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5
The Chapter Production Process and Costs
Production function shows the relation between the maximum amount of output and
inputs.
Example: 2 inputs Labor (L) and Capital (K)
Inputs called also factors.
Production Function: Q=f(L,K)
If L and K assume discrete values, then the production function is discrete. If L and K
assume continuous values, then the production function is continuous.
Short-run versus Long-run
In the short run, some inputs are fixed. Example: plant size (capital) is fixed in the shortrun; labor is variable in the short run.
In the long-run, all inputs are variable.
Measures of Productivity
Total product (TP) is the maximum amount of output for a given amount of inputs. For
example, when K=1 and L=2, then Q=4. Say L=2 workers and K=1 tractor can produce
Q=4 holes. Q=4 holes is the maximum output. You can always produce less than 4 holes
if, say, the workers slack.
When K is fixed, the Total Product function of Labor (TPL) will show how Q changes as
L changes while holding K fixed. It is also known as the short-run production function.
Mathematically,
TPL = Q = f(L/K), i.e. the amount of output as a function of L for a fixed K.
An example of a short-run production function (picture below):
K (plant size) is fixed at some level. As we vary L, the output (total product) changes
according the function below. If L=LA, Q=QA (say, LA=100 workers, QA=200 units of
output). If L=LB, Q=QB (say, LB=140, QB=220). If L=LC, Q=QC (say, LC=300, QC=230).
We will talk more about the shape of the production function later.
1
Q
QC
C
QB
QA
O
LA
TPL
B
A
LB
LC
L
Average Product
Average Product of Labor = APL = Q/L (units per worker)
Average Product of Capital = APK=Q/K (units per capital)
Marginal Product
The Marginal Product of Labor, MPL, shows the change in output associated with a one
unit change in labor, holding all other factors (inputs) constant.
MPL = Q when L is discrete
L
MPL = dQ when L is continuous
dL
MPL is units per worker. For example, MPL=5 for the 1st worker, MPL=7 for the second
worker, etc.
Example: Calculating MPL (K is fixed at some level)
L
1
2
3
4
5
6
7
8
9
10
Q
15
31
48
59
68
72
73
72
70
67
MPL
15
16
17
11
9
4
1
-1
-2
-3
2
The Marginal Product of Capital, MPK, shows the change in output associated with a one
unit change in capital, holding all other factors (inputs) constant.
MPK = Q when K is discrete
K
MPK = dQ when K is continuous
dK
The relationship between AP and MP
As long as MP is above AP, AP is increasing. If MP is below AP, AP will decrease.
Intuition
GPA Analogy Example.
GPA is your average grade. Individual grade is like a marginal grade. If the grade from a
new course is greater than your existing GPA, your GPA will go up. If the new grade is
lower than your existing GPA, your GPA will go down.
Showing Average and Marginal Graphically
Suppose we have the following short-run production function, i.e, Q is a function of L
(the amount of K is fixed at some level).
Q
C
O
B
TPL
A
L
For this short-run production function (or total product function of labor), we derive the
APL and MPL functions (curves).
3
Recall, APL=Q/L. Graphically, APL at any point of the production function is the slope of
the line connecting the origin (L=0, Q=0) with that point,
Q
C
QA
O
TPL
B
A
LA
L
APL at A is QA/LA and is the slope of line (OA). Similarly for any other point. For the
above given total product function of labor, the average product of labor is first
increasing, then decreasing, i.e. APL as a function of L has an inverted U-shape.
APL
LB
L
Recall that MPL= Q . As discussed in class, if L is arbitrarily small, then MPL at any
L
given level of L can be shown by the slope of the tangent line to the point of function
corresponding to L.
4
Q
C
TPL
B
A
LA
LB
LC
L
MPL at A is the slope of tangent line through A. MPL is increasing until A, then starts
decreasing. A is the inflection point. Note that at B, MPL = APL. MPL=0 at C and
becomes negative after C.
If the slope of the tangent line at A is 4, then MPL=4 at LA. Say, LA=13. This means that
the marginal product of the 13th worker is 4.
MPL
LA
LC
L
If MPL>0, then Q is increasing.
If MPL<0, then Q is decreasing.
The relationship between TPL, MPL and APL is depicted in the following pictures.
5
Q
TPL
LA
LB
LC
APL, MPL
APL
L
LA
LB
LC
MPL
NOTE: In the book (page 160), the TPL, APL and MPL curves are plotted on one picture.
