Meade's neo-classical model of growth

Prof J.E.Meade has constructed a neo-classical model of economic growth which is designed to show the way in which the simplest form of economic system would behave during the process of economic growth.

ASSUMPTIONS

The basic assumptions for J.E.Meade’s model are as follows:-

 (1) The economy is question in a closed economy with no relationship with the outside world.

 (2) There is no government activity involving taxation and expenditure (laissez-faire in nature).

 (3) Perfect competition exists in the market.

 (4) Constant returns to scale prevail in the economy.

 (5) There are only two commodities- consumption good and a capital good.

 (6) There is full employment of land, labour and machinery.

 (7) All machinery is alike

 (8) The ratio of labour to machinery can be easily varied, hence there is perfect      malleability of machinery.

 (9) There is perfect substitutability between capital goods and consumption goods

 (10) Any given stock of machines, no matter how old or new they are, a certain percentage gets replaced every year. Meade calls this phenomenon the assumption of depreciation by evaporation.

THE MODEL

In the economy visualized above, the net output produced depends upon four factors:-

1)      The net stock of capital available in the form of machines

2)      The amount of available labour force

3)      The availability of land and natural resources

4)      The state of technical knowledge which continues to improve through the time.

This relationship is expressed in the form of the production function

                       

                        Y=F (K, L, N, t)

Here,   Y-Net output or net national income

K-existing stock of capital or machinery

L-labour force

N-land and natural resources

t- Technical progress

Hence, to increase National income, three factors of production can be changed

ΔY=MPP_K ΔK + MPP_L ΔL +ΔY’   ……………………………………….. (1)

Here, Δ shows an every time increase

MPP_k- Marginal output of Capital

MPP_l –Marginal product of labour

     ΔK- increase n machines

    ΔL- increase in labour stock

 ΔY’-technological progress

ΔY  = MPP_K (ΔK)K+  MPP_L (ΔL)L + ΔY’ …………………………........ (2)

Y           Y        K             Y       L         Y         

Here,

ΔY shows ratio of growth rate of population

  Y

ΔK shows capital stock growth rate

 K

ΔL shows ratio of labour growth rate 

 L

ΔY =y, MPP_k  = U, MPP_L =Q, Δy’ = r,  ΔK =k, ΔL =l

 Y              K                L             y           K          L

y = Uk + Ql + r………………………………………………………………. (3)

Equation (3) shows that growth rate of income Y depends on marginal productivity of capital ‘U’,  + stock of capital ‘K’ + marginal product of labour Q + growth rate of population ‘l’ +technological change ‘r’.

U, Q, r are independent variables and Y depends on it. T is proportionate to U and Q.

Meade says that in an economic system, the indicator of real growth rate is real per capita income and not the national income. Population growth rate has dominance in NY which needs to be subtracted to know the real NY.

Y-l= Uk + Ql - l+ r

So, Y-l = Uk – (1-Q) l + r …………………………………………….......... (4)

Here, -(1-Q) shows that two factors U, r help in economic growth rate but labour factor leads to decrease in NY. The more the proportion of labour, the lesser the income.

U_k =MPP_K (ΔK) . K

          Y           K

One of the important factors contributing to the growth rate of output is the annual rate of capital accumulation in the economy.

Uk. U +Vk /Y

Uk = MPP_K  (sY) K                                             (because Δk=sY)

            Y          K

  

   =MPP_K. S

Here, Uk = vs (where MPP_K = V)

By putting its value in equation (4), we get:-

y-l= vs -(1-Q)l+ r…………………………………………………………... (5)

TECHNICAL PROGRESS

Having examined the main factors, Prof. Meade discusses the conditions which may lead to changes in the rate of economic growth over time. Assuming l and r to be given and constant, changes in growth rate would be determined by the behaviour of V,S, and Q over time. If there is no change in population, and technical progress®, an increase in the rate of savings(s) would raise per head capital and bring a decline in marginal product of capital (v). This decline in V will be less if it is possible to substitute capital for land and labour.

