nec production and distribution theory

NEC PRODUCTION AND DISTRIBUTION THEORY

Three main manners of interpretation of capital/profit and labor/wage in NCE

1. Psychological interpretationa) Capital as effect of „waiting”, of postponing (shifting

in time) instaneous consumption of goods/income. Profit as the reward for „waiting”

b) Profit as the reward resulting from the difference between the value (utility) of current (present) and future goods

c) Supply of labor (by households and individuals) and wages as categories related to the utility and disutility of labor

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Manners of interpretation of capital/profit and labor/wage in NEC

Capital and profit as categories occuring in the so called• economic dynamicsStatics Resources of capital and labor are given with regard to quantity and qualitative features, production technologies andproduction costs are fixed (do not change)1. Prices of final goods are fixed2. There occur no profits: zero profit hypothesisDynamics: all above mentioned conditions/constraints are subject to change. In particular, there appear new technologies

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Capital and profit as catergories occuring in the so called economic dynamics (cont.)

1. Profit (rate of interest) as the reward for economic risk

a) Risk as immanent feature of physical capital formation and modernization process

b) Profit as the function of time of (physical) investment duration

c) Diversification of rate of profit as resulting from risk diversification

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Capital and profit as categories occuring in the socalled economic dynamics – cont.2. Profit as the reward for innovations (J.A.Schumpeter)a) Equilibrium /statics: no profits, no entrepreneurs,

manufacturing based on routine methodsb) Evolution/development: there appear innovations and

enterpreneurs (enterpreneur=innovator)c) Origin of profit: difference between social marginal costs

(=market price) and individual (in a given enterprise) marginal costs (of production, distribution)

d) Imitation (diffusion) of innovation, gradual disappearence of profits and the return to statics

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NEC production and distrtibution theory1. Theory of marginal productivity of production factors

(MPT) and marginal distribution theory (MDT) as the main foundation of neoclassical microeconomics

2. Law of diminishing marginal productivity (LDMP) (law of diminishing returns on production factors)

a) Universal nature of MPT/MDPb) Productive and value-generating character of all production

factorsc) Marginal product of a given production factor (MP) as the

measure of (1) its share (contribution to) in the value of manujfactured (extracted) goods, (2) foundation of its reward and (3) base for its market price

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NEC production funkction - PF as basic model of neoclassical production and distribution theory1. Definition: general and neoclassicalGeneral: quantitative manner of defining the relation betweenthe product and inputs of production factors which are requiredfor its manufacturing (extracting)The very nature of that relation is determined by the technology,understood here as the so called abstractive technologyAbstractive technology: set of technical characteristics (features)of production function:1. Capital intensity of technology2. Scope of substitution between production factors (in particular:

labor for capital and vice versa)3. Technologically determined economies of scale

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NEC production function – PF as basic model of...Definition and features of NEC PF

P = F(x1,x2,…xn)x1,x2,…xn homogenous production factors

P = F(x1,x2,…xn) 0 product can not be negative

P = F(K,0) = F(0,L) = F(0,0) = 0 (complementarity of production factors; K – capital, L – labor)

MPK = f'K(P); MPL = f'

L(P)– marginal product of K and L

MPK 0; MPL 0 ; marginal products have to be positive (economic sense: rationality of economic behavior)

f’’K(P)<0, f’’L(P)<0 ; Law of DMP

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NEC production function – PF as basic model of...a) Substituability of L and K, notion of capital vintage and vintage

PF, and the interpretation of technical/technological progress (change) in the NEC production theory1. Full substituability (ex ante and ex post): labor can be fully substituted for capital and vice versa, the so called disembodied technological progress, residual and exogenous (with regard to economy) character of technological progress

2. Limited substituability (takes place only ex ante, labor is not substituted for capital, and vice versa, ex post); there occur capital vintages and, subsequently, the vintage production factor, technological progress can be both embodied (within a given capital vintage) and disembodied; there appears the problem of the so called life time of (physical) capital3. No substituability (K/L relation is fixed/rigid both ex post and ex ante)4. „Cambridge contra Cambridge” controverse (NEC versus PKE)

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Basic analytical forms of NCE PFs

Main criteria for distinguishing types of PFs

1. Technological economies of scale: interdependence between the quantitative increase of product and the increase of inputs of production factors

P = F(aK, aL); F= arF(K,L); r – level of scale economiesr= 1 costant; r>1 increasing; r<1 decreasing

Economies of scale = grade of homogenousness of PF

2. Elasticity of substitution (L for K or vice versa) : relation between marginal rate of substitution of L for K (or K for L) and capital intensity of technology (K/L)

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Basic analytical forms of NCE PFsMain criteria for distinguishing types of PFs