It is not a good practice to put variables with different units of measurement on the same
axis. TPL is total output, while APL and MPL are output per worker. I believe the book is
sloppy in this case (although its scaling is correct). But the same graph in Powerpoint
slides for Chapter 5, 7th slide (if you use them) is very misleading and shouldnt be used.
In short, it is better to show TPL separately from APL and MPL.
When L is between 0 and LA, MPL is both positive and is increasing. We say there is
increasing marginal returns to labor in this range.
When L is between LA and LC, MPL is positive, but decreasing. We say there is
diminishing or decreasing marginal returns to labor in this range.
When L is beyond LC, MPL is negative and decreasing. We say there is a negative
marginal returns to labor in this range.
6
When there are increasing marginal returns to L (i.e. MPL is increasing), it means output
is increasing at an increasing rate as L increases. For example, when 1st worker is hired,
output increases from 0 to 5 units; when 2nd worker is hired, output increases from 5 to 11
units; when 3rd worker is hired, output increases from 11 to 18 units; etc.
When there are diminishing (decreasing) marginal returns to L (i.e. MPL is positive but
decreasing), it means output is increasing at a decreasing rate as L increases. For
example, when the 12th worker is hired, output increases from 140 to 155 units; when the
13th worker is hired, output increases from 155 to 168 units; when the 14th worker is
hired, output increases from 168 to 178 units; etc.
Negative MPL means that output is decreasing as L is increasing.
For most technologies, as the usage of an input increases (holding other inputs fixed),
marginal product of that input initially increases, then begins to decline and eventually
becomes negative.
The Law of Diminishing Returns to a Factor
Marginal Product of a variable factor (input) must eventually decline as more of the
variable factor (input) is combined with other fixed factors (inputs).
Example: Labor is the variable factor (input) and capital (plant size) is the fixed factor
(input). When there are relatively few workers, the advantages of additional
specialization are so great that each worker makes the others more productive. Hence MP
of labor is increasing with additional worker. When there are more workers, the
disadvantages of additional crowding are so great that each worker makes the others less
productive.
In the picture above (the short-run production function), MPL is increasing until point A,
i.e. in that region we have increasing returns to L. After B, MPL is decreasing, i.e. we
have diminishing returns to L. Moreover, after point C MPL becomes negative, i.e. after
point C output would increase if we decreased the amount of factor L.
MPL eventually will decrease as L increases (keeping K constant). Otherwise, there
would be no limit to the usage of L.
The Role of the Manager in the Production Process
The manager should make sure the firm operates on the production function and the right
amount of inputs re used.
Produce on the Production Function
7
Q
TPL
QA
O
A
LA
L
For example, if the firm employees LA number of workers, the manager should make sure
the output is maximum, i.e. QA. The workers should be provided with the right incentives
to work hard.
Use the Right Level of Inputs
Recall, MPL shows the change in output due to a 1 unit change in L. It is a measure of
physical productivity of labor.
The economic productivity of labor can be measured by the Value Marginal Product of
labor, VMPL.
VMPL is the value of output (i.e. revenue) generated by the last unit of labor.
Let P be the price of output. Then,
VMPL = P
MPL
For example, suppose you have 5 workers. The last, 5th workers marginal product is 4
units of output. Suppose also the price of output is $6 (i.e. you can sell each unit of output
for $6). Then, VMPL=4 6=$24
Similarly, we can talk about the Value Marginal Product of Capital (VMPK). It is the
value of output (revenue) generated by the last unit of capital.
VMPK = P
MPK
Example: finding the right level (optimal level) of workers
8
Suppose capital is fixed at some level. The relationship between output and labor is given
in Table 5.2. One unit of labor costs $400. Price of output is $3.
Table 5.2
L
0
1
2
3
4
5
6
7
8
9
10
11
Price of output (P)
$3
3
3
3
3
3
3
3
3
3
3
3
MPL
76
172
244
292
316
316
292
244
172
76
-44
VMPL= P
$228
516
732
876
948
948
876
732
516
228
-132
MPL
Wage (w)
$400
400
400
400
400
400
400
400
400
400
400
Note from the table that initially, when labor usage is low (b/w 0 and 5, MPL is
increasing, i.e. we have increasing marginal returns to L). When labor usage is b/w 5 and
10, MPL is positive, but decreasing, i.e. we have decreasing (diminishing) marginal
returns to L. After L=10, MPL is negative, i.e. we have negative marginal returns to L.
What is the right (optimal) number of workers to employ in this example? Use the
principle of marginal analysis.
