit of
output.
MR = DTR / DQ
Q = 1000: TR = 8000
Q = 1010: TR = 8080
Q = 1020: TR = 8160
What is the MR of pizza 1010 and pizza 1020?
MR = DTR / DQ
Q = 1010: MR = (8080 - 8000)/(1010 - 1000)
= 80/10 = $8.00 = price
Q = 1020: MR = (8160 - 8080)/(1020 - 1010)
= 80/10 = $8.00 = price
Since you always sell your pizzas for the
market price ($8), the additional revenue you
make per pizza from additional pizzas is
always that amount ($8).
For the small, price-taking firm, the MR is
always equal to the market price. (If you were a
big company and could set your own price, MR
would not be equal to price.)
Comments:
MR = P
for small, price-taking firms, but
not for large, price-making firms.
AR = P
for both large and small firms.
Profit (p)
p = TR - TC
Q = 1000:
Q = 1010:
Q = 1020:
TC = 6000, TR = 8000
TC = 6050, TR = 8080
TC = 6150, TR = 8160
What is your profit if you produce and sell
1000, 1010, and 1020 pizzas?
p = TR - TC
Q = 1000: profit = 8000 - 6000 = $2000
Q = 1010: profit = 8080 - 6050 = $2030
Q = 1020: profit = 8160 - 6150 = $2010
Q = 1000:
Q = 1010:
p = 2000
p = 2030
MR = 8, MC = 5
Notice MR > MC for pizza 1010.
Also profit from producing 1010 pizzas is
greater than profit from producing 1000 pizzas.
MR > MC
When the additional revenue from producing
another unit of output is greater than the
additional cost, your profit increases when
you produce more.
You should expand production.
Q = 1010:
Q = 1020:
p = 2030
p = 2010
MR = 8, MC = 10
Notice MR < MC for pizza 1020.
Also profit from producing 1020 pizzas is less
than profit from producing 1010 pizzas.
MR < MC
When the additional revenue from producing
another unit of output is less than the additional
cost, your profit decreases when you produce
more. You’ve gone too far.
Cut back.
MR = MC
You are at the point where the additional
revenue from producing another unit of output
is just equal to the additional cost. You
should neither expand nor contract.
You are at the profit- maximizing output level.
MR > MC: expand
MR < MC : cut back
MR = MC: profit-maximizing output level
Suppose that at a price of $5.95, the profitmaximizing output level is 1015 pizzas.
Suppose also that the ATC reaches its minimum
of $5.95 at that output level.
What are TR, TC, and profit for 1015 pizzas?
TR = P Q = (5.95)(1015) = 6039.25
Recall that ATC = TC/Q
So (ATC)(Q) = TC
and TC = (ATC)(Q) = (5.95)(1015) = 6039.25
p = TR – TC = 6039.25 - 6039.25 = 0
You are just breaking even.
Breakeven Point
when the price is equal to the minimum value
of the ATC curve.
p=0
Total Revenue = Total Cost
Breakeven Point
MC
$
breakeven
point
$5.95
ATC
AVC
1015
Quantity
Suppose now the going price of pizza is $5.00.
What would be the Total Revenue, if you
produced and sold 1000, 1010, and 1020
pizzas?
Q = 1000: TR = P Q = (5)(1000) = $5000
Q = 1010: TR = P Q = (5)(1010) = $5050
Q = 1020: TR = P Q = (5)(1020) = $5100
Q = 1000: TC = 6000, TR = 5000
Q = 1010: TC = 6050, TR = 5050
Q = 1020: TC = 6150, TR = 5100
What would be the profit, if you produced and
sold 1000, 1010, and 1020 pizzas?
Q = 1000: p = TR - TC = 5000 - 6000 = -1000
Q = 1010: p = TR - TC = 5050 - 6050 = -1000
Q = 1020: p = TR - TC = 5100 - 6150 = -1050
a negative profit means a loss
You lose $1000 when you produce 1000
pizzas or 1010 pizzas, and you lose even
more when you produce 1020 pizzas.
How much would you lose if you shut down?
You would still have your fixed cost ($2000)
to pay. (You still have to pay the rent until
you can get out of your lease.)
You would have no revenue because you have
nothing to sell.
p = TR - TC
= 0 - TFC
= 0 - 2000
= - 2000
Notice that you'd lose more by not operating
than by operating. If you produce and sell
1010 pizzas, you lose 1000 dollars which is
not as bad as losing 2000 dollars.