2. Elasticity of substitution of L for K

MRSK/L = ðK/ ðL , p>0, k = K/L

MRSK/L = p kδ δ>0 elasticity of substitution of L for K

Economic sense of elasticity of substitution:

Ratio of relative change in MRSK/L to relative

change in K/L

δ = d(MRSK/L)/ MRSK/L : dk/k

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General features of NEC distribution theory (MDT)

1. Strictly related to MPT2. Technical character: shares of production factors in

(manufactured/extracted) product are determined by; Changes in the quantity of production factors (and, implicitly,

their marginal productivity) Possibilities of technologically determined susbstitution

betweeb production factors3. Social and institutional condtions do not affect the shares of

production factors In the equlibrium, prices of goods are equal to their marginal

production (distribution etc.) costs > zero profit hypothesis

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Let’s assume, there is the macroeconomic NEC PF

P= f(K,L) If it is homogenous of grade 1 (constant economies to scale), it is equivalent to the function

y = f(k);Where: y=P/L (labor productivity

k=K/L (technical equipment of labor, capital intensity of technology)

negativekdk

dw

dk

dr

positivekkf

kkfkfkfdkdw

negativekfdkdr

kkfkfrkyw

wrky

kfrkfy

:

)(

)()()(/

)(/

)()(

);()(

''

''''

''

'

'

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Conclusions from the model1. Wage rate changes directly (proportionally) to changes in K/L ratio

which means that in the process of capital accumulation (economic growth) the reward of laboreres grow

2. Rate of interest (profit) changes inversely to changes in K/L ratio. In the process of capital accumulation, the unit reward of capital diminishes. It does not necessarily means that the share of capital in social product falls. The tendency of capital share to diminish may be effectively compensated by the substitution of labor for capital, as well as by technological progress (given specific features of that substitution and progress).

3. Fair distribution is when the production factors are rewarded accordingly to their marginal products

4. Fair distribution is taking place when the conditions of perfect competition are fulfilled.

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Analytical forms of PFCOBB-DOUGLASA PF

1. Constant economies to scale

2. Constant and equal to 1 elasticity of substitution

3. Constant elasticities of product with respect to K and L

P = F(aK, aL) F= aF(K,L)

r=1

MRSK/L = p kδ δ=1

r

EE

LAKP

KPKP

1)1(

1;//

1

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LP

LAKMP

KP

LAKMP

L

K

)1...(

...

1)1(

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1. Marginal product of capital is proportional to its average product

2. Marginal product of labor is proportional to its average product

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LQEPQE

PLLP

LMPQ

PKKP

KMPQ

LLPKKP

LL

KK

/1;/

)1()1(

//

1. QK and QL - respectively, product generated by capital and labor, whereas QK/P oraz QL/P stand for the shares of capital and labor in the social product

2. Conclusion: in the Cobb-Douglas PF the elasticities of product with respect to capital and labor are equal their shares in the social product and remain constant

3. Cobb-Douglas PF may take a generalized form in which it is subject to any positive economies of scale (EP/K + EP/L = r #1; r>0)

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Assumption which is underlying the Cobb –Douglas PF (elasticity of substitution constant abd equal to 1) may be generalizedIf we assume that the elasticity of substitution (δ) is constant but not necessarily equal to 1, we receive a more general class of production functions. These are the CES (Constant Elasticity of Substitution) PFsWhat is the conomic sense of δ : it is the ratio of relative change in MRSK/L

(marginal rate of substitution of L for K) to

relative change in K/L (capital intensity)

δ = d(MRSK/L)/ MRSK/L : dk/k

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Marginal rate of substitution of labor for capital (MRS) may be expressed as the relation of marginal labor product (MPL) to marginal capital product (MPK). For macroeconomic production function, it is the relation of unit wage (w) to unit reward of capital (r)

k

dk

p

dp

dL

dK

MRS

MRSd

r

w

MP

MPp

L

Kk

LK

lk

K

L

::)(

;

/

/

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Thus, in macroeconomic approoach, the elasticity of substitution measures how the relation of unit rewards or prices of production factors changes when the relative „saturation” of economy with capital (as described by the K/L ratio) increases or decreases.

1. δ = 1; shares of labor and capital in the social product remain constant (Cobb-Douglas PF)

2. δ>1; share of labor increases, share of capital decreases (CES PFs)

3. δ<1; share of labor decreases, share of capital increases (CES PFs);

4. Elasticities of product with respect to K and L are no more constant (fixed) in the CES PFsCobb-Douglas PF is a special case of CES PFsVariable Elasticity of Substitution (VES) PFs

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nec production and distribution theory

Documents

profit rate

innovatororigin of profit

profit hypothesisdynamics

inputs of production

given production factor

social marginal costs

categories occuring

distribution theorydefinition