Topic 5. Production and cost
(3) The long run: Isoquant and
Isocost analysis
November 1st 2004
Lecture slides available from Nancy’s
website:
http://www.staff.city.ac.uk/n.j.devlin
The aim of today’s lecture is to:
 Introduce you to Isoquant and
Isocost analysis.
This enables us to show how the firm
will choose the optimal
combination of inputs (when all
inputs are variable) to produce a
given output
Essential reading:
 Sloman chapter 5, especially
Sections 5.3 and 5.4.
1. Production function analysis
Capital
10
9
More than
500,000 units
of output
8
7
6
X
5
4
Fewer than
500,000 units
of output
3
2
1
0
0
1
2
3
4
5
6
7
8
9
Labour
Two inputs are used to produce
output: L (workers) and K (machines).
X = Production of 500,000 units of
output per week, by 4 workers using 5
machines
10
2. Isoquants
Iso = same
Isoquant = same quantity
Capital
10
9
More than
500,000 units
of output
8
7
6
X
5
Fewer than
500,000 units
of output
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
Labour
The slope of the isoquant is the
Marginal rate of technical
substitution (MRTS).
 MRTS = ΔK/ΔL
 MRTS = MPL/MPK
 MRTS is falling as you move
down the isoquant.
 Why?
10
2a. Isoquant map
Capital
10
I2
I1
9
I3
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
Labour
I1 = 400,000 units of output
I2 = 500,000 units of output
I3 = 600,000 units of output
10
2b. Technical efficiency
Capital
10
9
8
7
X
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
Labour
Production is technically efficient if
output cannot be raised without
using more of at least one input.
 The isoquant summarises all
technically efficient points
 Production of 500,000 units of
output at X would be technically
inefficient.
10
2c. Demonstrating returns to scale
using isoquants
Capital
10
I2
I1
9
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
Labour
I2 uses twice as many inputs as I1. I1
produces 400, 000 sausages.
If I2 produces…
800,000
> 800,000
< 800,000
Returns to scale are…
constant
increasing
decreasing
10
2d. Marginal product of one variable
factor (SR)
Capital
10
I1
9
I2
I3
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
Labour
K is fixed; Lis variable. The marginal
product (MP) of L is the extra output
from one extra worker.
I1 produces 400,000
I2 produces 450,000
I3 produces 480,000
MP is 50,000 for the 5th worker and
30,000 for the 6th worker.
MP may be increasing, constant or
diminishing.
10
3. Isocost lines
Input possibilities
1 The total amount available to be
spent on workers and machines is
£1,000 per week.
2 The rental cost of a machine is
£200 per week.
3 The weekly wage of a worker is
£100.
Therefore, the employer can hire 5
machines and no workers or 10
workers and no machines or some
combination of workers and machines.
All possible input possibilities form the
isocost line.
3a. Isocost line
Capital
10
9
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
Labour
 slope of the isocost line = PL/PK
10
3b. Isocost lines at different input
prices
Capital
10
9
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
Labour
10
3c. Isocost lines at different levels
of Total Cost
Show the effects on the isocost line
of:
 higher total cost
 lower total cost
Capital
10
9
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
Labour
10
4. Minimising the costs of
producing a given output
Capital
10
9
8
C1
7
Y
6
C2
5
4
C3
3
X
2
1
0
0
1
2
3
4
5
6
7
8
9
Labour
 at X, MRTS = PL/PK
 MRTS = ΔK/ΔL
 MRTS = MPL/MPK
So at X
MPL/MPK = PL/PK
And
MPL/PL = MPK/PK
10
5. Maximising output for a given
cost
Capital
10
9
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
Labour
10
6. The distinction between technical
and economic efficiency.
Capital
10
9
8
C1
7
Y
6
C2
5
4
3
X
2
1
0
0
1
2
3
4
5
6
7
8
9
Labour
Both X and Y are technically efficient
ways of producing 500,000 units of
output.
X is also an economically efficient
(cost-effective) way to produce
500,000 units of output.
Y is technically efficient, but is not
economically efficient.
10
7. Derivation of long-run costs from an
isoquant map.
Capital
10
9
8
7
Expansion
path
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
Labour
 Expansion path: the tangency
points of the isoquant and
isocost curves.
 Shows the minimum cost
combinations of L and K to
produce each level of output;
the LRTC are shown by the
isocost.
10
K
8a. Deriving a LRAC curve from an isoquant map
At an output of 20
LRAC = C2 / 20
O
C1
C2
10
0
20
0
L
K
8b. Deriving a LRAC curve from an isoquant map
Note: increasing returns
to scale up to 40 units;
decreasing returns to
scale above 40 units
O
C1
C2
C3 C4
10
C5 0C6
70
0
60
50 0
40
30 0
20 0
0
C7
L