Lecture No.11 Explain Solow Swan Model Of Economic Growth Also Give Golden Rules Of Economic Growth.

Lecture No.11

Explain Solow Swan Model Of Economic Growth Also Give Golden Rules Of Economic Growth.

What Are the Golden Rule Of Economic Growth.

Explain New Classical Theory Of Economic Growth.

Background:

Solow swan model was represented by two different economist. Robert M.Solow in February 1956. write an article (A contribution to the theory of economic growth) an other economist Trevor Swan to write an article economic growth and capital accumulation in November 1956. These two articles have provided a new theory which is an improvement on Harrod Domar model. This theory is called new classical theory of economic growth. The reason of this is that the assumption of the theory are related to the classical economics. For example in this theory they have assumed perfect competition, application of marginal productivity theory, distance of full employment. Solow Swan model explains that there is a possibility of factors substitutions. It mean that we can substitute one factor to another. In this way the production function of solow Swan model becomes a type of cobb Douglas production function which explain that productivity is subject to diminishing marginal productivity and there is a possibility of factors substitution for example this can be explain with the help of following diagram:

Production function in solo swan model.

Figure No 11.1:

In the above diagram, it is showing that have differenced IQ. We can substitute capital for labour or labour for capital this production function shows constant returns to scale this can be written in mathematical found as below:

Y  =  f(k, L)     OR      Q  =  f(k, N)     Y  =  AK^aL^b

In equation number (2) capital A is constant, K for capital, L for labour. a and b are parameters. The total of these 2 elasticity is equal to 1, as shown below:

a + b = I constantly return to scale.

If a+b > 1   it will show increasing return to scale.

If a+b < 1   it will show decreasing return to scale.

In new classical solow Swan model we have assumed that factor are paid according to their marginal productivity. In this way national income is weighted average, rate of capital and Labour which change can be written down as below:

a, 1- a,  They are weighted average of capital and labour. In solow swan model, saving is proportion to income and net investment is the change in capital stock. So in this way we can have feeling function.

S =sy

I = ΔK               dk/dt

S = I

sy = ΔK

we can develop solow system model with the help of above elementary equation as below.

    (1)    ΔY/Y = a  ΔK/K + 1 – a (ΔN/N)

for equilibrium position saving must be equal to investment, So we can have equation (2) as below.

(2)               SY = ΔK

Substituting ΔK in equation (1), we can have equation 3.

(3)          Δy/y          = a  sy/k + 1 – a (ΔN/N)

S= factor of proportionality:

Δy/y =a  sy/k + 1 – a (ΔN/N)

Equation (3) explains that rate of growth of output is directly proportion to output and capital ratio. From equation (2) rate of growth of capital stock is as below:

(4)    Δy/y =  sy/k        OR  Δk/k =  S y/k                       

Equation (4) for explained that for a given marginal propensity to save rate of growth of capital stock is proportional to output capital ratio. We can considered to Extreme causes 1 hi capital labour ratio all low capital labour ratio.

In solow swan model, in the equilibrium position rate of income must be equal to the growth rate of capital stock.

So, In equilibrium position we will have equation (5)

(5)         Δy/y  =  sy/k               =   equilibrium condition

We can write down equation (5) in form of as (6).

          Δk/k  = a s y/k + 1-a ΔN/N

Because Δk/k =  Δy/y : aslo putting the value of equation (3) in Δk/k.

By substituting the value of Δk/k given in equation (4). We will have equation (6).

Because Δk/k is equal to Δy/N  as shown in equation 4.

Therefore we can write

The equation (9) explain that for equilibrium, growth rate of output, growth rate of capital and growth rate of labour must be equal. If these 3 growth rate are equal, long run equilibrium would be restored with output and capital stock growing at the same rate as that of labour force. If these 3 rate are not equal in eqilibrium. There will be this equilibrium in the long run. The situation can be explain with the help of a figure given below:

Figure No 11.2:

in the above diagram equilibrium E0, Explain that growth rate of output and growth rate of of capital both are equal and output capital ratio y/k in equilibrium formed because through cobb-Douglas production function factor can be substituted, and so capital change with labour, In this way 3 growth rate  ΔY/Y , ΔK/K , ΔN/N  on other points. 

At E1 and E2 are not showing equilibrium point because at E1 ΔY/Y > ΔK/K

.Similarly at Point E2                  Δk/k > ΔY/Y

Golden Rules of Economic Growth

Golden rules of economic growth is not a new concept. It is actually a result of new classical theory this concept was given by the admen Phillips, Mr John, Robinson and Swan.

The basic concept in these rules is that in what way consumption can be maximized in the society and how this objective can be achieved. In nutshell we can say that golden rules explain that to how society can achieved maximum consumption level. in a simple model we can see in solow Swan model that every component of the model expand proportionally. Solow swan model given an equilibrium growth rate with the flexibility of substitution of factor of production. In this way we can have different ratio of capital and labour. The question arises that at what level of capital labour ratio. We can maximize consumption.

We can considered two extreme cases.

(1) A high capital labour ratio:           High K/L ratio

(2) A low capital labour ratio:             Low K/L ratio

(1)     A high capital labour ratio: High k/L ratio

In this situation high level of stock will be required to keep up with the growing supply of labour and for a high capital stock,  High level of saving is necessary which will depressed consumption level. Other component of the economy will also depressed. In this way with a high K/L ratio. We cannot achieve maximum level of consumption in the economy.

(2)      Low capital labour ratio:  Low K/L ratio

In this case low level of capital stock will keep production level at a slow rate. In this way national income will be depressed and when income will be depressed consumption will be low because consumption is a function of income C=f(y). In this way a low K/L ratio will not provide is maximum level of consumption.

(3)             Intermediate range of ratio: K/L

To maximum consumption only a intermediate range of K/L ratio can provide us help. In this way, First golden rule of economic growth will be in the intermediate range K/L ratio.

First golden rules: This first golden rule will be achieved when a consumption will be maximum but it will only be when growth rate of investment will be equal to marginal productivity of capital.

Rule 1  -------------   n  = mpk.

n = Growth rate of investment this has been explained with the help of diagram no 11.2.

Author: Nasir Mehmood Ch                 مصنف: ناصرمحمود چوہدری 

Email: Nasirmehmoodch97@gmail.com