Chapter 9
Production
Input → Output
Production Function
Short Run (at least one input fixed)
total product
average product
marginal product
diminishing marginal product
Long Run (all inputs variable)
production technique
isoquants
returns to scale
Chapter 10
Costs (short run)
family of cost curves
Costs (long run)
optimal decision
Types of Firms
Monopolistic
Competition
Monopoly
Perfect
Competition
Oligopoly
Formulas
**Costs include all costs both explicit and implicit
**Profit refers to economic profit or profit over and above a normal return
TP  Output  Q  F L; K 
TR = P*Q
MPL 
Q
L
OR
MPL 
Q
L
AFC = ATC – AVC
ATC = AFC + AVC
TC
Q
Q
L
FC = TC – VC
TC = FC + VC
ATC 
APL 
AFC 
AR 
FC
Q
TR
Q
AVC 
MR 
VC
Q
TR
Q
Profit = TR – TC Profit = (P – ATC)*Q
MC 
TC
Q
MR 
OR
OR
MC 
TC
Q
TR
Q
**Profit Max: Choose Q such that MR = MC
1
Output = TP = Q = F(K,L)
Production Function
Short Run: Time period such that at least one input is fixed
Kapital (K) is typically fixed
Labor (L) is typically variable
-add additional units of L to a fixed K stock
Long Run: Time period such that all inputs are variable
Average Product (Labor)
APL = Q/L
Marginal Product (Labor)
MPL = ∆Q/∆L
MPL 
OR
Q
L
Calculus Rules:
Y  F(X )  2X
Y
2
X
Y
 4X
X
Y  F(X )  2X 2
Y  F ( X )  X 2 
Y
2
 2 X 3  3
X
X
Y  F ( X )  aX b
1
X2
1
Y  F(X )  X 2  X
Y 1
 X
X 2
1
2
2

1
2 X
Y
 baX (b1)
X
Output = Q = F(K,L)
Q = meals per week
K = equipment hours per week (pan, oven, stove)
L = person hours per week
For Example:
Q = F(K,L) = 2*K*L
K=2
L=3
Q=
K= 2
L=5
Q=
K=4
L=3
Q=
K=5
L=3
Q=
K=5
L=5
Q=
Input/Output Matrix
Labor
person-hrs/wk
1
2
3
4
1
Kapital
equip-hrs/wk
2
3
4
5
Short-Run – Long-Run
Examples:
Law of Diminishing Marginal Productivity:
3
5
Back to our example……….
K is fixed &
L is variable
Q = F( K , L ) = 2*K*L
K=
K=
TP = Q = F( K , L ) =
TP = Q = F( K , L ) =
APL = Q/L =
APL = Q/L =
MPL = ∆Q/∆L =
MPL = ∆Q/∆L =
MPL 
Q

L
MPL 
What will APL look like (graph)?
What will MPL look like (graph)?
4
Q

L
Exercise 9.1
Sketch a graph of SR Prod Function when K = 4
Graphing calculator or plug & chug
1
(see pg. 266)
1
Q  F K , L   K L  K 2 L2
Q
L
APL  Q
L
MPL  Q
TP (Q)

L

L
0
APL
MPL
4
9
16
25
36
49
64
Diminishing Returns (graph)??
5
(practice: discrete/continuous)
6
Reality??
Diminishing marginal productivity and specialization
(Kelly's Cleaners)
L
0
TP (Q)
0
1
4
2
14
3
27
4
43
5
58
6
72
7
81
8
86
APL
MPL
Recall, MPL is given by slope of TP curve
0<L<4
MPL is
4<L<8
MPL is
L>8
MPL is
Recall APL is TP divided by L
Graphs?
7
APL can also be found geometrically using a ray from the origin that intersects the TP curve.
APL = Q/L
APL(2) =
APL(L) = slope of ray from the origin to intersection of TP
APL(4) = APL(8) =
APL(6) =
What is the relationship between MPL and APL?
MPL > APL
APL rising (increasing productivity)
MPL < APL
APL falling (decreasing productivity)
MPL = APL
APL is at Maximum
 Q 
L
Q ( L)
APL 
 