If the prices stay low, in the long run, when
you can get out of your lease and therefore
get rid of your fixed costs, you would get
out of the business. In the short run,
however, you would continue to operate.
P = 5 and at Q = 1010, AVC = 4.01.
P
> AVC
P Q > AVC . Q
TR > TVC
Revenues are more than enough to pay the
variable costs. You will have a little of the
revenue left to pay part of the fixed costs.
So you lose less than if you produced nothing
and had no revenues at all to help pay the
fixed costs.
Price = $5
Q = 1010: MR = 5, MC = 5, p = - 1000 (a loss)
Could you do better with a different output
level?
No. Since MR = MC, this is the profitmaximizing (or loss-minimizing) output
level.
Suppose the going price of pizza is $4.00.
Suppose also that, when you are producing
1000 pizzas, AVC = $4.00, which is the
lowest value of AVC curve.
How does the price compare to AVC when you
are producing 1000 pizzas?
P = $4.00 is equal to AVC = $4.00
If the price is $4, what is TR when you are
producing 1000, 1010, and 1020 pizzas?
Q = 1000: TR = P Q = (4)(1000) = $4000
Q = 1010: TR = P Q = (4)(1010) = $4040
Q = 1020: TR = P Q = (4)(1020) = $4080
Q = 1000: TR = 4000, TC = 6000
Q = 1010: TR = 4040, TC = 6050
Q = 1020 TR = 4080, TC = 6150
What is your profit when you produce 1000,
1010, and 1020 pizzas?
Q = 1000: p = TR - TC = 4000 - 6000 = - 2000
Q = 1010: p = TR - TC = 4040 - 6050 = - 2010
Q = 1020: p = TR - TC = 4080 - 6150 = - 2070
Your loss at Q = 1000 is the same as if you
shutdown (2000). Elsewhere the loss is bigger.
Shutdown Point
The minimum value of Average Variable Cost.
If price < min. of AVC curve, don’t operate.
If price > min. of AVC curve, operate.
If price = min. of AVC curve, you lose the same
amount whether you operate or not.
(In the long run, if things don’t improve, get out
of the business.)
Shutdown Point
MC
$
ATC
AVC
$4.00
shutdown
point
1000
Quantity
Suppose now the price of a pizza is $3.50.
What is the Total Revenue when you're
producing 1000, 1010, and 1020 pizzas?
Q = 1000: TR = P Q = (3.50)(1000) = 3500
Q = 1010: TR = P Q = (3.50)(1010) = 3535
Q = 1020: TR = P Q = (3.50)(1020) = 3570
Q = 1000:
Q = 1010:
Q = 1020:
TC = 6000, TR = 3500
TC = 6050, TR = 3535
TC = 6150, TR = 3570
What is the profit or loss when you're
producing at these output levels?
p = TR - TC
Q = 1000: p = 3500 - 6000 = -2500
Q = 1010: p = 3535 - 6050 = -2515
Q = 1020: p = 3570 - 6150 = -2580
Total Fixed Cost is 2000.
Q = 1000: p = -2500,
Q = 1010: p = -2515
Q = 1020: p = -2580
What would your loss be if you shut down?
p = -2000 (the amount of fixed cost)
Notice that, when the price is 3.50 (below the
minimum AVC value of 4), you'd lose more
if you operate than if you shut down.
Remember AVC is the cost per pizza of the
variable inputs (such as labor & raw materials).
The price per pizza ($3.50) doesn't even cover
your variable costs per pizza ($4), and you
still have to pay fixed costs. Producing at a
different output level wouldn't help, because
you're already at the lowest value of AVC
when you're producing 1000 pizzas.
You should not be operating!
Breakeven Point &
Shutdown Point
$
MC
breakeven
point
$5.95
ATC
AVC
$4.00
shutdown
point
1000 1015
Quantity
Operating & Not Operating: The 5 Cases
Price > min. ATC curve:
Operate with positive profits.
Price = min. ATC curve (breakeven point) :
Operate with zero profits.
Price is between min. AVC and min. ATC:
Operate with a loss.
Price = min. AVC curve (shutdown point):
You lose the same amount whether you operate or not.
Price < min. AVC curve:
Don’t operate.
Breakeven Point &
Shutdown Point
$
breakeven
point
MC
ATC
AVC
shutdown
point
Quantity