Transcript 8. Production

Production refers to the transformation of
inputs or resources into outputs of goods and
services
Creation of utility
 Created
 Satisfy
by human labor and capital
human wants directly or indirectly
 Are
comparatively scarce and have economic
value
 Have
a definite monetary price/cost
Factors of Production
INPUTS
Land
Labor
Capital
•Immobile
•Passive
•Heterogeneous
•Active
•Mobile
•Variable
•productivity
•Structures
•Equipment
•Cap.goods
•Money
Enterprise
•Innovative function
•Risk
•Decision making
INPUTS
CAPITAL
LABOR
Workers
Entrepreneur
Land &
Structures
Machinery
plant &
equipment
Natural
Resources
 Inputs


Fixed Inputs
Variable Inputs
 Short
 Long

Run- At least one input is fixed
Run - All inputs are variable
The length of long run depends on industry.
 Level
of production can be altered changing
the proportion of variable inputs
Output = Fixed inputs + Variable inputs
Scale of production can be altered by changing
the supply of all the inputs only in the long run
•
Output = Total inputs(variable inputs)
 Total
Product - total volume of goods produced
during a specific period of time
 Average
Product - the per unit product of a
variable factor
 Marginal
Product - the rate at which total
product increases / addition to total product
resulting from a unit increase in the quantity of
the variable factor
Production Function With Two Inputs
K
6
5
4
3
2
1
Q = f(L, K)
10
12
12
10
7
3
1
24
28
28
23
18
8
2
31
36
36
33
28
12
3
36
40
40
36
30
14
4
40
42
40
36
30
14
5
Q
39
40
36
33
28
12
6 L
Input & output are measured in physical units
Assumption- Technology is constant the during analysis
period
- All units of L & K are homogenous
Discrete Production Surface
Total Product
TP = Q = f(L)
Marginal Product
TP
MPL =
L
Average Product
TP
APL =
L
Production or
Q/Q
=
E
Output Elasticity L L/L
=
Q/ L = MPL
APL
Q/L
Total, Marginal, and Average Product of Labor, and
Output Elasticity
L
0
1
2
3
4
5
6
Q
0
3
8
12
14
14
12
MPL
3
5
4
2
0
-2
APL
3
4
4
3.5
2.8
2
1
0
Total, Marginal, and Average Product of Labor, and Output Elasticity
L
Q
MPL
APL
EL
0
1
2
3
4
5
6
0
3
8
12
14
14
12
3
5
4
2
0
-2
3
4
4
3.5
2.8
2
1
1.25
1
0.57
0
-1
Production Function with One Variable Input
Total 16
Product
D
E
14
Law of 12Diminishing Returns
states that
when increasing
10
amounts of Variable inputs are
B
8
combined with a fixed level of
6
another input, a point
will be
A
4
reached where MP will decline.
C
F
TP
2
Marginal
& Average
Product
0
0
1
2
3
4
5
6
7
Labor
6
5
B’
C’
4
D’
E’
A’
3
F’
2
AP
1
0
0
1
2
3
4
5
6
-1
-2
-3
MP
7
Labor
The Law of Diminishing Returns &
Stages of Production
Total 16
Product
D
E
14
C
F
12
TP
I
10
8
Inflection pt.
6
G
B
A
4
2
Marginal
& Average
Product
0
0
6
1
2
Stage I of Labor
5
C’
A’
3
4
Stage II of Labor
B’
4
3
D’
5
6
Stage III of Labor
E’
F’
2
AP
1
0
0
1
2
3
4
5
6
-1
-2
-3
7
Labor
MP
7
Labor
The Law of Diminishing Returns &
Stages of Production
Total 16
Product
D
E
14
C
F
12
TP
I
10
B
8
G
6
A
4
2
Marginal
& Average
Product
0
0
6
2
Stage I of Labor
5
3
C’
A’
3
MPL is increasing
MPK is negative
2
1
0
1
4
Stage II of Labor
B’
4
0
1
2
D’
MPL & MPK Positive
3
4
5
6
Stage III of Labor
E’
F’
AP
MPL is negative
5
6
-1
-2
-3
7
Labor
MP
7
Labor
Marginal Revenue
MRPL = (MPL)(MR)
Product of Labor
Marginal Resource
Cost of Labor
TC
MRCL =
L
Optimal Use of Labor MRPL = MRCL
Optimal Use of the Variable Input
L
2.50
3.00
3.50
4.00
4.50
MPL
4
3
2
1
0
MR = P
$10
10
10
10
10
Assumption : Firm hires additional units of labor at constant
wage rate = $20
Optimal Use of the Variable Input
L
2.50
3.00
3.50
4.00
4.50
MPL
4
3
2
1
0
MR = P
$10
10
10
10
10
MRPL
$40
30
20
10
0
MRCL
$20
20
20
20
20
Assumption : Firm hires additional units of labor at constant
wage rate
Use of Labor is Optimal When L = 3.50
$
40
30
20
MRCL = w = $20
10
dL = MRPL
0
2.5
3.0
3.5
4.0
4.5
Units of Labor
Used
 The
marginal product of labor equation for a
firm is given by: MPL = 10(K/L)0.5
 Currently the firm is using 49 units of capital
and 100 units of labor. Capital usage is fixed,
but labor can be varied. If the price of labor
is $20 per unit and the firms' output sells for
$4, is the firm producing efficiently in the
short run? If not, explain and determine the
optimal rate of labor input.
 MRPL