If the rate of technical progress along with population growth is assumed to be constant, the growth rate in income per head will vary directly with  VS.

Y-l = vs - (1-Q)l  + r ………………………………………………………. (6)

So, y = vs + r                                                                                 (because l=0)

So, y= vs                                                                                        (because r= 0)

The effect of technical progress on total NY is shown above. The total stock of machinery (capital) is represented on x-axis and total amount of output is on y-axis. OF₁ is the production function which shows the quantity of output produced in a year with the given quantity of machinery when the technical knowledge is given. If in a year, the quantity of machinery is OK, the production in that year will be KA. The slope of the curve at point A shows the marginal productivity of machinery which declines as we move towards the right along the curve.

The state of steady economic growth requires

1)      All elasticities of substitution between various factors are equal to unity.

2)      Technical progress is neutral towards all factors.

3)      The proportion of profits saved, of wages saved, and of rent saved is all constant.

y = Uk + Ql + r

According to Meade, there is a critical growth rate of capital growth rate of income equal to growth rate of capital stock.

I  = s Y  = s                                                                               (because Δk= I =sY= S)

k    k        k

CRITICAL GROWTH RATE

The equilibrium position ultimately depends upon the rate of accumulation of the capital stock. According to Meade, there is critical growth rate of the capital stock which makes the growth rate of income equal to the growth rate of capital stock.

A more or less growth rate in capital stock than “the critical growth rate” will not bring equality of y on k. If we put ‘a’ for the critical growth rate, basic relationship will be

a = Ua + Ql + r

a =Q +r *

       1 - U

CONDITIONS OF INSTABILITY

(1) s Y  >  Ql + r

       K          1 - u

If at any time there is any deviation from the level of steady growth, forces will set in to bring the growth rate of capital stock at an equilibrium level of  Ql + r ;

                                                                                                        1 - u

Suppose k or  s Y  >  Ql + r

                          K          1 - u

In such a situation, income will be growing at lower rate than the capital stock as a result, savings will decline so will the capital growth rate thereby bringing sY/k towards the critical level.

(2) s Y  <  Ql + r

       K          1 - u

Conversely, if  ) s Y  <  Ql + r  then income would increase more rapidly that the capital

                            K          1 - u

stock, savings would increase and so will the capital stock. As a result sY/k would rise towards the critical level     Ql + r

                                             1 - u

Thus under the 2 assumptions and 3 conditions noted above, the growth rate of NY and capital stock would both lead towards constant Ql + r. 

                                                                              1 - u

A CRITICAL APPRAISAL

Professor Meade’s model has been severely criticized due to its unrealistic assumptions

-This model is steeped in the classical tradition of a perfectly competitive economy where all production units are assumed independent of each other. But these are unrealistic assumptions as they do not match the reality.

-The assumption of constant returns to scale is also defective as it is observed that increasing returns to scale prevail in real scenario.

-Mrs. Robinson calls Meade’s model pseudo-causal because it merely states that monetary policy keeps the prices of consumption goods constant while money wage rate ensures full employment.

-Another serious defect of the neo-classical model is stems from the assumptions that all the machines are alike and there is perfect malleability of machines. The latter implies that the ratio of labour to machinery can be changed both in the short and the long run. But this is unrealistic because the ratio of labour to machinery cannot be changed in the short run. This Meade sidetracks the problem of foresight by assuming perfect malleability of machines and depreciation by evaporation. This makes his model impracticable.

-According to Professor Butterick, there is no place for uncertainty in Meade’s model. The interrelationship between all the variables is considered very certain. This detracts from the practicability point of view and remains just a theory.

-Like most of the growth models, this model is also of laissez-faire economy. But this is an unrealistic assumption which neglects the importance of foreign trade in economic development.

-Another serious defect of this model is that it completely neglects the role of institutional factors in the development process. Meade forgets that social, cultural, political, and institutional factors play an important part in economic growth. In the absence of these factors –the model becomes one of the fictional or hypothetical model.

