1. Technology and Costs Lecture 4
ECON 4100: Industrial Organization
Technology and Costs
Lecture 4

2. Introduction
Costs
Cost minimization and profit maximization
economies of size and scale
fixed, sunk, avoidable, and variable costs

3. The Neoclassical View of the Firm
Concentrate upon a neoclassical view of the firm
the firm transforms inputs into outputs
Inputs
Outputs
The Firm
There is an alternative approach (Coase)
What happens inside firms?
How are firms structured? What determines size?
How are individuals organized/motivated?

4. The Single-Product Firm
Profit-maximizing firm must solve a related problem
minimize the cost of producing a given level of output
combines two features of the firm
production function: how inputs are transformed into output
Assume that there are n inputs at levels x1 for the first, x2 for the second,…, xn for the nth. The production function, assuming a single output, is written:
Q = F(x1, x2, x3,…,xn)
cost function: relationship between output choice and production costs. Derived by finding input combination that minimizes cost n
Minimize
 wixi
subject to F(x1, x2, x3,…,xn) = Q1 xi
i=1

5. Review input choice: one output and two inputs
The production function
can be illustrated
as a set of
isoquants, one for
each level of output
Now assume that input 1 becomes cheaper
Cost of producing
output Q1 is minimized
by finding the point
where an isocost line
is tangent to the
Q1 isoquant
This makes the isocost lines less steep x2
The input choice
is x11 of input 1
and x12 of
input 2
Production cost can be
illustrated as a set of
isocost lines, with slope
w1/w2. The lower the
isocost line, the lower
the cost.
The cost-minimizing input combination changes
The new cost-
minimizing point
x12
x22
More of
input 1 is
used and less
of input 2 Q2 Q1 Q0
x11
x21 x1

6. This analysis has interesting implications
different input mix across
time: as capital becomes relatively cheaper
space: difference in factor costs across countries
Analysis gives formal definition of the cost function
denoted C(Q): total cost of producing output Q
average cost = AC(Q) = C(Q)/Q
marginal cost:
additional cost of producing one more unit of output.
Slope of the total cost function
formally: MC(Q) = dC(Q)/d(Q)

7. Cost curves: an illustration
Typical average and marginal cost curves
$/unit
Relationship between AC and MC MC
If MC < AC then AC is falling AC
If MC > AC then AC is rising
MC = AC at the minimum of the AC curve
Quantity

8. Economies of scale
Definition: average costs fall with an increase in output
Represented by the scale economy index
AC(Q)
S =
MC(Q)
S > 1: economies of scale
S < 1: diseconomies of scale
S is the inverse of the elasticity of cost with respect to output
dC(Q) dQ
dC(Q)
C(Q)
MC(Q) 1
hC = = = =
C(Q) Q dQ Q
AC(Q) S

9. } } An example Take a simple example
Output Total Cost Average Cost Marginal Cost Scale Economy
($) ($) ($) Index }
145
140.5 91
140.5/91 = 1.54
136
Average cost is
taken as the mean
of 145 and 136 }
121
122.5
157
122.5/157 = 0.78
124
Average cost is
taken as the mean
of 121 and 124
Check the
relationship to
the elasticity of
the cost curve
Percentage increase in cost of increasing output from 5 to 6
= 11.8%
( )/2
6-5
Percentage increase in output
= 18.2%
(6+5)/2
hC = 11.8/18.2 = 0.65 and 1/ hC = 1/0.65 = 1.54

10. Minimum efficient scale:
output at which economies of scale are first exhausted
$/unit
With average cost curve AC1 minimum efficient scale is MES1
AC1
With average cost curve AC2 minimum efficient scale is MES2
AC2
MES1
Quantity
MES2

11. Sources of economies of scale
Natural monopoly
If the extent of the market is less than MES then the market is a natural monopoly: S > 1 in such a market.
But a natural monopoly can exist even if S < 1.
Economies of scale
Sources of economies of scale
“the 60% rule”: capacity related to volume while cost is related to surface area
product specialization and the division of labor
“economies of mass reserves”: economize on inventory, maintenance, repair
indivisibilities

12. Indivisibilities Some inputs can be employed only in indivisible units
transport routes
major items of capital equipment VC $
Three implications:
cost is “lumpy” or fixed at F1
maximum rated capacity Q1
average fixed cost F1/Q falls with output up to rated capacity F1 FC
Quantity Q1 $
ATC
Other inputs vary with output: variable costs
Average total costs exhibit economies of scale over some range
AVC
AFC
Quantity Q1

13. Consistent with evidence on excess capacity: see Federal Statistics
If projected output is greater than current capacity, install higher-rated capacity equipment or add additional capacity
It may be cheaper to have spare capacity than operate up to capacity
If projected output is greater than Q* it is cheaper to install higher capacity even though there is spare capacity
$/unit
AC1
AC2
Consistent with evidence on excess capacity: see Federal Statistics Q* Q1 Q2
Quantity

14. Fixed costs, indivisibilities and sunk costs
Indivisibilities make scale of entry an important strategic decision:
enter large with large-scale indivisibilities: heavy overhead
enter small with smaller-scale cheaper equipment: low overhead
Some indivisible inputs can be redeployed
aircraft
Other indivisibilities are highly specialized with little value in other uses
market research expenditures
rail track between two destinations
College degrees
The latter are sunk costs: nonrecoverable if production stops
Fixed costs and sunk costs affect market structure by affecting entry

15. Next Multi-product firm basic structure of multiproduct firms
multiproduct economies of scale
ray average cost
economies of scope
Read Chapter 4

17. Assume two identical firms each with costs AC1
If they are to produce a given output at lowest cost, they must operate at the same marginal cost
$/unit MC
Why? Assume firm A is operating at MCA and firm B is operating at MCB
MCA
AC1
Transferring one unit of output from A to B lowers total cost
MC´A
MC´B
MCB
If the two firms operate at the same marginal cost they must produce identical outputs
Suppose not: firm A has output QA and firm B has output QB QB QA
Quantity
Transferring one unit of output from A to B lowers total cost

18. If total output is 2Q1 then we know that each firm has
It follows that AC2 represents the lowest possible average cost if output is produced by two firms: AC2 is obtained by adding AC1 to itself horizontally
AC1 is average cost if
output is produced by
one firm.
Now assume that
output is produced by
two firms.
If total output is 2Q1 then
we know that each firm has
to produce Q1 and average
cost is AC1
$/unit
This market is a natural monopoly up to output QM even though this is greater than MES Q*: it is less costly for output to be produced by one rather than two firms: subadditivity
If total output is 2Q2 then
we know that each firm has
to produce Q2 and average
cost is AC2
If total output is 2Q* then
we know that each firm has
to produce Q* and average
cost is AC*
AC1
AC2
AC1
2Q1 Q1
AC2
2Q2 Q2
AC* Q* QM
2Q*
Quantity