Chapter 10--Costs of the Firm
Chapter Outline
 Costs In The Short Run
 Allocating Production Between Two Processes
 The Relationship Among MP, AP, MC, And AVC
 Costs In The Long Run
 Long-run Costs And The Structure Of Industry
 The Relationship Between Long-run And Short-run
Cost Curves
10-1
Figure 10.1: Output as a Function
of One Variable Input [Chapter 9]
IRTS
CRTS
DRTS
10-2
Figure 10.2: The Total, Variable,
and Fixed Cost Curves
Note:
similar curvature of TC
and VC: VC=0 if Q=0
Before Q=43 -> IRTS,
thus VC increases at a
decreasing rate
After Q=43,  DRTS,
VC increases at an
increasing rate
TCQ = FC + VCQ = rK0 + wL where TCQ, VCQ indicate that costs
depend on output unlike FC which is independent of Q.
Fixed cost (FC): cost that does not vary with the level of output in
the short run (the cost of all fixed factors of production).
Variable cost (VC): cost that varies with the level of output in the
short run (the cost of all variable factors of production).
Total cost (TC): all costs of production= the sum of variable cost
and fixed cost.
10-3
Figure 10.3: The Production Function
Q = 3KL, with K = 4 (CRTS)
Slope =∆Q/∆L =12
10-4
Average Costs In The Short Run
 Average fixed cost (AFC): fixed cost divided by the quantity
of output, AFCQ = rKo/Q =FC/Q
 Average variable cost (AVC): variable cost divided by the
quantity of output, AVCQ = wL/Q=VCQ/Q
 Average total cost (ATC): total cost divided by the quantity
of output, ATC = AVC + AFC= (wL+rKo)/Q = TCQ/Q
 Marginal cost (MC): change in total cost that results from a
1-unit change in output,
MC = ∆TCQ/Q = ∆VCQ/Q since ∆FC/Q = 0
Graphing The Short-run Average and Marginal Cost Curves
 Geometrically, average variable cost at any level of output
Q may be interpreted as the slope of a ray to the variable
cost curve at Q .
10-5
Figure 10.5: The Marginal, Average Total, Average
Variable, and Average Fixed Cost Curves
The MC intersects both the ATC and the AVC at their minimums
10-6
Figure 10.6: Quantity vs. Average Costs
10-7
Marginal Costs
 Is the same as the cost of expanding output (or the savings
from contracting).
 By far the most important of the seven cost curves. Reason:
a typical firm makes a marginal decision whether to
expand or contract production. This involves cost-benefit
analysis (CBA).
 Geometrically, at any level of output may be interpreted as
the slope of the total cost curve at that level of output.
– And since the total cost and variable cost curves are
parallel, it is also equal to the slope of the variable cost
curve.
Marginal and Average Costs
-When MC is less than average cost (either ATC or AVC), the average cost
curve must be decreasing with output; and when MC is greater than
average cost, average cost must be increasing with output.
10-8
Figure 10.7: Cost Curves for a Specific
Production Process : Q= 3KL ,K=4
Given that Q= 3KL ,K=4, so Q =3*4L = 12L and L = Q/12, w=$24, r=$2,
thus TCQ = wL +rK0 =2*4 + 24(Q/12) = 8 + 2Q
Thus,
TCQ= 8 + 2Q so that ATCQ = (8+2Q)/Q = 8/Q + 2
FC = $8 so that AFCQ = 8/Q
VC =2Q so that AVC = 2Q/Q =2 and MC =∆TCQ/∆Q = 2 – slope of the
TCQ
ATC = TCQ=/Q = AVC +AFC = 2 + 8/Q
10-9
Figure 10.9: The Relationship Between MP, AP,
MC, and AVC
Chap.9: MPL cuts the APL at the maximum value of the APL.
Chap. 10: MCQ cuts the AVC at the minimum value of the AVC.
These relationships serve a vital link for day-to-day management of a profitmaximizing firm: productivity (Chap. 9) is inversely linked to cost-control – a
crucial understanding in all Accounting courses!
MCQ = ∆VCQ/∆Q and if Q= f(L), then ∆VCQ = ∆wL so that ∆VCQ/∆Q =
∆wL/∆Q. Given a fixed wage (w), then w∆L/∆Q = w/MPL = MCQ
The same reasoning applies to AVC = w/APL
10-10
Figure 10.10: The Isocost Line
Given: w=$4, r =$2 and C=
$100
Thus, wL + rK =C
K= C/r - (w/r)*L –Isocost
for the firm ≈ Budget
Constraint for the Consumer
4L +2K= 100
w∆L + r∆K = ∆C =0
-w∆L= r∆K
-w/r = ∆K/∆L =-4/2=-2
Costs In The Long Run
Isocost line: a set of input bundles each of which costs the same amount.
To find the minimum cost point we begin with a specific isoquant then
superimpose a map of isocost lines, each corresponding to a different cost
level.
--The least-cost input bundle corresponds to the point of tangency
between an isocost line and the specified isoquant.
10-11
Figure 10.11: The Maximum Output
for a Given Expenditure
1. At B, MPL/MPK < PL/PK.
In order to fix this, less
labor and more capital is
advised until the
MPL/MPK = PL/PK at A.
