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Production and Cost:A Short Run Analysis
Production
Inputs:
Labour Machinery
LandRaw Materials
Production: transformation of resources into output of goods and services.
The Organization of Production
Output: goods and services
Q = f ( L, K, R, T )
Simplifying, Q = f (L, K)
The Production Function
The Short Run The Long Run
One of the factors is fixed
Say K is fixed at Ko
Q = f ( L, Ko )
ALL factors are variable
Q = f ( L, K )
Q = f ( L, Ko )….. Only L is variable
The Short Run Production Function
Production Q
Labour L
10
5
3
1 2 3
a
b
c
4
d
0
9
As Labour input is raised while keeping
capital constant output rises. But
beyond a point (point c) output starts to fall as capital becomes
over-utilized.
Production Q
Labour L
15
10
5
1 2 3
a
b
c
4
d
0
Constant Returns to Factor
20 CRF:
If Labour input is raised x times output is exactly raised x times at all levels of L.
Example: photocopying, writing software codes etc.
Production Q
Labour L
2
10
5
1 2 3
a
b
c
4
d
0
Increasing Returns to Factor
20
IRF:
If Labour input is raised output is raised at an increasing rate.
Example: Heavy industrial production (metals etc) etc.
Production Q
Labour L
21
17
10
1 2 3
a
b
c
4
d
0
Decreasing Returns to Factor
23
DRF:
If Labour input is raised output is raised at a decreasing rate.
Example: subsistence agricultural production etc.
Production Q
Labour L
a
0
A typical manufacturing industry production function
b
La LbSTAGE I STAGE II STAGE III
Most manufacturing production functions exhibit both IRF and DRF.
Stage I : IRFStage II : DRFStage III : diminishing production
APL = Q / L
Average Product of Labour
MPL = ∆Q / ∆L
Marginal Product of Labour
Find the Marginal Products for production functions with
a) Constant Returns to Factor
b) Increasing Returns to Factor
c) Decreasing Returns to Factor
Exercise 1
Q
L
15
105
1 2 3
ab
c
4
d
0
Constant Returns to Factor
20
For Production functions with CRF
MP is constant.MPL
L
5
1 2 3
a’ b’
c’
4
d’
0
Q
L
10
2
5
1 2 3
a
b
c
4
d
0
Increasing Returns to Factor20
For Production functions with IRF
MP is rising.MPL
L 2
1 2 3
a’b’
c’
4
d’
0
35
10
Q
L
17
10
23
1 2 3
a bc
4
d
0
Decreasing Returns to Factor
21
For Production functions with DRF MP is diminishing.
MPL
L
10
1 2 3
a’
b’
c’
4
d’
0
7
42
a
21
Q, MPL
Labour L
a
0
MPL for a typical manufacturing industry production function
MPL is rising in stage
I, falling in stage II and negative in
Stage III
b
La Lb
STAGE I STAGE II STAGE III
MPL
Q
Find the Average Products for the manufacturing production functions
Exercise 2
Q, MPL
Labour L
a
0
APL for a typical manufacturing industry production function
APL is rising upto point c.
At point c MPL = APL
Note that the blue line showing the APis also tangent to the production curve.
b
La Lb
STAGE I STAGE II STAGE III
Qc
Q, MPL
Labour L
a
0
APL for a typical manufacturing industry production function
b
La Lb
STAGE I STAGE II STAGE III
Qc
APL is falling beyond point c.
But APL is never negative
Q, MPL
Labour L
a
0
MPL for a typical manufacturing industry production function
b
La Lb
STAGE I STAGE II STAGE III
Qc
APL
Q, MPL
Labour L
a
0
MPL and APL for a typical manufacturing industry production function
b
La Lb
STAGE I STAGE II STAGE III
MPL
Qc
APL
Q, MPL
Labour L
a
0
APL & MPL for a typical manufacturing industry production function
MPL is rising in stage
I, falling in stage II and negative in
Stage III
b
La Lb
STAGE I STAGE II STAGE III
MPL
c
APL
Exercise 3Consider an improvement in production technology. How will this affect total, average and marginal products?
