Technology and Cost. 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?
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Chapter 4: Technology and Cost
Inputs
Outputs
The Firm
Chapter 4: Technology and Cost
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)
n
wixi
Minimize
subject to f(x1, x2, x3,…,xn) = q1
xi
i=1
Chapter 4: Technology and Cost
Chapter 4: Technology and Cost
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
Chapter 4: Technology and Cost
Chapter 4: Technology and Cost
AC(Q)
S =
MC(Q)
dC(Q)
dQ
dC(Q)
C(Q)
MC(Q)
1
hC =
=
=
=
C(Q)
Q
dQ
Q
AC(Q)
S
Chapter 4: Technology and Cost
Chapter 4: Technology and Cost
Indivisibilities, sunk costs and entry
Chapter 4: Technology and Cost
Lerner Index is
inversely related to
the number of firms
Suppose that elasticity of demand h = 1
Then total expenditure E = P.Q
If firms are identical then Q = Nqi
Suppose that LI = (P – c)/P = A/Na
Suppose firms operate in only on period: then (P – c)qi = K
As a result:
Chapter 4: Technology and Cost
Chapter 4: Technology and Cost
C(1Q, 2Q)
RAC(Q) =
Q
Chapter 4: Technology and Cost
C(Q1, Q2) = 10 + 25Q1 + 30Q2  3Q1Q2/2
3Q2
C(Q1,Q2)
MC1 =
= 25 
2
Q1
3Q1
C(Q1,Q2)
MC2 =
= 30 
2
Q2
Chapter 4: Technology and Cost
C(Q1, Q2) = 10 + 25Q1 + 30Q2  3Q1Q2/2
Q1 = 0.5Q; Q2 = 0.5Q
C(0.5Q, 0.5Q)
RAC(Q) =
Q
10 + 25Q/2+ 30Q/2  3Q2/8
10
55
3Q

+
=
=
Q
2
8
Q
Now assume 1 = 0.75; 2 = 0.25
C(0.75Q, 0.25Q)
RAC(Q) =
Q
10 + 75Q/4+ 30Q/4  9Q2/32
10
105
9Q

+
=
=
Q
4
32
Q
Chapter 4: Technology and Cost
C(Q)
AC(Q)
S =
=
MC(Q)
Q.MC(Q)
C(Q1,Q2,…,Qn)
S =
MC1Q1 + MC2Q2 + … + MCnQn
Chapter 4: Technology and Cost
C(Q1, Q2) = 10 + 25Q1 + 30Q2  3Q1Q2/2
MC1 = 25  3Q2/2 ; MC2 = 30  3Q1/2
Substitute into the definition of S:
C(Q1,Q2,…,Qn)
S =
MC1Q1 + MC2Q2 + … + MCnQn
10 + 25Q1 + 30Q2  3Q1Q2/2
=
25Q1  3Q1Q2/2 + 30Q2  3Q1Q2/2
It should be obvious in this case that S > 1
This cost function exhibits global economies of scale
Chapter 4: Technology and Cost
C(Q1, 0) +
C(0 ,Q2) 
C(Q1, Q2)
SC =
C(Q1, Q2)
10 + 25Q1 +
10 + 30Q2 
(10 + 25Q1 + 30Q2  3Q1Q2/2)
> 0
SC =
10 + 25Q1 + 30Q2  3Q1Q2/2
Chapter 4: Technology and Cost
Chapter 4: Technology and Cost
Chapter 4: Technology and Cost
Chapter 4: Technology and Cost
(Diet)
(LX)
(Super)
0
0.5
1
Low
High
Each product is located
on the line in terms
of the amount of the
characteristic it has
This is the
characteristics
line
Chapter 4: Technology and Cost
(Diet)
(LX)
(Super)
0
0.5
1
Low
High
A switching cost s is incurred in changing the process to either of the other products.
There are additional marginal costs of making Diet or Super  from adding or removing sugar. These are r per unit of “distance” between LX and the other product.
There are shared costs F: design, packaging, equipment.
Chapter 4: Technology and Cost
m
S
Total costs are:
C(zj, qj) =
F + (m  1)s +
[(c + rzj  z1)qj]
j=1
If production is 100 units of each product:
one product per firm with three firms
C3 = 3F + 300c
one firm with all three products
C1 = F + 2s + 300c + 100r
C1 < C3 if
2s + 100r < 2F
F > 50r + s
This implies a constraint on setup costs, switching costs and marginal costs for multiproduct production to be preferred.
Chapter 4: Technology and Cost
Chapter 4: Technology and Cost
237
Chapter 4: Technology and Cost
Chapter 4: Technology and Cost
Illustration of ray average costs
Chapter 4: Technology and Cost