0
L
L
Chain Rule & Quotient Rule
Q Q
  APL  MPL
L L
Do Exercises 9.2, 9.3, 9.4 (see pages 270-272)
8
Long Run Production Decision
Both K & L are now variable
Read pgs. 275 - 281
Q  F ( K , L)  2 KL
Describe all possible combinations of K & L that give rise to a particular level of output
Q = 16
Q = 32
Q = 64
K = 8/L
K
1
2
4
6
8
L
8
4
2
1.33
1
K = 16/L
K
1
2
4
6
8
12
16
K = 32/L
K
1
2
4
6
8
12
16
18
24
32
L
16
8
4
2.67
2
1.33
1
L
32
16
8
5.33
4
2.67
2
1.78
1.33
1
35
30
25
K=8/L
20
K=16/L
15
K=32/L
10
5
0
0
5
10
15
20
25
9
30
35
Q  F ( K , L)  2 KL
Substitutability between K & L
Marginal rate of technical Substitution (MRTS):
When L is small,
When L is large,
10
Q  F ( K , L)  2 KL
Q = 16
16  2 KL  K 
16
8
 K   K  8L1
2L
L
Q = 32
32  2 KL  K 
32
16
K
 K  16 L1
2L
L
Q = 64
64  2 KL  K 
64
32
K
 K  32 L1
2L
L
Q = 16
MRTS 
K

L
Q = 32
MRTS 
K

L
Q = 64
MRTS 
K

L
When L is small,
When L is large,
11
Special Production Processes
How to choose between K & L to produce a given level of output at the lowest cost?
MPL
PL
MPK
PK
budget (Cost)
K (PK) & L (PL)
MPK
MPL
>
PK
PL
MPK
MPL
<
PK
PL
MPK
MPL
>
PK
PL
12
isocost line:
C  K * PK  L * PL
L K
Space:
Solve for K in terms of L
Re-write to see slope
Intercepts:
K
C/PK
C = K * PK + PL * L
slope = - PL/PK
C/PL
13
L
PL ↑
K
C/PK
C/PL2
C/PL1
L
PK ↑
K
C/PK1
C/PK2
C/PL
14
L
K
All else equal, when K becomes
more expensive relative to L, the
firm will use a more L intensive
production technique
K intensive technique
slope = - PL/PK
PL1/PK1 > PL2/Pk2
L intensive technique
L
You can think about income and substitution effects here
L and K demand by firms
15
MRTS 
K K

L L
isocost line:
C  K * PK  L * PL
Low cost production:
Recall our earlier result
MPL
P
 L
MPK PK
Can we reconcile these two terms?
MPL
P
 L
MPK PK
MRTS 
K PL