2. At C, MPL/MPK >PL/PK.
In order to fix this, more
labor and less capital is
advised until the
MPL/MPK = PL/PK at A.
3. At A, MPL/MPK = PL/PK.
Thus, the firm is
optimizing its employment
of K at K* and L at L* to
minimize its costs in
producing Q0.
C
A
Firm should set MRTSL,K =
-MPL/MPK = -w/r
B
10-12
Figure 10.12: The Minimum Cost
for a Given Level of Output
Firm should set MRTSL,K =
-MPL/MPK = -w/r
OR MPL/w = MPK/r
10-13
Figure 10.13: Different Ways of Producing 1
Ton of Gravel (Nepal) versus the US
Gravel is made by hand in Nepal (isocost line), but by machine in the
U.S.(isocost line) because the relative prices of labor and capital differ so
dramatically in the two countries.
That is,
|
WUS WNepal
||
|
rUS
rNepal
10-14
Figure 10.15: The Long-Run Expansion Path
Recall the (1) Price Expansion Path (PEP) and
(2) Income Consumption (ICP) in case of
the Consumer
The Relationship Between Optimal Input Choice And
Long-run Costs
Output expansion path (OEP)- the locus of tangencies
(minimum cost input combinations) traced out by an isocost line
of given slope as it shifts outward into the isoquant map for a
production process.
10-15
Figure 10.16: The Long-Run Total, Average,
and Marginal Cost Curves
The Long-run
MC =LMCQ =
∆LTCQ/∆Q
The long-run
average cost, LACQ
= LTCQ/Q
There are no fixed
costs (FC) in the LR!
Plot (Q1, TCQ1), (Q2, TCQ2) and so forth from Figure 10.15
onto top Panel of Figure 10.16.
Since in the LR, there are no FCs this means that all costs are
variable.
The long-run total cost (LTC) always passes through the origin
since the firm can always liquidate all its inputs.
10-16
Figure 10.17: The LTC, LMC and LAC Curves for a
PF exhibiting Constant Returns to Scale (CRTS)
Constant returns to scale - long-run total costs are thus
exactly proportional to output.
10-17
Figure 10.18: The LTC, LAC and LMC Curves for a
Production Process with Decreasing Returns to Scale
Decreasing returns to scale - a given proportional
increase in output requires a greater proportional
increase in all inputs and hence a greater
proportional increase in costs.
10-18
Figure 10.19: The LTC, LAC and LMC Curves for a
Production Process with Increasing Returns to Scale
Increasing returns to scale - long-run total cost rises
less than in proportion to increases in output
Next: Examine the importance of long-run costs for
the structure of an industry.
10-19
Figure 10.20: LAC Curves Characteristic of Highly
Concentrated Industrial Structures
Ever declining LAC is a cost
advantage that allows an
existing firm defensive
barriers against possible
competitors (barriers to entry)
Industry dominated by a few
firms if Q0 forms a
substantial share for an
industry.
Long-run Costs And The Structure Of Industry
Natural monopoly: an industry whose market output is
produced at the lowest cost when production is concentrated in
the hands of a single firm[Panel A].
Minimum efficient scale: the level of production required for
LAC to reach its minimum level, Q0 [Panel B].
10-20
Figure 10.21: LAC Curves Characteristic of
Unconcentrated Industry Structures
Survival in an industry requires a low-cost structure (U-shaped LAC) and if
Q0 is small share for the industry, then many firms are in the industry (Panel
A).
Similarly, if the LAC is flat (Panel B) or rising (Panel C), it is possible to have
many firms, each producing a small portion of the industry output.
Industry – collection of firms that produce identically or similar products.
10-21
Figure 10.22: The Family of Cost Curves
Associated with a U-Shaped LAC
The LAC is the “envelope” of all ATC curves
LMC = SMC at the value of output (Q2 in this case) where ATC is tangent to
the LAC.
At the minimum point of the LAC, LMC = SMC = ATC = LAC
 For Plant sizes 1 (ATC1) and 2 (ATC2), the SMC1 and SMC3 do not hit LAC
or ATC at its minimum.
 Only and only with Plant Size 2 (ATC2) does the LMC hit the ATC and LAC
from below at its minimum. Plant Size 2 minimizes both SR and LR costs.
10-22
Figure A10.1: The Short-run and LongRun Expansion Paths
OE is the LR expansion path
With K fixed at K = K2*, the SR expansion path is a horizontal line through
point (0, K2*).
Given that K2* is the optimal K for producing Q = 2, the LR and SR
expansion paths intersect at point T.
The SR TCQ of producing a given level of output is the cost given by the
relevant isocost line. For example, for Q3, the SR TCQ is given by STC3
10-23
Figure A10.2: The LTC and STC Curves Associated with the
Isoquant Map in Figure A.10.1
As Q approaches Q=2 (the level of output for which the fixed
factor is at optimal level), STCQ approaches LTCQ.
The STCQ and LTCQ curves are tangent at Q=2
Beyond Q=2, STCQ increases faster than LTCQ due to
diminishing returns that partly governs the behavior of STCQ in
the SR.
10-24