Q, MPL
Labour L
A
0
MPL and APL for a typical manufacturing industry production function
B
La Lb
Q1
A’
B’
Q2
Q, MPL
Labour L 0
APL & MPL for a typical manufacturing industry production function
MPL is rising in stage
I, falling in stage II and negative in
Stage III
MPL1
APL1 MPL2
APL2
Cost
• Total cost = C = Cost of labour + Cost of Capital= [wage rate] . [ labour input]
+ [rental rate] . [Capital input]
= [w.L] + [r. K]
• In Short Run whe labour is the only variable input, capital is constant at Ko
C = w.L + r.Ko Cost depends only on labour input.
Exercise 4Mrs. Smith, the owner of a photocopying service is contemplating to open her shop after 4 PM until midnight. In order to do so she will have to hire additional workers. The additional workers will generate the following output. (Each unit of output = 100 pages). If the price of each unit of output is Rs.10 and each worker is paid Rs.40 per day, how many workers would Mrs. Smith hire?
Worker hired
0 1 2 3 4 5 6
Total Produ
ct
0 12 22 30 36 40 42
Worker hired
0 1 2 3 4 5 6
Cost 0 40 80 120 160 200 240
Total Produ
ct
0 12 22 30 36 40 42
Revenue
0 120 220 300 360 400 420
Profit 0 80 140 180 200 200 180
Average and Marginal Costs
Short Run Costs• In the short run some inputs (K) are fixed and some inputs (L)
are variable. So, Cost includes a fixed part and a variable part.
Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC)TC = [ r. Ko ] + [ w. L ]
• In the Short Run a Q ↑ must be due to a ↑ in L.
• So as Q ↑ → L↑ → (w. L) ↑ → (TVC) ↑
• TVC = V(Q)
• In the Short Run, K is fixed at Ko and r is also constant.
• So as a Q ↑, fixed cost [r.Ko] is unchanged.
Explaining the shape of the TVC and TC:
• The TC and TVC in this diagram relate to the manufacturing industry production.
• TVC are rising with Q. Since TC = TVC + a constant, TC also takes the same shape. Up to point a TVC rises at a falling rate owing to Increasing Returns to Factors.
• Between a and b, TVC rises at a rising rate owing to Decreasing Returns to Factors.
• Beyond point b, TVC rises at a even faster rate owing to diminishing production. (the irrelevant part of the SR production function and hence of costs)
TC, TVC, TFC
TC
TVC
TFC
Qba
TFC and AFC
TFC is fixed at [r.Ko] for the entire range of Q.
AFC = TFC / Q
• As Q ↑, the fixed cost gets distributed over a larger volume of production.
Hence, AFC↓ as Q↑
TC, TVC, TFC
TFC
Qba c
AFC
AFC
TVC and TC and MC
Marginal Cost = MC = ∆TC/∆Q= ∆TFC/∆Q + ∆TVC/∆Q = 0 + ∆[w. L] / ∆Q= ∆[w. L] / ∆Q = w. ∆L / ∆Q = w. [1/MPL]Or, MC = w/ MPL• That is MPL and MC are inversely
related. A higher MPL implies a lower MC.
• The range of Q for which MPL↑, MC would fall. (up to point a)
• The range of Q for which MPL↓, MC would rise. (beyond point b)
• The range of Q for which MPL is constant, MC would also be constant. (a very short span around point a)
• The value of Q for which MPL is maximum, (Point a) MC would be minimum.
TC, TVC, TFC
TC
TVC
Qba c
MCMC,AVC, ATC
TVC and AVC
Average Variable Cost = TVC/Q
Or AVC = [w.L] / Q = w [L/Q]= w . [1/ APL]Thus AVC and APL are
inversely related. Hence, AVC ↓ up to
point c, reaching a minimum there and rising there after.
At c , MPL = APLHence AVC = MC
TC, TVC, TFC
TC
TVC
Qba c
MCMC,AVC, ATC
AVC
ATC
Average Total Cost = TC/Q
The minimum of ATC corresponds to a point like point d.
Note that at d, ATC = MC
TC, TVC, TFC
TC
TVC
Qba c
MCMC,AVC, ATC
d
ATC
ATC = AVC + AFCThe vertical distance
between ATC and AVC is AFC. That’s it.
Qba c
MC,AVC, ATC
AVC
AFC
ATC
d
The Cost Condition
This diagram shows the AVC, ATC and the MC curves.
Note that - • MC = AVC where
AVC is minimum. • MC = ATC where
ATC is minimum.
Qba c
MC,AVC, ATC
AVC
ATC
MC
d