Should the first worker be employed? 1st workers VMPL=$228, but he costs the firm
$400. The firm loses $400-$288=$172. You might be tempted to say the 1st worker
shouldnt be hired. But if we look beyond the 1st worker, given that we already have one
worker, if we hire a 2nd worker, VMPL-w=$516-$400=$116. Hence we partially
recovered the loss from the 1st worker. If we hire the 3rd worker, then VMPL-w=$732$400=$332. With 3 workers we have profits. But 3 is not the optimal level of L. We
should also hire the 4th, 5th, 6th, 7th, 8th and 9th workers. The last worker hired is the 9th
worker. Beyond L=9, VMPL<w, so adding additional workers will only reduce our
profits. The right (optimal) number of workers to hire in this example is L=9. L=9 is the
equilibrium number of workers to hire.
The input should be employed up to the point where value of output produced by the last
unit of an input (i.e. VMP) equals to the cost of that unit and the input usage is in the
range where marginal return to the input decreases (diminishes).
In case of Labor, optimal level of L is when VMPL=w and the marginal product of L is
decreasing. If we cannot get an exact equality of VMPL and w, we should stop at level of
L such that VMPL is the closet to w and VMPL>w.
9
On picture:
VMPL, w
w1
w0
w2
L
L1 L0
L2
L
The VMPL curve is bell shaped. VMPL is increasing when MPL is increasing (recall,
VMPL= P VMPL) and VMPL is decreasing when MPL is decreasing.
The profit maximizing level of L, for given w is the level at which VMPL=w in the range
of diminishing (decreasing) marginal product of L (if cannot get exact equality of VMPL
and w, stop at L where VMPL is the closest to w and VMPL>w).
You can check that L0 is the right (i.e. equilibrium or optimal) level of L. Given w0, the
firm has no incentive to deviate from L0. If it goes to the right of L0, the VMPL of each
extra worker is less than w, so profits will decrease. If it goes to the left of L0, it saves in
w but loses more in VMPL. In contrast, if the firm is at L, it doesnt stay there. The firm
will increase L from L since each extra L will bring in more than its cost.
If wage increased to w1, the profit maximizing level of L would be L1. If wage was w2,
the profit maximizing level of L would be L2.
Hence, for any given w, we find the profit maximizing (i.e. optimal or equilibrium or
right) level of L from the downward sloping part of VMPL curve. This means that the
downward sloping part of VMPL curve is the firms demand curve for labor.
Isoquants
Iso = Equal
Quant=Quantity
Isoquant combination of inputs that can be used to efficiently produce a given level of
output.
Efficiency means the maximum amount of output that the combination of two inputs can
produce. (One can also produce less output with this combination, which would be
inefficient).
Example: The picture below shows two isoquants. Q=10 units can be produced, for
example, by input combination A, B or C (or any other combination on that isoquant).
10
Q=17 units can be produced by combination D, E or F (or any other combination on that
isoquant).
K
D
E
A
B
F
C
Q=17
Q=10
L
The shape of the isoquant shows the degree of substitutability of inputs.
In picture (a), the production process is such that inputs (gas and oil) are perfect
substitutes.
In picture (b), the production process is such that the inputs (frames and wheels) are
perfect complements.
In picture (c), the production process is such that the inputs are imperfect substitutes.
11
The isoquants in picture (c) are common. A dress can be made with a relatively small
amount of labor (L1) and a large amount of cloth (C1). Or, the same dress can also be
made with less cloth (C2) if more labor (L2) is used. To decrease cloth from C1 to C2 ,
C , requires increasing labor from L1 to L2. However, in order to have another decrease
in cloth equal to C , L should increase now significantly more from L2 to L3. Hence,
the substitutability of L for C diminishes as L increases.
Marginal Rate of Technical Substitution (MRTS)
MRTS is the amount of one input that must be substituted for one unit of another input in
order to maintain the same level of output.
If K and L are the inputs, then
MRTSKL =
K
L
MRTSKL =
dK
dL
for discrete case
for continuous case
MRTSKL shows the amount of input K that must be substituted for 1 unit of input L in
order to stay on the same isoquant.
MRTSKL is the absolute value of the slope of the isoquant.
K
A
C
L
At A, MRTSKL is the absolute value of the slope of the tangent through A. At C, it is the
absolute value of the slope of the tangent through C.
The slope of isoquant is decreasing, i.e. if one input is increasing (decreasing), the other
one should decrease to (increase) stay on the same isoquant.
