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1. Production
Outline:
•Introduction to the production function
•A production function for auto parts
•Optimal input use
•Economies of scale
•Least-cost production

2. The production function
•Production is the process of transforming
inputs into semi-finished articles (e.g.,
camshafts and windshields) and finished
goods (e.g., sedans and passenger trucks).
•The production function indicates that
maximum level of output the firm can
produce for any combination of inputs.

3. General description of a
production function
Let:
Q = F (M, L, K) [1]
Where Qis the quantity of output produced
per unit of time (measured in units, tons,
bushels, square yards, etc.), Mis quantity of
materials used in production, Lis the
quantity of labor employed, and Kis the
quantity of capital employed in production.

4. Technical efficiency
The production function
indicates the maximum output
that can be obtained from a
given combination of inputs—
that is, we assume the firm is
technically efficient.

5. A production function for
auto parts
Consider a multi-product firm that supplies parts
to major U.S. auto manufacturers. Its production
function is given by Let
Q = F(L, K)
Where Q is the quantity of specialty parts
produced per day, L is the number of workers
employed per day, and K is plant size (measured
in thousands of square feet).

6. Number of PlantSize(000s)
Workers 10 20 3040
10 93 120145165
20 135190235264
30 180255300337
40 230315365410
50 263360425460
60 293395478510
70 321430520555
80 346460552600
90 368485580645
100 388508605680 This table [1] shows the quantity of output
that can be obtained from various
combinations of plant size and labor

7. The short run
•Inputs that cannot be varied in
the short run are called fixed
inputs.
•Inputs that can vary are called
(not surprisingly) variable
inputs
The short run refers to
the period of time in
which one or more of
the firm’s inputs is
fixed—that is, cannot
be varied

8. The long run The long run is the period
of time sufficiently long to
allow the firm to vary all
inputs—e.g., plant size,
number of trucks, or
number of apple trees.

9. Marginal product
•Marginal productis the additional (or extra)
output resulting from the employment of one more
unit of a variable input , holding all other inputs
constant.
•In our example, the marginal product of labor
(MP
L)is the extra output of auto parts realized by
employing one additional worker, holding plant size
constant

10. Number of Total Marginal
Workers ProductProduct
10 93
20 135 4.2
30 180 4.5
40 230 5
50 263 3.3
60 293 3
70 321 2.8
80 346 2.5
90 368 2.2
100 388 2.0
110 400 1.2
120 403 0.3
130 391 -1.2
140 380 -1.1 Production of specialty parts,
assuming a plant size of
10,000 square feet

11. Law of diminishing returns
As units of a variable input are added (with all
other inputs held constant), a point is reached
where additional units will add successively
decreasing incrementsto total output—that is,
marginal product will begin to decline.
Notice that, after 40 workers are
employed, marginal product begins to
decline

12. 500
400
300
200
100
0 102030405060708090100110120130140
Total Output
20,000-square-foot plant
10,000-square-foot plant
Number of Workers
The total product of labor

13. The marginal product of labor when plant size is
10,000 square feet
5.0
4.0
3.0
2.0
1.0
0
102030405060708090100110 130140
Marginal Product
Number of Workers
–1.0
–2.0
120

14. Optimal use of an input
By hiring an additional unit of
labor, the firm is adding to its
costs—but it is also adding to
its output and thus revenues.

15. Marginal revenue product of
labor (MRP
L)
The marginal revenue product of labor (MRP
L)
is given by
MRP
L= (MR)(MP
L) [6.2]
Where MRmarginal revenue—that is, the
additional (extra) revenue realized by selling
one more unit.
Example: If MP
Lis 5 units, and the firm can
sell additional units for $6 each, then:
MRP
L= (MR)(MP
L) = (5)($6) = $30

16. Marginal cost of labor (MC
L)
What additional cost does the
firm incur (wages, benefits,
payroll taxes, etc.) by hiring one
more worker?

