ppa 723: managerial economics lecture 10: production
TRANSCRIPT
Managerial Economics, Lecture 10: Production
Outline
Production Technology in the Short Run
Production Technology in the Long Run
Managerial Economics, Lecture 10: Production
ProductionA production process transform inputs
or factors of production into outputs.
Common types of inputs:capital (K): buildings and equipmentlabor services (L)materials (M): raw goods and processed
products.
Managerial Economics, Lecture 10: Production
Production FunctionsA production function specifies:
the relationship between quantities of inputs used and the maximum quantity of output that can be produced
given current knowledge about technology and organization.
For example, q = f(L, K)
Managerial Economics, Lecture 10: Production
Short Run versus Long Run Short run: A period of time so brief that at
least one factor of production is fixed.
Fixed input: A factor that cannot be varied practically in the short run (capital).
Variable input: a factor whose quantity can be changed readily during the relevant time period (labor).
Long run: A time period long enough so that all inputs can be varied.
Managerial Economics, Lecture 10: Production
Total, Average, and Marginal Product of Labor
Total product: q
Marginal product of labor: MPL = q/L
Average product of labor: APL = q/L
The graphs for these concepts appear smooth because a firm can hire a "fraction of a worker" (part time).
ManagerialEconomicsLecture 10:Production
Output, q,
Units per day
B
A
C
11640
L , Workers per day
Marginal product, MPL
Average product, APL
AP L, MPL
110
90
56
(a)
b
a
c
11640
L , Workers per day
20
15
(b)
Figure 6.1 ProductionRelationships with Variable Labor
APL = Slope of
straight line
to the originMPL = Slope of
total product
curve
APL = MPL at
maximum APL
Managerial Economics, Lecture 10: Production
Effects of Added LaborAPL
Rises and then falls with labor.Equals the slope of line from the origin to
the point on the total product curve.
MPL First rises and then falls. Cuts the APL curve at its peak.Is the slope of the total product curve.
Managerial Economics, Lecture 10: Production
Law of Diminishing Marginal Returns
As a firm increases an input, holding all other inputs and technology constant,
the marginal product of that input will eventually diminish,
which shows up as an MPL curve that slopes downward above some level of output.
Managerial Economics, Lecture 10: Production
Long-Run Production: Two Variable Inputs
Both capital and labor are variable.
A firm can substitute freely between L and K.
Many different combinations of L and K produce a given level of output.
Managerial Economics, Lecture 10: Production
Isoquant An isoquant is a curve that shows efficient
combinations of labor and capital that can produce a single (iso) level of output (quantity):
Examples:A 10-unit isoquant for a Norwegian printing firm
10 = 1.52 L0.6 K0.4
Table 6.2 shows four (L, K) pairs that produce q = 24
( , )q f L K
Managerial Economics, Lecture 10: Production
Figure 6.2 Family of IsoquantsK, Units ofcapital per day
e
b
a
d
fc
63210 L , Workers per day
6
3
2
1
q = 14
q = 24
q = 35
Managerial Economics, Lecture 10: Production
Isoquants and Indifference Curves
Isoquants and indifference curves have most of the same properties.
The biggest difference:An isoquant holds something measurable
(quantity) constantAn indifference curve holds something that
is unmeasurable (utility) constant
Managerial Economics, Lecture 10: Production
Three Key Properties of Isoquants
1. The further an isoquant is from the origin, the greater is the level of output.
2. Isoquants do not cross.
3. Isoquants slope downward.
Managerial Economics, Lecture 10: Production
The Shape of Isoquants
The slope of isoquant shows how readily a firm can substitute one input for another
Extreme cases:perfect substitutes: q = x + yfixed-proportions (no substitution):
q = min(x, y)
Usual case: bowed away from the origin
Managerial Economics, Lecture 10: Production
Figure 6.3a Perfect Substitutes: Fixed Proportions
y, Idaho potatoesper day
x, Maine potatoes per day
q = 3q = 2q = 1
Managerial Economics, Lecture 10: Production
Figure 6.3b Perfect Complements
Boxesper day
Cereal per day
q = 3
q = 2
q = 1
45° line
Managerial Economics, Lecture 10: Production
Figure 6.3c Substitutability of Inputs
q = 1
K, Capital perunit of time
L, Labor per unit of time
Managerial Economics, Lecture 10: Production
Marginal Rate of Technical Substitution
The slope of an isoquant tells how much a firm can increase one input and lower the other without changing quantity.
The slope is called the marginal rate of technical substitution (MRTS).
The MRTS varies along a curved isoquant, and is analogous to the MRS.
Managerial Economics, Lecture 10: Production
Figure 6.4 How the Marginal Rate of Technical Substitution Varies Along an Isoquant
K, Units ofcapital per year
e
b
K = –18
–7
–4–2
L = 1
d
c
63
11
1
4 520 L, Workers per day
39
21
14
108 q = 10
a
Managerial Economics, Lecture 10: Production
The Slope of an IsoquantIf firm hires L more workers, its output
increases by MPL = q/L
A decrease in capital by K causes output to fall by MPK = q/K
To keep output constant, q = 0:
or
( ) ( ) 0L KMP L MP K
L
K
MP KMRTS
MP L
Managerial Economics, Lecture 10: Production
Returns to ScaleReturns to scale (how output changes
if all inputs are increased by equal proportions) can be:
Constant: when all inputs are doubled, output doubles,
Increasing: when all inputs are doubled, output more than doubles, or
Decreasing: when all inputs are doubled, output increase < 100%.