MRTS decreases as we move along the isoquant from left to right, i.e. MRTSKL
decreases as L increases.
the substitutability of L for K decreases as L increases.
12
The Relationship between MRTS and MP
Q
Q
Recall that MPL = L and MPK = K .
Then,
(Change in output due to change in L) =
Q = L MPL
(Change in output due to change in K) =
Q = K MPk
Consider the initial combination of inputs L and K that produce Q amount of output.
Now suppose K decreased by K .
(Change in output due to change in K) =
If we want to stay on the same isoquant, we have to increase L.
(Change in output due to change in L) = L MPL
K MPk
To stay on the same isoquant,
(Change in output due to change in K)+ (Change in output due to change in L) =0
Or
K MPk
+ L MPL = 0
After rearranging,
MPL
K
=
L
MPK
Recall also that MRTSKL =
K
L
.
Hence,
MRTSKL =
MPL
MPK
Thus, in the previous picture, the absolute value of MRTSKL at point C is the ratio of MPL
at C and MPK at C.
Isocosts
Two inputs: K and L. One output: Q.
w=price of input L (eg. wage rate)
r = price of input K (eg. rental rate of capital)
13
C= money spent on inputs
The isocost curve shows the combination of inputs that will cost the same amount of
money.
C = wL + rK would be the cost of buying L and K at w and r.
On picture,
K
Isocost
C
r
Slope=-w/r
C
w
L
C, i.e. the cost, is constant along the isocost curve.
Higher isocost curves mean higher costs.
The slope of isocost is determined by the relative factor prices: w/r
What happens to isocost if w/r increases, i.e. labor becomes relatively more expensive
than capital?
What happens to isocost if w/r decreases, i.e. capital becomes relatively more expensive?
Cost Minimization
Given w and r, what is the optimal combination of inputs to produce a given level of
output?
Optimal combination of inputs means the least-cost combination for producing a given
level of output.
14
K
A
B
C
Q=100
L
Q=100 units of output can be produced using a combination of inputs represented by A,
B or C (or any other combination on the isoquant for Q=100). Which combination is the
optimal?
The optimal combination of inputs for producing Q=100 units is the one that results in
the lowest costs, i.e. is on the lowest isocost.
K
A
B
C
Q=100
L
The combination of inputs represented by B is the optimal combination for producing
Q=100 units. It is also the point where the slope of the isoquant equals the slope of the
isocost, i.e.
MRTSkl = w/r
Recall that MRTSKL = MPL/MPK,
Thus, at optimal combination of inputs,
15
MPL
MPK
=
w
r
Or
MPL
MPK
=
w
r
MPL/w is the marginal product of labor per dollar spent. MPK/r is the marginal product of
capital per dollar spent.
For example, suppose w=10 and r=4. A given level of output, say Q, is produced with
some (L,K) combination such that MPL= 5 and MPK=20. Is the input combination used
optimal? No.
MPL/w = 5/10=1/2, i.e. the last dollar spent on labor resulted in 0.5 units of output.
MPK/r = 20/4=5, i.e. the last dollar spent on capital resulted in 5 units of output.
Then, the firm could reduce the costs of producing Q if it reduces L and increases K.
Here is why. Say the firm decreases the amount spent on L by $1 (i.e. buys less L).
Output goes down by 0.5 units. But the firm can recover these 0.5 units by spending less
than $1 to buy extra capital. Hence, the firm can reduce the cost of producing Q by
reducing L and increasing K.
The firm is at the optimal input combination if marginal product of labor per dollar spent
MPL
MPK
=
is equal to marginal product of capital per dollar spent, i.e. w
r.
As output expands, the isoquants shift up.
Expansion path is the optimal combination of inputs as the scale of output expands.
16
K
C3
C2
C1
L
Note that optimal input combination is a necessary but not a sufficient condition for profit
maximization. For example, in the above picture, combination A is optimal for output
level Q1. However, Q1 may not be a profit maximizing output level. Profit maximization
requires optimal input combination plus optimal level of output.
Optimal Input Substitution
A change in the price of an input will lead to a change in the cost-minimizing input
combination.
Suppose when cost (price) of labor is w0 and cost (price) of capital is r0, the costminimizing input combination for producing Q0 units is (L0, K0). If the firm uses (L0, K0)
combination, the cost of producing Q0 is, say, C0.
17
K
C0
Slope=-w0/r0
K0
Q0
L0
L
Next, say capital became cheaper (price of labor didnt change), i.e. price of capital
decreased from r0 to r1. What is the new optimal input combination for producing the
same output (Q0)?