L
= MRCL = w
28 ≠ 20 Not efficient
= 196
Isoquants show combinations of two inputs
that can produce the same level of output.
K
6
5
4
3
2
1
10
12
12
10
7
3
1
24
28
28
23
18
8
2
31
36
36
33
28
12
3
36
40
40
36
30
14
4
40
42
40
36
30
14
5
39
40
Q
36
33
28
12
6 L
Isoquants
Economic Region of Production
Firms will only use combinations of two inputs that are in
the economic region of production.
Ridge line
W
Marginal Rate of Technical Substitution
Q = f(L,K)
dQ=Q/ L *dL + Q/ K *dK= 0
dK= (-) Q/ L
dL
Q/ K
Q/ L = MPL and Q/ K = MPK
dK = - MPL = MRTS
dL
MPK
(L) MPL = -(K) MPK
Marginal Rate of Technical Substitution
K
Absolute value of the slope of isoquant is called the MRTS
MRTS = -(-2.5/1) = 2.5
Perfect Substitutes
Perfect Complements
2K
1L
Capital
Capital
6
4
6
B
4
2
2
-1K
2L
0
2
C
4
6
A
8
10
12
Labor
0
2
4
6
Labor
Isocost lines represent all combinations of
two inputs that a firm can purchase with the
same total cost.
C  wL  rK
C  Total Cost
w  Wage Rate of Labor ( L)
C w
K  L
r r
r  Cost of Capital ( K )
Capital
10
AB
A
C = $100, w = r = $10
slope = -w/r = -1
8
vertical intercept = 10
6
1K
1L
4
2
B
2
4
6
Labor
8 10
Isocost Lines
Capital
14 A’
Isocost Lines
A
10
8 A”
AB
C = $100, w = r = $10
A’B’
C = $140, w = r = $10
A’’B’’
C = $80, w = r = $10
AB*
C = $100, w = $5, r = $10
4
B”
0
4
8
B
B’
10 12 14 16
B*
20
Labor
Isocost Lines
AB
C = $100, w = r = $10
A’B’
C = $140, w = r = $10
A’’B’’
C = $80, w = r = $10
MRTS = w/r
Optimal input combinations:
Slope of isoquant = Slope of isocost line
(absolute)Slope of isoquant = (absolute) Slope of isocost line
MRTS =
w
r
Since MRTS = MPL/ MPK
MPL = w
MPK
r
MPL = MPK
w
r
If MPL = 5, MPK =4, and w = r
MPL > MPK
w
r
MRP(input) = MRC(input)
with constant input prices
MRP(input) = input price
To maximize Profits:
MRPL = w = (MPL)(MR)
MRPK = r = (MPK)(MR)
MPL = w
MPK r
MPL = MPK
w
r
Returns to scale refers to the degree
by which output changes as a result of
a given change in the quantity of all
inputs used in production.
•Long run function
•Both L & K are changing
Production Function Q = f(L, K)
Q = f(hL, hK)
If  = h, constant returns to scale.
If  > h, increasing returns to scale.
If  < h, decreasing returns to scale.
Constant
Returns to
Scale
Increasing
Returns to
Scale
Decreasing
Returns to
Scale
Cobb-Douglas Production Function
Q = AKaLb
For example: the inputs are doubled i.e. instead of K & L,
we are using 2K & 2L, then by how much the production
will increase.
New Q = A(2K)a(2L)b
= A(2)a+bKaLb
= 2a+bAKaLb
= 2a+bQ
Now Q = 2a+bQ
If a + b = 1, constant returns to scale.
If a + b > 1, increasing returns to scale.
If a + b <1, decreasing returns to scale.
Do the following production functions have
constant, increasing or decreasing returns of
scale? ( K, L, M are inputs)
a. Q = 0.5X + 2Y + 40Z
b. Q = 3L + 10K + 500
c. Q = K/L
d. Q = 4A + 6B + 8AB
e. Q = 10L 0.5 K 0.6
A. constant returns to scale.
B. diminishing returns to scale.
C. Decreasing returns to scale
D. increasing returns to scale.
E. increasing returns to scale
 Technology
– cost effective at high level of
production
 Specialization of labour
Diseconomies of scale
 Transportation cost
 Difficult to manage
a.
b.
Medical Testing Labs, Inc., provides routine testing services for
blood banks in the Los Angeles area. Tests are supervised by
skilled technicians using equipment produced by two leading
competitors in the medical equipment industry. Records for the
current year show an average of 27 tests per hour being
performed on the Testlogic-1 and 48 tests per hour on a new
machine, the Accutest-3. The Testlogic-1 is leased for $18,000 per
month, and the Accutest-3 is leased at $32,000 per month. On
average, each machine is operated 25 eight-hour days per month.
Does Medical Testing Lab usage reflect an optimal mix of testing
equipment?
If tests are conducted at a price of $6 each while labor and all
other costs are fixed, should the company lease more machines?
a) (27*25*8)/ 18000 = (48*25*8) / 32000 = 0.3
In both instances, the last dollar spent on each machine
increased output by the same 0.3 units, indicating an
optimal mix of testing machines.
b) For each machine hour, the relevant question is Testlogic-1
27 ×(25×8)× $6 > $18,000 or $32,400 > $18,000.
Accutest-3
48 ×(25×8)× $6 > $32,000 or $57,600 > $32,000.
In both cases, each machine returns more than its marginal
cost (price) of employment, and expansion would be
profitable.
Exercise
The marginal product of labor for international
trading is given by the equation
MPL = 10K0.5/L0.5
Currently the firm is using 100 units of capital and
121 units of labor. The capital stock is
constant but the labor can be varied. If the
price of labor is 10/- and price of output is Rs.
2/- per unit, is the firm operating efficiently
in the short run? If not, determine the optimal
rate of labor input.
Answer: not optimally, L = 400
The production function is : Q = 20K0.5L0.5
With marginal product functions
MPK = 10L0.5/K0.5
MPL = 10K0.5/L0.5