17. -maximizing rule of thumb
The firm should employ additional units of
the variable input (labor) up to the point
where MRP
L= MC
L
1
1
In terms of calculus, we have:
MRP
L = (MR)(MP
L) = (dR/dQ)(dQ/dL)
and
MC
L= dC/dL

18. Example
Example:
•The firm has estimated that the cost of hiring an
additional worker is equal to $160 per day, that is,
MC
L= P
L= $160.
•Assume the firm can sell all the parts it wants at a
price of $40. Hence, MR = $40
•Thus the MRP
L= (MR)(MP
L) = ($40)(MP
L)

19. Number of Total Marginal Marginal Marginal
Workers ProductProductRevenue Product Cost
10 93 160
20 135 4.2 168 160
30 180 4.5 180 160
40 230 5 200 160
50 263 3.3 132 160
60 293 3 120 160
70 321 2.8 112 160
80 346 2.5 100 160
90 368 2.2 88 160
100 388 2.0 80 160
110 400 1.2 48 160
120 403 0.3 12 160
130 391 -1.2 -48 160
140 380 -1.1 -44 160

20. Problem
Let the production function be given by:
Q = 120L –L
2
The cost function is given by
C = 58 + 30L
The firm can sell an unlimited amount of output at a
price equal to $3.75 per unit
1.How many workers should the firm hire?
2.How many units should the firm produce?

21. Production in the long run
•The scale of a firm’s operation denotes the levels of
allthe firm’s inputs.
•A change in scalerefers to a given percentage
change in all the firm’s inputs—e.g., labor, materials,
and capital.
•If we say “the scale of production has increased by
15 percent,” we mean the firm has increased its
employment of allinputs by 15 percent.

22. Returns to scale
Returns to scale
measure the percentage
change in output
resulting from a given
percentage change in
inputs (or scale)

23. 3 cases
1.Constant returns to scale: 10 percent
increase in all inputs results in a 10 percent
increase in output.
2.Increasing returns to scale:10 percent
increase in all inputs results in a more than
10 percent increase in output.
3.Decreasing returns to scale:10 percent
increase in all inputs results in a less than
10 percent increase in output.

24. Sources of increasing returns
1.Specialization of plant and equipment
Example:Large scale production in furniture
manufacturing allows for application of specialized
equipment in metal fabrication, painting, upholstery,
and materials handling.
2.Economies of increased dimensions
Example:Doubling the circumference of pipeline
results in a fourfold increase in cross sectional area,
and hence more than doubling of capacity, measured
in gallons per day.
3.Economies of massed reserves.
Example: A factory with one stamping machine needs
to have spare 100 parts in inventory to be prepared
for breakdown—does a factory with 20 machines need
to have 2,000 spare parts on hand?

25. Economies of increased dimensions
r
hrhrhSA  22
2
 hrV
2


26. Effect of a 1 inch change in vessel
radius
Surface Area and Volume
PIr (in.)h (in.)S.A. (sq. in.)V (cu. in.)
3.14166 10 4146.902 1130.973
3.14167 10 4838.053 1539.380
Change in S.A (%)Change in V. (%)
16.6667 36.111

27. Intermodal Freight
Containers
The shift from the 20
foot to the 40 foot
freight container has
made shipping goods
more economical
See link

28. Fixed and Sunk Costs
•Fixed costs (FC)are elements of cost
that do not vary with the level of output.
Examples: Interest payments on bonded
indebtedness, fire insurance premiums,
salaries and benefits of managerial staff.
•Sunk costsare costs already
incurredand hence non-recoverable.
Examples: Research & development
costs, advertising costs, cost of
specialized equipment.

29. Definitions
Variable cost (VC)is the sum of the
firm’s expenditure for variable inputs such
as hourly employees, raw materials or
semi-finished articles, or utilities.
Average total cost (SAC)is total cost
divided by the quantity of output.
Average variable cost (AVC) is
variable cost divided by the quantity of
output.
Marginal cost (SMC)is the addition to
total cost attributable to the last unit
produced

30. Annual Output Total CostFixed CostVariable Cost
(Thousands of Repairs)($000s) ($000s) (000s)
0 270.0 270 0.0
5 427.5 270 157.5
10 600.0 270 330.0
15 787.5 270 517.5
20 990.0 270 720.0
25 1207.5 270 937.5
30 1440.0 270 1170.0
35 1687.5 270 1417.5
40 1950.0 270 1680.0
45 2227.5 270 1957.5
50 2520.0 270 2250.0
55 2827.5 270 2557.5
60 3150.0 270 2880.0 Firm’s Costs in the Short Run

