Microéconomie, chapter 7 - CEScermsem.univ-paris1.fr/davila/teaching/SBS/Ch07_Pindyck-09.pdf ·...
Transcript of Microéconomie, chapter 7 - CEScermsem.univ-paris1.fr/davila/teaching/SBS/Ch07_Pindyck-09.pdf ·...
1 Solvay Business School – Université Libre de Bruxelles
1
Production costs
Microéconomie, chapter 7
2 Solvay Business School – Université Libre de Bruxelles
2
Points to be addressed What costs to take into account?
Short run costs
Long run costs
Short and long run cost curves
Returns to scale and economies of scale
3 Solvay Business School – Université Libre de Bruxelles
3
Introduction
Technology and input prices determines the production costs for the firm
Economic efficiency requires to produce at a minimum cost at each level of output
4 Solvay Business School – Université Libre de Bruxelles
4
What costs to take into account?
Rentals of office space, machinery are obvious costs for the firm
What if the firm owns already these inputs and needs not renting them?
Then the unearned income from not renting them to others are costs for the firm (opportunity cost)
5 Solvay Business School – Université Libre de Bruxelles
5
What costs to take into account?
Opportunity cost Unearned income from the most profitable
alternative uses of the firm’s assets It is an implict cost that must be taken into
account
6 Solvay Business School – Université Libre de Bruxelles
6
Opportunity cost
Example The firm owns its office space Does this firm not incur any cost for the use
of office space? Yes, the firm could have rented the office
space it owns to receive some income
7 Solvay Business School – Université Libre de Bruxelles
7
What costs to take into account?
Sunk costs Any past spending that cannt be recovered They do not influence the production
decisions of the firm and need not be taken into account
8 Solvay Business School – Université Libre de Bruxelles
8
Sunk costs
Example The firm seeks to rent some office space It has already made a downpayment of €500.000 for
the purchase of an office building The sale price is €5,5 millions (€5 millions are still to
be paid) Before the settlement, the firm finds another building
equally convenient for €4,25 millions Which building should the firm buy?
9 Solvay Business School – Université Libre de Bruxelles
9
Sunk costs
Example The firm should buy the second building The downpayment of €500.000 is a sunk
cost that has no influenec of the decision What the firm must consider is
to spend €4,25 millions more, or to spend €5 millions more
10 Solvay Business School – Université Libre de Bruxelles
10
What costs to take into account?
Some costs change with the output level, others are constant
Total cost is composed of: 1. Fixed costs
Independent of the output level 2. Variable costs
Depend on the output level
11 Solvay Business School – Université Libre de Bruxelles
11
Fixed and variable costs
Total output depends on fixed inputs and variable inputs
Total cost consists of fixed costs (from fixed inputs) and variable costs (from variable inputs)
12 Solvay Business School – Université Libre de Bruxelles
12
Fixed costs and variable costs
Which costs are fixed and which variable depends on the time horizon
In the short run, most costs are fixed In the long run, all costs are variable
13 Solvay Business School – Université Libre de Bruxelles
13
Fixed costs and sunk costs
Fixed and sunk costs are often confounded
Fixed cost: Cost independent of the level of output, to be
paid only if production takes place Sunk cost:
Cost independent of the level of output, paid even if production does not take place
14 Solvay Business School – Université Libre de Bruxelles
14
Average and marginal costs
Marginal cost (MgC): It is the additional cost from producing one
more unit of output Fixed costs do not influence the marginal
cost:
€
MgC =ΔCΔq
=ΔVCΔq
15 Solvay Business School – Université Libre de Bruxelles
15
Average and marginal costs
Average cost (AC) It is the total cost per unit of output
€
AC =Cq
=VCq
+FCq
16 Solvay Business School – Université Libre de Bruxelles
16
Short run marginal cost
If labor is the only variable input in the short run and wage is w, then
€
MgC = w ΔLΔq
€
VC = wL
€
= w 1MgPL
The MgC increases as the MgP of labor decreases
17 Solvay Business School – Université Libre de Bruxelles
17
L
F(K,L)
Short run cost curves
q
In the short run capital is fixed
18 Solvay Business School – Université Libre de Bruxelles
18
L
f (L)
Short run cost curves
q
In the short run capital is fixed
19 Solvay Business School – Université Libre de Bruxelles
19
L,q
f –1 (q)
Short run cost curves
f (L)
q,L
The inverse of the short run production
function gives the short run cost function
20 Solvay Business School – Université Libre de Bruxelles
20
q
f –1 (q)
Short run cost curves
L
The inverse of the short run production
function gives the short run cost function
