long run production

8/8/2019 Long Run Production

1/33

Long run Production

function


2/33

The long run . ., ,llo w th e firm to va ry a ll in p u ts e g p la n t size a m o u n t o f c


3/33

Production with Two VariableInputs

When a firm has more than onevariable input it can produce agiven amount of output with many

different combinations of inputs E.g., by substituting Kfor L

-7 3


4/33

Isoquants

An isoquantidentifies all inputcombinations (bundles) thatefficiently produce a given level of

output Note the close similarity to

indifference curves

Can think of isoquants as contour

lines for the hill created by theproduction function

-7 4


5/33

5

Family ofIsoquants

K

,Unitsofc

apitalperd

ay

e

b

a

d

fc

63210 L, Workers per day

6

3

2

1

q = 14

q = 24

q = 35

T h e p ro d u ctio n fu n ctio na b o ve yie ld s th e isoq u a n ts

.o n th e le ft


6/33

Figure 7.8: IsoquantExample

-7 6


7/33

Properties of Isoquants

Isoquants are thin

Do not slope upward

Two isoquants do not cross Higher-output isoquants lie farther

from the origin

-7 7


8/33

Copyright 2002, Pearson Education Canada 8

There are an infinite number of

combinations of labour and capital thatcan produce each level of output.

The slope of an isoquantis equal to:- MPlabour / MPcapital = - MPL / MPK

= K / L The slope of the isoquant is called the

marginal rate of technical substitutionwhich can be defined as the rate at whicha firm can substitute capital for labourand hold output constant.


9/33

Figure 7.10: Properties ofIsoquants

-7 9


10/33

Figure 7.10: Properties ofIsoquants

-7 1 0


11/33

Substitution Between Inputs

Rate that one input can be substituted foranother is an important factor formanagers in choosing best mix of inputs

Shape of isoquant captures informationabout input substitution

Points on an isoquant have sameoutput but different input mix

Rate of substitution for labor withcapital is equal to negative theslope

-7 1 1


12/33

Marginal Rate of TechnicalSubstitution

Marginal Rate of TechnicalSubstitution for labor with capital(MRTSLK): the amount of capital needed

to replace labor while keeping outputunchanged, per unit of replaced labor Let Kbe the amount of capital that can

replace L units of labor in a way suchthat total output Q = F(L,K) is

unchanged.Then, MRTSLK = - K/ L, and

- K/ L is the slope of the isoquant

Therefore, MRTSLK = - slope of the isoquant


13/33

Marginal Rate of TechnicalSubstitution

marginal rate of technicalsubstitution (MRTS) - the number ofextra units of one input needed toreplace one unit of another input that

enables a firm to keep the amount ofoutput it produces constant

L

KMRTS

==

laborinincrease

capitalindecrease

!lope of Isoquant


14/33

How the Marginal Rate of TechnicalSubstitution Varies Along an Isoquant

K,Unitsof

capitalpe

rd

ay

L, Workers per day

45

7

10

16a

b

c

d

eq = 10

K = 6

L = 1

0 1

1

1

1

2 3

3

2

1

4 5 6 7 8 9 10


15/33

Substitutability of Inputs and MarginalProducts.

(LxMPL) = ( - KxMPK).

Along an isoquant output doesntchange ( q = 0), or

xtranits of

laborecrease in

he unitsf capital

isoquantofslope

0

===

=+

K

L

KL

MP

MPMRTS

L

K

solvingMPKMPL

ncrease in qer extra unitf labor

ecrease in qer extra unitf capital

T t S


16/33

16

T ere ore t e S ope o anIsoquant Is Equal to the Ratio

of MPL to MPK


17/33


Isocosts

An isocost is a graph that shows allthe combinations of capital andlabour available for a given cost.