The slope of isocost has changed (it is now w/r1). Isocost became steeper.
If we use the old input combination (L0,K0) to produce Q0 , the new isocost would be
line C1 going through (L0,K0) in picture below. C1 is the cost of producing Q0 units using
(L0, K0) when price of labor is w0 and price of capital is r1. But it is obvious from the
picture that at w0 and r1, (L0,K0) is not the cost-minimizing input combination for
producing Q0. (L1, K1) is the cost-minimizing combination. At (L1, K1) we have more
capital and less labor than at (L0,K0). Hence, as capital became relatively cheaper, the
firm substituted away from labor to capital, i.e. the firm became more capital-intensive.
K
Slope=-w0/r1
C1
C0
K1
Slope=-w0/r0
K0
C
L1
L0
Q0
L
More generally, to minimize the cost of producing a given level of output, the firm
should use less of an input and more of other inputs when that inputs price rises.
18
The Cost Function
For a given level of output, the cost function shows what is the minimum cost of
producing that level of output.
Short-Run Costs
Recall, some inputs are fixed in the short run. Others are variable.
(In the long-run, all inputs can be varied).
Fixed cost is a short-run concept. These are costs (expenses) that do not vary with output.
Variable costs are costs (expenses) that vary with output.
All costs are variable in the long-run.
The short-run cost function would show the cost of producing a given level of output
when variable inputs are employed in the cost-minimizing fashion.
In short run,
Total Costs = Fixed Costs + Variable Costs
Fixed Costs = FC
Variable Costs = VC(Q) (i.e. they vary with output)
Total Cost = C(Q) (i.e. also varies with output)
Total Cost; Variable Cost, Fixed Cost
The shape of the Total Cost is determined by the shape of the Variable Cost. At low
levels of output, the Variable Cost is increasing at a decreasing rate because the variable
19
factor (input) productivity is increasing. At high levels of output, the Variable Cost is
increasing at an increasing rate because the variable factor productivity is decreasing.
For example, suppose labor is the variable factor and capital is the fixed factor.
Then, the total product curve of labor (TPL) is
Q
C
TPL
B
A
LA
LB
LC
L
You see from above picture that at low levels of output, i.e. low levels of L, the marginal
product of labor is increasing ( there are increasing marginal returns to labor). This means
that to get, say an X% increase in output, labor should increase by less than X%. Which
is the same as saying to get an X% increase in output, costs will increase by less than
X%. Hence, when labor productivity is increasing (i.e. increasing MPL), costs will
increase at a decreasing rate.
If labor productivity is decreasing (i.e. decreasing MPL), to have an X% increase in Q, L
should increase by more than X%.
to have an X% increase in Q, costs will increase by
more than X%. Hence, when labor productivity is decreasing (i.e. decreasing MPL), costs
will increase at an increasing rate.
Average and Marginal Costs
Average Fixed Cost = AFC = FC/Q
Average Variable Cost = AVC = VC(Q)/Q
Average Total Cost =ATC = C(Q)/Q
C(Q) = VC(Q)+FC
Divide both sides by Q,
ATC = AVC+AFC
20
C (Q )
Marginal Cost =MC =
Q
MC shows the change in total costs due to a unit change in Q. MC is independent of FC.
C (Q )
Question: Does it matter if I calculate MC using
Q
VC (Q )
or
Q
?
Graphically,
Unit Costs
ATC, AVC, AFC and MC are also called unit costs. All are dollars per unit of output.
Recall, ATC=AVC+AFC. At low levels of output, ATC is very high because both AFC
and AVC are high. Initially, AVC is decreasing because of increasing productivity of the
variable input. AFC is decreasing because AFC=FC/Q, hence as Q increases, the given
amount of fixed costs is distributed over a larger and larger amount of output, so AFC
decreases. These decreases in AVC and AFC drive down ATC.
However, at higher levels of output, AFC and AVC behave differently. AFC keeps
decreasing and gets closer to zero. But AVC starts increasing because the productivity of
21
the variable input starts decreasing. Because at higher levels of output AFC is closer to
zero, then ATC gets dominated by AVC and rises. The distance between ATC and AVC
becomes smaller and smaller as Q increases.
There is no relationship between marginal and average fixed costs. There is an important
relationship between the Marginal cost and the Average Variable and, hence, the Average
Total Costs. As long as the marginal cost is above the average variable and average total
costs, the last two are increasing. When Marginal cost is below the average variable and
average total costs, the last two decrease.
