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

Q = f ( L, K, R, T ) Simplifying, Q = f (L, K)

The Short Run

One of the factors is fixed Say K is fixed at Ko Q = f ( L, Ko )

The Long Run

ALL factors are variable Q = f ( L, K )

The Short Run Production Function

Production Q 10 9 c d b 5 a 3 0 1 2 3 4 Labour L Q = f ( L, Ko )….. Only L is variable 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

Constant Returns to Factor

d 20 15 10 5 0 1 a b 2 c 3 4 Labour L 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 20 10 5 2 0

Increasing Returns to Factor

1 a b 2 c d 3 4 Labour L IRF: If Labour input is raised output is raised at an increasing rate.

Example: Heavy industrial production (metals etc) etc.

Production Q 23 21 17 10

Decreasing Returns to Factor

a b c d DRF: If Labour input is raised output is raised at a decreasing rate.

Example: subsistence agricultural production etc. 0 1 2 3 4 Labour L

A typical manufacturing industry production function Production Q a b Most manufacturing production functions exhibit both IRF and DRF. Stage I IRF Stage II : : DRF Stage III : diminishing production 0 STAGE I La STAGE II Lb Labour L STAGE III

Average Product of Labour APL = Q / L Marginal Product of Labour MPL = ∆Q / ∆L

Exercise 1

Find the Marginal Products for production functions with a) Constant Returns to Factor b) Increasing Returns to Factor c) Decreasing Returns to Factor

Q 20 15 10 5 0 MPL a b c d 1 2 3 4 L a’ b’ c’ d’ 5 0 1 2 3 4 L Constant Returns to Factor For Production functions with CRF MP is constant.

Q 20 10 5 2 0 MPL 10 5 3 2 0 d c b a 1 2 3 4 d’ L a’ b’ c’ L 1 2 3 4 Increasing Returns to Factor For Production functions with IRF MP is rising.

Q 23 21 17 10 b c d 0 MPL 10 7 4 2 0 L 1 a’ 2 3 4 b’ c’ 1 2 3 4 d’ L Decreasing Returns to Factor For Production functions with DRF MP is diminishing.

MPL for a typical manufacturing industry production function Q, MPL STAGE I a STAGE II b Q STAGE III MPL is rising in stage I, falling in stage II and negative in Stage III 0 La Lb Labour L MPL

Exercise 2

Find the Average Products for the manufacturing production functions

APL for a typical manufacturing industry production function Q, MPL STAGE I c a STAGE II b APL is rising upto point c.

Q STAGE III At point c MPL = APL Note that the blue line showing the APis also tangent to the production curve.

0 La Lb Labour L

APL for a typical manufacturing industry production function Q, MPL STAGE I c a STAGE II b APL is falling beyond point c.

Q STAGE III But APL is never negative 0 La Lb Labour L

MPL for a typical manufacturing industry production function Q, MPL STAGE I c a STAGE II b Q STAGE III 0 La Lb APL Labour L

MPL and APL for a typical manufacturing industry production function Q, MPL c STAGE I a STAGE II b Q STAGE III 0 La Lb APL Labour L MPL

APL & MPL for a typical manufacturing industry production function Q, MPL STAGE I a c STAGE II b STAGE III MPL is rising in stage I, falling in stage II and negative in Stage III 0 La Lb APL Labour L MPL

Exercise 3

Consider an improvement in production technology. How will this affect total, average and marginal products?

MPL and APL for a typical manufacturing industry production function B’ Q, MPL A’ B Q2 Q1 A 0 La Lb Labour L

APL & MPL for a typical manufacturing industry production function Q, MPL 0 APL2 MPL is rising in stage I, falling in stage II and negative in Stage III MPL2 APL1 Labour L MPL1

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 4

Mrs. 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 Total Product 0 0 1 12 2 22 3 30 4 36 5 40 6 42

Worker hired Cost Total Product Revenue Profit 0 0 0 0 0 1 40 12 120 80 2 80 22 220 140 3 120 30 300 180 4 160 36 360 200 5 200 40 400 200 6 240 42 420 180

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) TC = [ r. Ko ] + Total Variable Cost (TVC) + [ w. L ]

• In the Short Run,

K is fixed at Ko and r is also constant.

• So as a Q

↑ , fixed cost [r.Ko] is unchanged.

• In the Short Run a

Q ↑ must be due to a ↑ in L.

• So as Q

↑ → (w. L) ↑ → L ↑ → (TVC) ↑

• TVC = V(Q)

TC, TVC, TFC a TC TVC TFC 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) b Q

TC, TVC, TFC AFC a c TFC 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 ↑ AFC b Q

TC, TVC, TFC MC, AVC, ATC a c MC TVC b TC Q 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 MC, AVC, ATC a c MC TC TVC AVC b Q 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 after.

↓ up to point c, reaching a minimum there and rising there At c , MPL = APL Hence AVC = MC

TC, TVC, TFC MC, AVC, ATC a c TC MC TVC ATC Average Total Cost = TC/Q ATC The minimum of ATC corresponds to a point like point d.

Note that at d, ATC = MC d b Q

MC, AVC, ATC a c ATC AVC AFC d b Q ATC = AVC + AFC The vertical distance between ATC and AVC is AFC. That’s it.

MC, AVC, ATC MC ATC AVC 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.

a c d b Q