31. 3,000
0 60
Output(ThousandsofUnits)
TotalCost(ThousandsofDollars)
555045403530252015105
2,000
1,000
Costfunction

32. Annual Output Total CostAve. CostMarginal Cost
(Thousands of Repairs)($000s) ($000s) ($000s)
0 270.0
5 427.5 85.5 31.5
10 600.0 60.0 34.5
15 787.5 52.5 37.5
20 990.0 49.5 40.5
25 1207.5 48.3 43.5
30 1440.0 48.0 46.5
35 1687.5 48.2 49.5
40 1950.0 48.8 52.5
45 2227.5 49.5 55.5
50 2520.0 50.4 58.5
55 2827.5 51.4 61.5
60 3150.0 52.5 64.5

33. 64
0 60
Output(ThousandsofUnits)
Cost/Unit(ThousandsofDollars)
44
48
52
56
555045403530252015105
SMC
SAC
60

34. Relationship between Average
and Marginal
When average cost is falling, marginal cost lies
everywhere below average cost.
When average cost is rising, marginal cost lies
everywhere above average cost.
When average cost is at its minimum, marginal
cost cost is equal to average cost.
If your most recent (marginal)
grades are higher than your
GPA at the start of the term,
your GPA will rise

35. What explains rising (short-run)
marginal cost?
If labor is the only variable input then marginal cost
can be expressed by:L
L
MP
P
SMC
[7.1]
Recall that the marginal
product of labor will begin to
fall at some point due to the
law of diminishing returns.

36. 0.0
50.0
100.0
150.0
200.0
250.0
300.0
1 11 21 31 41 51
Output (Q)
Fixed Cost Per Unit Behavior of Average Fixed Cost
As output increases, fixed
cost can be spread more
thinly

37. Productioncosts is the long run
•In the long run there are no fixed inputs;
hence all costs are “variable.”
•The long run average cost curve shows the
minimum average cost achievable at each level
of output in the long run—that is, when all
inputs are variable.

38. Constant Returns to Scale
$5
0
Output(ThousandsofUnits)
Long-RunAverageCost
4
21614410872
SAC1
(9,000-square-
footplant)
-
SAC2
(18,000-square
footplant)(
SAC3
27,000-square-
footplant)
SMC1SMC2 SMC3
LAC=LMC

39. The U-Shaped Long Run Average Cost FunctionOutput
Long-Run Average Cost
SAC1
SMC2
Qmin
SMC1 SMC3
SAC2
SAC3
LMC
LMC
LAC
Increasing returns
Decreasing returns

40. Notice on the previous slide
that up to a scale of Q
MIN, the
firm experiences decreasing
(long run) unit cost. Economies
of scale are exhausted at the
point

41. Minimum Efficient Scale (Q
MES)
Q
MESis the minimumscale of
operation at which long unit
production costs can be
minimized.

42. LAC
Demand
Q
MES is large relative to he
“size of the market.”
Q
Cost per unit
0
1000 2000
To produce on an
efficient scale, you
must supply 50% of
the product demanded
at a price equal to
minimum unit cost

43. How large do you have to be to
minimize unit costs?
1
Not very large(as a percent of U.S. consumption) : Bricks, flour
milling, machine tools, cement, glass containers, cigarettes, shoes,
bread baking.
Fairly large(as a percent of U.S. consumption): Synthetic fibers,
passenger cars, household refrigerators and freezers, commercial
aircraft.
Very large(as a percent of U.S. consumption): Turbine
generators, diesel engines, electric motors, mainframe computers.
1
F.M. Scherer and D. Ross. Industrial Market Structure and
Performance, 3
rd
edition, 1990, pp. 115-116.

44. Output
Long-Run Average Cost
Qmin
(a)

45. Output
Long-Run Average Cost
Qmin
(b)

46. Output
Long-Run Average Cost
(c) Local telephone service,
electricity distribution, and
cable TV distribution are well
represented by this cost
function.