Changes in Q will result in movements along the cost curves (both total and unit cost
curves). Changes in operating conditions (input costs, technology) will shift the cost
curves.
Fixed and Sunk Costs
Sunk cost is a cost that is forever lost once it has been incurred. In other words, sunk
costs are irreversible business expenses.
Sunk costs are part of Fixed Costs that cannot be recovered.
Example: suppose you leased an equipment and paid $10,000. One year later, if you
decide you do not need it, you can return it and get a $6,000 refund.
$4,000 is the sunk cost. It is irreversible.
Sunk costs are irrelevant to present decisions.
In the previous example, suppose now the $10,000 payment was non-refundable. Then
your sunk cost is $10,000 and is irrelevant. If someone offers you $1000 for the
equipment, you should sell it.
Long-Run Costs
In the long-run, all inputs are variable. For example, the firm can change both the amount
of workers and the amount of capital (plant size).
Consider two plant sizes (i.e. two short runs):
Plant Size K1 and Plant Size K2, K2>K1
Call Plant Capacity the output level at which the corresponding short run average cost is
at minimum.
The sort run total costs for the two plants are depicted below.
22
TC
TC1
TC2
Q
Q
Q1
Q
Plant 2 is larger than Plant 1 and has higher fixed costs. At low levels of output it is
cheaper to produce in plant 1 than in plant 2. At Q1, total costs are equal in the two plants.
After Q1, it is cheaper to produce in plant 2. Note that the min ATC of plant 1 is at Q and
min ATC of plant 2 is at Q.
Similarly, there will be some Q2 and plant size K3 (K3>K2) such that it will be cheaper
to produce in plant 3 after Q2 (not shown in the above picture).
The picture below shows the short-run average total costs for 4 different plant sizes.
ATC
Plant 1
Plant 4
Plant 2
Plant 3
Q1
Q2
Q*
Q3
23
Up to Q1, it is optimal to produce in plant 1 as it has the lowest average total costs. As
output approaches the capacity in plant 1, it becomes optimal to increase plant size and
produce in plant 2. Q1 to Q2 is produced in plant 2. After Q2, it is optimal to produce in
plant 3.
As plant size increases, the crowding effect can decrease allowing the firm to take further
advantage of specialization and decrease the average costs. However, at some point,
increasing plant size further will not decrease the average total costs. For example, as size
becomes too large, it might be harder for management to coordinate and monitor
operations.
Hence ATC will increase ultimately.
The envelope of the short-run average cost curves is the Long Run Average Cost (LRAC)
curve.
The long-run average cost (LRAC) curve shows the minimum average cost of producing
alternative levels of output, allowing for optimal selection of both fixed and variable
inputs.
24
Unit Cost
LRAC
Economies of Scale
Diceconomies of Scale
Q*
Q
Hence, if there are economies of scale present, becoming larger can reduce average costs
and make the company more efficient. Economies of Scale is used as one argument for
mergers of two companies producing similar products.
If LRAC is constant as Q changes, then we have Constant Returns to Scale (or no
economies of scale).
AC
Plant 2
Plant 1
Plant 3
LRAC
Q
25
A REMINDER: ECONOMIC COSTS VERSUS ACCOUNTING COSTS
Recall, Economic Cost = Opportunity Cost. When the firm uses various resources for
production, the explicit outlays for these resources would be the Accounting Costs. But,
these explicit outlays are not everything the company gives up when using all those
resources. Those resources could have been used to produce some other good. The profits
that the company could have earned if the resources were utilized in their next best use
are implicit outlays and should be included in Economic Costs.
The costs we mention here mean economic costs.
Multiple-Output Cost Functions
So far, the firm was producing 1 output only. It can produce more than one output. Then
the firm is multi-product.
Economies of Scope
Multi-product firms exist because of Economies of Scope.
Economies of Scope exists when the total cost of producing two types of outputs together
is less than the total cost of producing each type of output separately.
Mathematically, economies of scope exist if
C(Q1, 0) + C(0, Q2) > C(Q1, Q2)
Intuition:
McDonalds can produce both hamburgers and French fries at a lower average cost than
what it would cost two separate firms to produce the same goods. This is because
McDonalds hamburgers and French fries share the use of food storage, preparation
facilities, and so forth during production.
Knowledge is another reason why it may be optimal to produce and sell related products
together. Information about one product can be relevant for another closely related
product.
26

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