Despite these defects, the Meade’s model had a chief merit of demonstrating the influence of population growth, capital accumulation, and technical progress on the growth rate of national income and per capita income over time. Further, the state of steady growth is indeed Mrs. Robinson’s Golden Age explained in a more realistic manner by studying the behaviour of those variables which she assumes to be constant.

REFERENCES

  The Economics of Development and Planning by M.L.Jhingan

  www.jstor.org/stable/2601522

en.wikipedia.org/wiki/James_Meade

The Economics Of Common Man

The Economics of Common Man

The Manmohan Singh Government has announced the diesel price hike, his words seems appealing to many of us. As a student of Economics, I do, in more than one way understand the PM's call for price hike. With the increase in Govt. expenditure, and with more projects to come, no Govt would consider cutting on its revenue side. Had it been BJP in Power, they would have done the same thing. All the points he has mentioned, from the economic pint of view, seems to be viable.

To stand tall, as a country, if FDI- in retail is what it takes for the boom in economy, then that's the way. With more competition, the consumers surely will be benefited, and in the long run, the small traders will have their share of gain. India has been very unique in terms of the economy, it is unpredictable and the global companies have also found it difficult to understand the market structure, and consumer pattern of India. In Ahmedabad itself, the ratanpol market, the CEPT and Nehrunagar footpath market, and global brands like Levis, etc. are doing equally well. The funniest part is- the same consumer who wears a Levi’s jeans also goes to the ratanpol market.

When it comes to Diesel Price Hike, Most of us will say that govt. can simply increase the prices by keeping the taxes constant, that way, the burden will not totally fall on the consumers. But as the say "Death and Taxes are Inevitable!" Just like any profit making organization, the Govt knows that the people will complain but finally accept the price hike. And surely, the govt. doesn’t want to give away its revenue.

But there is one thing that we all have overlooked in this matter-

The Govt's loss in figures, as stated by the PM- Rs 2,00,000 crores

The Govt Losses in the various major scams (considering year 2012)

Coal gate Scam-185,591.34 crores

UP NRHM SCam-10000 crores

Karnataka Board Land Scam- 200000crores

The total is 395591.34 crores

The figures say it all- Regardless the Scam under state or Central Govt, IF they hadn’t taken place, the economy would be running efficiently. I am not against FDI-retail, or Price hike-but I believe we can recover from further losses just by preventing Corruption. That way, the common man wouldn't need to taste the bitter medicine.

-Maitreyee Purohit

The dummy variable regression model

THE NATURE OF DUMMY VARIABLES:

In regression analysis, the dependent variable or regressand is frequently influenced not only by ratio scale variables but also by variables that are essentially qualitative in scale; like nature, sex, colour, qualifications, religions, etc. For example, it is observed in many countries that female workers are paid less for the same job as male workers. If such details are not considered in regression analysis, the results can vary and misguide us.

One way we can quantify the qualitative attributes is by constructing artificial variables that take on values of 1 or 0, 1 indicating the presence of that attribute and 0-indicating its absence. Such variables are thus essentially a device to classify data into mutually exclusive categories such as male and female.

ANOVA MODEL

ANOVA models are used to assess the statistical significance of the relationship between a quantitative regressand and qualitative or dummy regressors. They are often used to compute and compare the differences in the mean values of two or more groups or categories, and are therefore more general than the t-test which can be used to compare means of two groups or categories only.

The ANOVA model equation would look like this-

Y_i=β₁+β₂D_2i+u_i

Where, Y_i=annual starting salary

D=1-if college graduate

D=0- if otherwise

Mean starting salary of non college graduate=

E(Yi/D=0)=β₁+β₂(0)

                 =β₁

Mean Starting Salary of college Graduate=

E(Yi/D=1)= β₁+β₂(1)

                 = β₁+β₂

                 

ANCOVA MODEL

ANOVA model of the type discussed before is common in fields such as sociology, psychology, education, and market research. However, it is not that common in Economics. Typically in most economic research, a regression model contains some explanatory variables that are quantitative and some that are qualitative. Regression models containing a mix of quantitative and qualitative variables are ANCOVA models-Analysis of Co-Variance Models. ANCOVA models are an extension of the ANOVA models in that they provide a method of statistically controlling the effects of Quantitative regressors, called co-variates or control variables in a model that includes both quantitative and qualitative or dummy regressors.

