production and cost: a short run analysis
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Production and Cost: A Short Run Analysis. Production. The Organization of Production. Production: transformation of resources into output of goods and services. Inputs: Labour Machinery Land Raw Materials. Output: goods and services. The Production Function. - PowerPoint PPT PresentationTRANSCRIPT
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
10
5
1 2 3
a
b
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
3
5
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 3
Consider 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
Q
ba
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 + AFC
The vertical distance between ATC and AVC is AFC. That’s it.
Q
ba 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.
Q
ba c
MC,AVC, ATC
AVC
ATC
MC
d