L PK
We need to show that
MPL K

MPK L
Consider substituting Labor in place of Kapital
16
slope = 
PL
PK
Returns to scale……….Definitions………puzzle
-not diminishing returns
double all inputs…..double output?????
Increasing Returns to Scale: The property of a production process whereby
Constant Returns to Scale: The property of a production process whereby
Decreasing Returns to Scale: The property of a production process whereby
-Decreasing returns to scale: we should expect
-Increasing returns to scale: we should expect
We will return to this issue with costs later.
17
The Link Between Production & Costs
Fixed Cost (FC): Costs that
Variable Cost (VC): Costs that
Total Cost (TC):
TC = FC + VC
Recall Q = F (K, L)
Kapital (K) is fixed & Labor (L) is variable in the SR
In general:
 We think of variable costs as the wage paid to L
 We think of the fixed cost as the cost of K
A firm requires factory and equipment in order to operate.
The cost of this capital is considered a fixed cost of production.
 Borrow money to purchase K (pay interest)
 Own K outright (forgo interest)
 PK = r
rental rate (interest rate)
 FC = rK0
K0 = fixed stock of K
 Property taxes, rent, insurance (overhead)
A firm produces output by adding workers to an existing stock of K.
The cost of these inputs are considered variable costs of production.
 Pay wages to workers
 PL w wage rate
 VC = wL
L = Labor employed
TC(Q) = FC + VC(Q)
TC = rK0 + wL
(recall isocost line)
The relationship between the production function and cost curves. See PowerPoint handout.
18
Production at Kelly's Cleaners
K0 = 120 mh @ $0.25 per mh
L
0
Q(L)
0
1
4
2
14
3
27
4
43
5
58
6
72
7
81
8
86
MPL(L)
FC
w = $10 per ph
VC(Q)
TC(Q)
AFC(Q)
19
AVC(Q)
ATC(Q)
MC(Q)
20
21
Additional worker produces more than previous worker:
TC curve gets shallower as output rises due to increasing marginal productivity. To produce additional
equal increments of output, the firm must employ lesser amounts of inputs, costs rise at a decreasing rate.
Additional worker produces less than previous worker:
TC curve gets steeper as output rises due to diminishing marginal productivity. To produce additional equal
increments of output, the firm must employ greater amounts of inputs, costs rise at an increasing rate.
Additional worker produces same as previous worker:
TC curve has a constant slope as output rises due to a constant rate of productivity. To produce additional
equal increments of output, the firm must employ the same amounts of inputs, costs rise at a constant rate.
22
Cost of Production
Set Up:
I hire additional workers with a fixed capital stock and output increases.
I must pay each additional worker the same daily wage.
Situation A:
Diminishing marginal productivity sets in immediately. Each worker hired produces less than the
previously hired worker and therefore productivity is declining.
Because each worker is paid the same wage, this will lead costs to rise at an increasing rate.
TC rising at an increasing rate implies increasing MC.
Situation B:
Diminishing marginal productivity sets in eventually. At first, each worker hired produces more than the
previously hired worker and therefore productivity is rising. At some point however, each worker hired
produces less than the previously hired worker and therefore productivity is declining.
Because each worker is paid the same wage, this will lead costs to rise, first at a decreasing rate and then
eventually at an increasing rate.
TC rising at a decreasing rate implies decreasing MC, while TC rising at an increasing rate implies
increasing MC.
Rules:
ATC is U-shaped.
When output is low, ATC declines as output increases.
When output is high, ATC rises as output increases.
This is because at first when output increases the firm is spreading the initial FC over additional units
causing ATC to decline, but as output continues to increase, diminishing marginal productivity dominates
causing ATC to rise.
When MP is rising (rising productivity), MC is decreasing.
When MP is falling (falling productivity), MC is increasing
When MC is less than ATC, then ATC is falling.
When MC is greater than ATC, then ATC is rising
MC will intersect ATC when ATC is at its lowest level (efficient scale)
When MC is less than AVC, then AVC is falling.
When MC is greater than AVC, then AVC is rising
MC will intersect AVC when AVC is at its lowest level
23
Exercise 10.4
For a production function at a given level of output in the SR, the MPL is greater than the APL. How
will MC at that output level compare with AVC?
MC 
VC
Q
VC  wL  MC 

with w constant
given that
we have that
wL
Q
MPL 
Q

L
MC 
Because w is fixed, the ____________ MPL corresponds to the ____________ MC.
similarly
AVC 
VC wL

Q
Q
given that
we have that
APL 
Q

L
AVC 
Because w is fixed, the ____________ APL corresponds to the ____________ AVC.
24
We know that MC begins ____________ AVC and pulls AVC ____________
MC is ____________ continuing to pull AVC ____________
Then MC begins to ____________ (diminishing returns, MC min, MPL max)
Then MC approaches AVC until ____________
Then MC is ____________ AVC and pulls AVC ____________
Therefore MC = AVC at ____________
We know that MPL begins ____________ APL and pulls APL ____________
MPL is ____________ continuing to pull APL ____________
Then MPL begins to ____________ (diminishing returns, MPL max, MC min)
Then MPL approaches APL until ____________
Then MPL is ____________ APL and pulls APL ____________
Therefore MPL = APL at ____________
25
Show this relationship graphically for the Kelly’s Cleaners example (use Excel or plot by hand).
26
27
Recall what the optimal technique looks like
Different optimal techniques in different countries
28
29
30
K
3
6
9
12
15
18
21
24
Q = 2KL
K
L
1
1
2
2
4
4
8
8
16
16
Q = 2K + 3L
K
L
1
1
2
2
4
4
8
8
16
16
L
1
2
3
4
5
6
7
8
Q
30
90
180
240
300
360
400
420
Q
Q
A
B
C
D
E
F
G
H
Q = KL
K
L
1
1
2
2
4
4
8
8
16
16
K2 L 2
K
1
2
4
8
16
L
1
2
4
8
16
Q
Q
31
K+L
K
1
2
4
8
16
L
1
2
4
8
16
K1/2L1/2
K
L
1
1
2
2
4
4
8
8
16
16
Q
Q