Technology Change

and Related Technology

Issues

Technology is a production concept, it means the representation of the technical knowhow useful in producing goods. It is embodied in the production function.

The following few slides review technology concepts used in output selection.

Iso q ua nt

Va rio us ra ys fro m the o rig in

R1

R 2

R 3

R 4

K

L

No tic e the se fea ture s: 1. The iso q ua nt rep re sents c o m b ina tio ns o f K a nd L yie ld ing a c o nsta nt Q ; 2. The slop e o f a ra y re p resents a sp e c ific c a p ita l to la b o r ra tio , this is so m etim es c a lled a tec hniq ue ; 3. M ore la b o r inte nsive te c hniq ues c o rresp ond to ra ys with highe r sub sc rip ts; a nd 4. The slop e o f the iso q ua nt is the “m a rg ina l ra te of te c hnic a l substitution.

The case of variable techniques.

E

Q 2

Q 3

Q 1

L

K

Notic e severa l fea ture s: 1. The op tim a l input c om b ina tion is a t E; 2. Along isoq ua nt Q 1 weuse fewer re so urc e b ut outp ut is sub op tim a l; 3. Isoq ua nt Q 3 is una tta ina b le with out b ud ge t line . AB.

B

A

Output selection

E

Q 2

L

K

A

B

C

D

No tic e se ve ra l fe a ture s: 1 . The se ve ra l b ud g e tlines re p re se nt d iffe rent hyp o thetic b ud g e ts; 2 . Bud g e t line s C a nd D sa ve m o ne y, b ut the y d on’t m e et the req ure m e nt to p ro d uc eQ 2 outp ut; 3 . Yo u c a n think o f the p ro b le m a site ra tive ly trying lo wer a nd lo wer b ud g et lines.

One look at duality.

Now consider technology change.

In the two input case it entails

a shift in the position of the

isoquants.

C a p ita lInp ut

La b o rInp ut

A

B

C

Change over a period of time in the position of an isoquant.

Technical change might replace a cheaper product with a higher quality new product that is more costly.

Heart surgery then and now as an example:

1. Since 1960 the cost of heart surgery has risen dramatically.

2. But the survival probabilities (technical change) have also improved dramatically.

Consumer products: e.g. cars, refrigerators, cameras, food, apartments etc.

Generally these products decline in cost to consumers once quality is adjusted for.

Many decline in cost to the consumer even when no technical change in quality is evident. e.g. drinking water, eggs, gas.

Environment quality has it gotten better orworse in the United States?

I'

C 2

C 1

L2 L1La b orInp ut

C a p ita lInp ut

A

B

C

A '

B '

C '

..

Productivity increase without technical change.

Total factor productivity:

Definition: A measure of productivity that relates the change in output to the change in both capital and labor.

Formula for total factor productivity:

Begin with a linear production process,

Q = (bL + cK) and rewrite,

= Q/(bL + cK)

Here, is the total factor productivity.

Advantages over labor productivity …

Total productivity tracked over time in an actual manufacturing plant.

Learning curves

of two companies

tracked over

the cumulative volume of product.

Perc enta g e o f firm s using the innova tion

Tim e

L

M

Rate of adoption depends on profitability, the size of the investment. The shape of the curve is called the "logistic function."

Diffusion Process.

A side excursion to discuss efficiency

versus inefficiency. Like the questions of technical change and adoption

of innovations, this is also closely

related to technology.

E

Q 2

Q 3

Q 1

L

K

Notic e severa l fea ture s: 1. The op tim a l input c om b ina tion is a t E; 2. Along isoq ua nt Q 1 weuse fewer re so urc e b ut outp ut is sub op tim a l; 3. Isoq ua nt Q 3 is una tta ina b le with out b ud ge t line . AB.

B

A

Recall that equilibrium occurs at a point of tangency.

The "Optimal Input Selection Rule"

MPL / w = MPK/r

for the example of choices between capital and labor.

This is therefore the standard for allocative efficiency in production.

Efficiency and inefficiency theory in history.

Harvey Leibenstein Contending with the “economic model” Developments making the models consistent with inefficiency a. monitoring, monitoring costs b. efficiency wage theory c. satisficing theory

Technical inefficiency (the same as Leibenstein’s “X-inefficiency”

Definition: a. as a shortfall in output, given a set of inputs, compared to best possible practice; b. as an excess of inputs for a given output, this is the excess over what is possible in best possible practice.

o

o

o

o A

B

C DoE

O utp ut

Inp ut

Prod . Func tion

Technical inefficiency is a shortfall of output from the potential (or excessive use of inputs for a given output). Single input case.

Two input case: Technical inefficiency.

A

B

0

C

D

R1

R2

K

L

Both firm s sho wn (Firm 1 a t C , a nd Firm 2 a t D)a re tec hnic a lly ineffic ient using m ore inputs tha nne ed to p rod uc e Q 1 a nd p roduc ing less tha n thep otentia l outp ut from the ir input use .

Q 1

F(K,L) = AKLev-u

in logarithms:

y = a + k + l + (v - u)

here v is N(0,) and u is truncated normal.

Production function with composed error:

Recall: Allocative efficiency requires this "optimal input purchase rule."

MPL / w = MPK/r

Allocative Inefficiency.

Q = 100

E

A B

K

L

Tec hnic a l a nd a lloc a tive ineffic ie nc y c o m p a red .

An example study applying technical and allocative efficiency and inefficiency concepts.

Table 1. Mean Inefficiency of United States Hospitals   Measure Pooled Sample Partitioned

Technical Inefficiency

8.41* (8.37) 5.29 (5.45)

Allocative Inefficiency

4.31* (5.11) 5.60 (6.56)

Total Inefficiency 12.72* (9.94) 10.88 (8.02)

n 1661 1661

(standard deviations in parentheses) Source: Folland and Hofler, Health Economics, December 2001.

Table 2. Breakdown of Inefficiency Estimates by Hospital CategoryHospital type Inefficiency

Main sample 12.9%*

NonprofitFor-Profit

12.6*16.2*

UrbanRural

12.6*13.4*

Chain MemberIndependent

13.912.5*

TeachingNon-teaching

13.413.0*

High MedicareLow Medicare

11.713.9*

We found little or no difference between nonprofit and for-profit forms of hospital, nor other in other pairs.