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