21 Solvay Business School – Université Libre de Bruxelles
21
cost
Short run cost curves
w f –1 (q)
q
The inverse of the short run production
function gives the short run cost function
22 Solvay Business School – Université Libre de Bruxelles
22
cost VC
FC
Short run cost curves
q
The total cost curve includes the fixed costs
23 Solvay Business School – Université Libre de Bruxelles
23
VC
MgC
AC
q
Short run cost curves
q
cost
When AC>MgC the AC decreases
24 Solvay Business School – Université Libre de Bruxelles
24
cost VC
MgC AC
q’
Short run cost curves
q
When AC<MgC the AC increases
25 Solvay Business School – Université Libre de Bruxelles
25
cost VC
MgC
AC
q*
Short run cost curves
q
When AC>MgC the AC attains its
minimum
26 Solvay Business School – Université Libre de Bruxelles
26
Short run cost curves
When MgC < AC, then AC decreases When MgC > AC, then AC increases When MgC = AC, then AC attains its
minimum
27 Solvay Business School – Université Libre de Bruxelles
27
output
cost
MgC
AC
Short run cost curves
AVC
q q’ q*
28 Solvay Business School – Université Libre de Bruxelles
28
Short run and long run
In the short run some costs are fixed, e.g. from the use of capital
In the long run there is no fixed costs Both capital and labor are variable inputs
29 Solvay Business School – Université Libre de Bruxelles
29
Cost minimization
The firm chooses the combination of inputs that allows to produced any given level of output at the minimum cost
Assume Two inputs: labor (L) and capital (K) Price of labor : the wage w Price of capital
r = depreciation rate + interest rate r = rental cost (they coincide if capital markets are
competitive)
30 Solvay Business School – Université Libre de Bruxelles
30
Cost minimization
The isocost line It contains all the combinations of L and K
with the same cost C = wL + rK
There is one for each possible level of cost C The slope -(w/r) is the rate at which labor can
be replaced by capital without changing the cost
31 Solvay Business School – Université Libre de Bruxelles
31
Cost minimization
labor
capital
Output Q1 can be obtained through
K2,L2 or K3,L3 but at a higher cost than the minimum throuhg K1,L1 on
the isocost line C1
Q1
C0 C1 C2
A K1
L1
K3
L3
K2
L2
32 Solvay Business School – Université Libre de Bruxelles
32
Inputs substitution
When the wage w changes, the slope -(w/r) of the isocost lines changes too
In particular, a more expensive labor is replaced by more capital
33 Solvay Business School – Université Libre de Bruxelles
33
Inputs substitution
C2
The new combination of inputs uses less labor and
more capital K2
L2
B
C1
K1
L1
A
Q1
If labor costs increase, the slope of the
isocost line increases
labor
capital
34 Solvay Business School – Université Libre de Bruxelles
34
Cost minimization The minimization of costs is
characterized by the tangency of the isocot line and the isoquant
€
TRMS = ΔKΔL
= - MgPL
MgPK
€
slope of the isocost lines = - wr
€
MgPL
MgPK
=wr
when the cost is minimized
35 Solvay Business School – Université Libre de Bruxelles
35
At the combination of inputs that minimizes costs, one additional euro in capital is as productive as one additional euro in labor
€
MgPL
w=
MgPK
r
Cost minimization
36 Solvay Business School – Université Libre de Bruxelles
36
Cost minimization Example:
let w = €10, r = €2, and MgPL= MgPK. Is the firm minimizing costs? One less unit of labor decreases q in MgPL units, and decreases
costs in €10 One more unit of capital increases q in PMgK units and increases
costs in €2 Since MgPL= MgPK output does not change but costs decreases
in €8 = €10 - €2 The firm has incentives to replace labor with capital Decreasing labor increases MgPL Increasing capital decreases MgPK The firm will replace labor with capital until:
€
MgPLw
=MgPKr
37 Solvay Business School – Université Libre de Bruxelles
37
Cost minimization
For any given input prices w and r, for each level of output q the re is an isocost line that minimizes costs
The expansion path draws the bundles of inputs the minimize costs at each level of output
38 Solvay Business School – Université Libre de Bruxelles
38
Expansion path
• r= €20 and w= €10 • the expansion path gives the bundles of inputs that produce each q at a minimum cost given the input prices
capital
25
50
75
100
150
50 labor 100 150 300 200
A
€2000
200 Units
B
€3000
300 Units
C
The expansion path
39 Solvay Business School – Université Libre de Bruxelles
39
The expansion path
The expansion path determines the long run total cost curve: For any given w and r, the tangency of an
isocost and an isoquant gives the minimum cost of producing the output of the isoquant
The total cost curve graphs the combinations of output and cost thus obtained
40 Solvay Business School – Université Libre de Bruxelles
40
Long run cost curves
Long run average cost 1. With increasing returns to scale:
As inputs double, output more than doubles Average cost decreases
3. With decreasing returns to scale: As inputs double, output less than doubles Average cost increases
41 Solvay Business School – Université Libre de Bruxelles
41
Long run cost curves
If returns to scale are first increasing and then decreasing, then the average cost curve AC is “U”-shaped
The shape in U is a consequence of the returns to scale of all factors and not of decreasing marginal returns as in the short run
42 Solvay Business School – Université Libre de Bruxelles
42
Long run cost curves
When AC decreases, MgC < AC When AC increases, MgC > AC therefore, the long run MgC curve is U-
shaped too when returns to scale are first increasing and then decreasing
MgC = AC at the minimum of AC
43 Solvay Business School – Université Libre de Bruxelles
43
Long run cost curves
output
cost
AC
MgC
A
44 Solvay Business School – Université Libre de Bruxelles
44
Long run cost curves
When the proportions of inputs change with the level of output, the expansion path is not a straight line We cannot rely on the returns to scale to
obtain the form of the cost curves We have to use the notion of economies of
scale
45 Solvay Business School – Université Libre de Bruxelles
45
Economies of scale
Average cots AC decreases first as output increases because
1. Workers specialize 2. Production is organized more efficiently 3. The firm can obtain better prices for inputs
46 Solvay Business School – Université Libre de Bruxelles
46
Economies of scale
Average cost AC eventually increases becases
1. The organization of production can become very complex
2. A strong demand for inputs will increase their prices
47 Solvay Business School – Université Libre de Bruxelles
47
Economies of scale
There can be Economies of scale
As output doubles, cost les than doubles Diseconomies of scale
As output doubles, cost more than doubles
48 Solvay Business School – Université Libre de Bruxelles
48
Constant economies of scale
Total cost
output 100 300 200
cost
1000
2000
3000
D
E
F
49 Solvay Business School – Université Libre de Bruxelles
49
Economies of scale
Total cost
output 100 300 200
cost
1000
2000
3000
D
E
F
Economies of scale
50 Solvay Business School – Université Libre de Bruxelles
50
Economies of scale
Proportional cost
output 100 300 200
cost
1000
2000
3000
D
E
F
Economies of scale
Diseconomies of scale
51 Solvay Business School – Université Libre de Bruxelles
51
Economies of scale
The economies of scale are measured by the elasticity EC of cost with respect to output
EC is the increase (in percentage terms) in the cost induced by an increase of output of 1%
€
=MgCAC
52 Solvay Business School – Université Libre de Bruxelles
52
Economies of scale
if EC = 1, then MgC = AC Costs are proportional to output No economies or diseconomies of scale: constant
economies of scale
EC < 1 when MgC < AC Economies of scale MgC and AC are decreasing
EC > 1 when MgC > AC Diseconomies of scale MgC and AC are increasing
53 Solvay Business School – Université Libre de Bruxelles
53
A U-shaped long run AC curve represents Economies of scale at low levels of output
Diseconomies of scale at high levels of output
Economies of scale
54 Solvay Business School – Université Libre de Bruxelles
54
Long run cost curves
output
cost
AC
MgC
A
55 Solvay Business School – Université Libre de Bruxelles
55
In the long run output can increase from Q1 to Q2 with
a smaller increase in the cost than in the short run
Long run expansion path
labor
capital
L2
Q2
K2
D
C
F
E
Q1
A
B L1
K1
L3
P Short run Expansion path
Long run cost curves
56 Solvay Business School – Université Libre de Bruxelles
56
output
cost
Mg1C
AC1
Long and short run cost curves
q
57 Solvay Business School – Université Libre de Bruxelles
57
output
cost
Mg1C
AC1
MgC2
AC2
Long and short run cost curves
q
58 Solvay Business School – Université Libre de Bruxelles
58
output
cost
MgC1 MgC2
ACLT AC1 AC2
MgC3
AC3
Long and short run cost curves
q* q q’
59 Solvay Business School – Université Libre de Bruxelles
59
Long and short run cost curves
In the long run the firm can change K The long run AC curve is the lower
envelope to all short run AC curves It gives the minimum average cost of
producing each level of output
60 Solvay Business School – Université Libre de Bruxelles
60
In the long run the firm chooses the size (K) that minimizes AC for the chosen level of output
The long run AC curve shows Economies of scale at low levels of output Diseconomies of scale at high levels of output
The long run MgC curve satisfies MgC<AC when long run AC decreases satisfies MgC>AC when long run AC increases satisfies MgC=AC at the minimum long run AC
Long and short run cost curves
61 Solvay Business School – Université Libre de Bruxelles
61
output
cost
MgC1 MgC2
MgCLT
ACLT AC1 AC2
MgC3
AC3
Long and short run cost curves
q* q q’