18/33

Isocost lines

In e q u a tio n fo rm th e to ta l co st is= + ,C w L rK=w h e re C To ta l co st o r b u d g e t

,le v e l= ,w th e w a g e ra te= ,L th e a m o u n t o f la b o r ta ke n= ,r th e re n ta l p rice o f ca p ita l

a n d=K th e a m o u n t o f ca p ita l.taken


19/33

-T h is eq u a tio n ca n b e re e x p re sse d a s

= ( / ) - ( / ) .K C r w r L W h e n w e w rite th e iso co st lin e in th e

fo rm

= ( / ) - ( / )K C r w r L

W e see

= , = / ,If L 0 th e n K C r= , = / ,If K 0 th e n L C w

, = / .A n d th e slo p e o f th e lin e w rLK

i Sh i h C bi i f


20/33


Isocost Lines Showing the Combinations ofCapital and Labour Available for $5, $6, and

$7(Figure 7A.3)


21/33

Producers Equilibrium

An isoquant shows all technicallyefficient combinations of twoinputs. But, when producers are

faced with several technicallyefficient combinations the decisionis taken on the basis of economic

efficiency, i.e ., use thatcombination which minimises thecost of production


22/33

Hence, to be technically efficient , aproducer must determine the

combination of inputs thatproduces the output at minimumcost. A profit maximising firm will

try to use a combination of inputsthat will minimise the cost ofproducing a given level of output.

The maximum output level for anyfirm is determined by isoquants,

but they would not give theminimum cost of production; for

this we would need the isocost.


23/33

Combining the isoquants and

isocosts will help us to understandthe producers equilibrium, or theoptimal combination of inputs inthe long run


24/33


The Cost MinimizingEquilibrium Condition

Slope of isoquant = - MPL / MPK

Slope of isocost = - w / r

For cost minimization we set theseequal and rearrange to obtain:

-MPL / MPK = -w/ r

Fi di th L t C t C bi ti f


25/33


Finding the Least-Cost Combination ofCapital and Labour to Produce 50 Units of

Output

Profit-maximizingfirms will minimizecosts by producing

their chosen levelof output with thetechnologyrepresented by thepoint at which the

isoquant istangent to anisocost line.

Point A on this

diagram

n m z ng os o ro uc on


26/33


n m z ng os o ro uc onfor qx = 50, qx = 100, and qx

= 150 (Figure 7A.6)

Plotting a seriesof cost-minimizingcombinationsof inputs -shown here asA, B and C -

enables us toderive a costcurve.


27/33

Returns to Scale

Just as the law of diminishing returnsto a factor in the short runphenomenon, return to scale is the

long run phenomenon, in which thescale of production is determinedon the basis of change in both the

inputs in the production process. The long run production process is

described by the concept of returns

to scale.


28/33

Law of Return to Scale

The word scale refers to the long-runsituation where all inputs arechanged in the same proportion.

What would be the level of outputwhen all inputs are increased byexactly the same proportion in the

long run ?


29/33

If all inputs into the production

process are doubled, three thingscan happen:

output can more than double

increasing returns to scale(IRTS)

output can exactly double

constant returns to scale(CRTS)

output can less than double

decreasing returns to scale


30/33

Constant Return to Scale

Refers to the situation where outputchanges by the same proportion asinputs

Eg if all inputs are increased by 10%,output also rises by 10%, Inputs aredoubled then output is also doubled


31/33

Increasing Return to Scale

Refers to the case where outputchanges by a larger proportion thaninputs

Eg if all inputs are increased by 10%,output rises by more than 10%,Inputs are doubled then output is

more than doubled Division of labour & Specialisation


32/33

Decreasing Returns to Scale

Refers to the case where outputchanges by a smaller proportionthan inputs

Eg if all inputs are increased by 10%,output rises by less than 10%,Inputs are doubled then output is

less than doubled Managerial Diseconomies


33/33

The Long-Run ProductionFunction

One way to measure returns to scaleis to use a coefficient of outputelasticity:

If EQ > 1 then IRTS

If EQ = 1 then CRTS

If EQ < 1 then DRTS

inputsallinchangePercentageQinchangePercentage=QE

long run production

Documents