Consider an example very quantitative and qualitative variables are used

Y_i=β₁+β₂D_2i+β₃X_i+u_i

Y_i=annual salary of college teachers

X_i=years of teaching experience

D_i=1-if male

   =0-if female

Assuming E(ui)=0;

Mean salary of a female college teacher=β₁+β₃X_i

Mean salary of a male college teacher  =β₁+β₂+β₃X_i

FEATURES:

1)      We’ve used only one dummy variable to distinguish two categories-Male and Female. If the no of qualitative variables are ‘m’, dummy variables will be (m-1)

2)      Assigning of 1 or 0 values to two categories is arbitrary

3)      The category which is assigned value 0 often referred to as bench mark category- In the above example, female salary is the base salary-which is the main intercept term.

4)      The coefficient β2 attached to Dummy variables D is called ‘Differential Intercept Co-efficient’.

COMPARING TWO REGRESSION MODELS:

Qualitative or quantitative analysis is majorly done to see the change in given time series, or before and after certain policy implication. In such cases, two regression functions need to be compared.

In case of India, there has been a great hype about change in consumption and saving pattern after the Economic Policy Implication of 1990s. To compare the change, Data pre and post reform need to be analyzed separately.

1950-1991-Pre Reform Period

1991-2008-Post Reform Period

Pre-Reform Period: 1950-1991

Y_t^*=A₁+A₂X_t+U_{1t    (}eq-1)                                                                

Y_t=B₁+B₂X_t+U_2t    (eq-2)

Here, Y= savings

           X= income

          U=error term

A1-pre reform consumption intercepts

B1-post reform consumption intercept

A2-pre reform MPC

B2-post reform MPC

Equation (1) and (2) have four possibilities:

fig 1

            (1)A1=B1 and A2=B2 i.e. two regressions (1) and (2) are identical. This is the case of “coincidental regression"

 (2) A1#b1 and a2=B2 i.e. two regressions differ only in location, their intercept. This is the case of “Parallel Regression”.

fig 2

 fig 3

                               fig 4

                                                                                                                     

(3)-A1=B1, A2#B2- two regressions have same intercepts and different slopes. It is the case of  “Concurrent Regression”.

(4) A1#B1, A2#B2- two regressions are totally different. This is the case of dissimilar regression.

REGRESSION MODEL FOR THE TWO COMPARED REGRESSIONS:

Y_t=C₁+C₂+C₃X_t+C₄D_tX_t+U_t

Here, Y=savings, x=income, D_t=1 for observations from 1992-2008

                                                D_t=0 for observations before 1992

Thus E (Y_t/D_t=0, X_t) =C₁+C₃X_t      (eq-3)

        E (Y_t/D_t=1, X_t) =(C₁+C₂)+(C₃+C₄)X_t        (eq-4)

Here, Eq(1)=Eq(3) and Eq(2)=Eq(4);

 As A₁ =C₁ and A₂ =C₂;

B₁=(c₁+C₂), and B2(C₃+C₄)

U_t is ignored as per the assumption,

So, C₂= Differential intercept

And C₄=Slope Coefficient

SUMMARY AND CONCLUSIONS

1)      Dummy Variables taking values 1 and 0 are a means of introducing qualitative regressors in a regression model

2)      Dummy Variables are a data classifying device in that the divide samples into various sub groups based on their qualities. If there are differences in them, they will be reflected in differences by running sub group regressions

3)      Although a versatile tool, it needs to be handles carefully- (i) if regression contains a constant term, no. of dummy variables must be 1 less than the no. of classifications. (ii) the coefficient  attached to the dummy variable must always be interpreted in relation to the base or reference group-i.e. the group that receives the value of 0. (iii) if a model has several qualitative variables with several classes, introducing dummy variables can consume large no. of degrees of freedom. Therefore, they need to be carefully chosen.