If the price of capital is Rs. 5/- and price of labor is Rs.
4/- per unit, determine the expansion path for the firm.
The firm currently is producing 200 units of output per
period using input rates of L = 4 and K =25. is this an
efficient input combination? Why or why not? If not,
determine the efficient input combination for producing
an output rate of 200.
If the price of labor increases from Rs 4 to Rs 8 per unit,
determine the efficient input combination for an output
rate of 200. What is the capital –labor ratio now?
Answer: K= 0.8L,
L= 11.18 and K= 8.94,
L = 7.905 and K = 12.65
Suppose the price of one unit of labor is $10 and price of
one unit of capital is $2.50.





Use this information to determine the isocost equations
corresponding to a total cost of $200 and $500.
Plot these two isocost lines on a graph
If the price of labor falls from $10 per unit to $8 per unit,
determine the new $500 isocost line and plot it on the
same diagram used in part (b)
Answer: K = 80- 4L and K = 200 – 4L,
K = 200 – 3.2L
4. Given the production function Q = 30K0.7L0.5
and input prices r = 20 and w = 30.
 Determine an equation for the expansion
path
 What is the efficient input combination for
an output rate of Q = 200? For 500?
Answer: K = 2.1L, for 200: L = 3.15 and K =
6.62, for 500: L = 6.765 and K = 14.207
The revenue dept. of a state govt. employs
certified public accountants (CPAs) to audit
corporate tax returns and book keepers to audit
individual returns. CPAs are paid $31200 per yr,
while the annual salary of a bookkeeper is
$18200. Given the current staff of CPAs and
bookkeepers, a study made by the dept’s
economist shows that adding one year of a CPA’s
time to audit corporate returns results in an
additional tax collection of $52000. In contrast,
an additional bookkeeper adds $41600 per year
in additional tax revenue.




If the dept’s objective is to maximize tax revenue
collected, is the present mix of CPAs and bookkeepers
optimal? Explain
If the present mix of CPAs and bookkeepers is not
optimal, explain what re-allocation should be made.
That is, should the department hire more CPAs and
fewer bookkeepers or vice versa.
Answer: CPAs – 1.67 and bookkeepers – 2.29