James Meade

According to the assumptions given above, the net output produced by the economy depends on the following four things: (1) The amount of existing stock of machines in the economy (2) The amount of labor for production process (3) The amount of land or natural resources available for productive use in the economy (4) The technological progress in the economy which is expected to improve over time.

Hence the production function for the economy is given by:

${\displaystyle Y=F(K,L,N,t)}$

Where:

         ${\displaystyle Y=}$ net output or net real income
         ${\displaystyle K=}$ existing stock of machines
         ${\displaystyle L=}$  the amount of labour
         ${\displaystyle N=}$ amount of land
         ${\displaystyle t=}$  time

Time is accounted for because with the passage of time the production would increase without any increase in ${\displaystyle K}$, ${\displaystyle L}$, or ${\displaystyle N}$. An increase in ${\displaystyle Y}$ with time (denoted by ${\displaystyle \Delta Y}$) can take place in three ways. First, the machine stockpile may increase if the community starts saving part of their income thereby accumulating real capital. If the increase in the stock of capital taking place in one year is given by ${\displaystyle \Delta Y}$, the output would increase by ${\displaystyle V\Delta K}$ where ${\displaystyle V}$ denotes the marginal net physical product of a machine.

Secondly, ${\displaystyle L}$, the working population, may grow. If ${\displaystyle \Delta L}$ denotes an increase in the amount of labour productivity employed in a single year and ${\displaystyle W}$ measures the marginal product of labour, the output will increase in that year by ${\displaystyle W\Delta L}$.

Finally, the net output can increase if there is an increase in the technical progress (hence enabling increased efficiency). The total increase in net output due to technical progress is given by ${\displaystyle \Delta Y'}$. Hence the total increase in net output in one year is the sum of the three influences. Combining this we get the equation:

${\displaystyle \Delta Y=V\Delta K+W\Delta L+\Delta Y'}$

Dividing both sides by ${\displaystyle Y}$, we get

${\displaystyle {\frac {\Delta Y}{Y}}={\frac {V}{Y}}.\Delta K+{\frac {W}{Y}}\Delta L+{\frac {\Delta Y'}{Y}}}$

Or,

${\displaystyle {\frac {\Delta Y}{Y}}={\frac {VK}{Y}}.{\frac {\Delta K}{K}}+{\frac {WL}{Y}}.{\frac {\Delta L}{L}}+{\frac {\Delta Y'}{Y}}}$ (Equation 1)

Here ${\displaystyle {\frac {\Delta Y}{Y}}}$ is the annual proportionate rate of growth of output, ${\displaystyle {\frac {\Delta K}{K}}}$ the annual proportionate rate of growth of machinery stock, ${\displaystyle {\frac {\Delta L}{L}}}$ the annual proportionate rate of growth of productively employed labour and ${\displaystyle {\frac {\Delta Y'}{Y}}}$ the annual proportionate rate of growth of output due solely to increase in technical progress.

Meade denotes these four proportionate rates of growth as ${\displaystyle y,k,l}$ and ${\displaystyle r}$ respectively. ${\displaystyle {\frac {VK}{Y}}}$ is the proportion of net national income to be paid in net profits (provided the owners of machinery receive a reward equal to the value of the net marginal product of the machinery). Meade denotes this as ${\displaystyle U}$ and calls it "the proportional marginal product of machinery". Under the assumption of constant returns to scale, it is equal to the proportion of national income received in profits. Similarly ${\displaystyle {\frac {WL}{Y}}}$ represents the proportional marginal product of labour and is equal to the proportion of the net national income going to wages under conditions of constant-returns competitive equilibrium. Meade denotes this as ${\displaystyle Q}$. Hence equation 1 can be written as

${\displaystyle Y=UK+Ql+r}$ (Equation 2)

This shows the growth rate of output ${\displaystyle y}$ as being the weighted sum of three other growth rates, the sum of the growth rate in the stock of machines ${\displaystyle k}$ weighted by the marginal importance of machinery in the productive process i.e., in a competitive equilibrium by the proportion of the national income going to profits ${\displaystyle U}$ plus the growth rate of the population ${\displaystyle I}$ weighted by the marginal importance of labour in the productive process or, in a competitive equilibrium by the proportion of income going to wages ${\displaystyle Q}$ plus the growth rate of technical progress ${\displaystyle r}$ Hence equation 2 can be written as

${\displaystyle y-l=Uk-(1-Q)L+r}$ (Equation 3)

Since ${\displaystyle y-l}$ is the difference between the growth rate of total output and growth rate of the workforce, the growth rate of the real income per head can be measured. For example, if the total real income is increasing by 10 percent every annum but the working population is growing at 8 percent per annum, the income per head is rising by approximately 2 percent per annum.

Equation 3 shows that the growth rate of real income per head (y – l) is the output of three factors.

Firstly it is raised by the growth rate in real capital ${\displaystyle k}$ weighted by its proportional marginal product or by the proportion of net national income which would be paid min profits in a competitive equilibrium ${\displaystyle U}$. Secondly it is depressed by the growth rate in the working population ${\displaystyle l}$ weighted by one minus the proportional marginal product of labour ${\displaystyle l-Q}$. Lastly it is raised by the amount of technology in the economy ${\displaystyle r}$.

The element ${\displaystyle UK}$ in equation 3 can also be written down as ${\displaystyle {\frac {VK}{Y}}.k}$ since the growth rate of machine stock is ${\displaystyle {\frac {SY}{K}}}$ where ${\displaystyle S}$ is the proportion of the net national income that is saved. Therefore, we have ${\displaystyle Uk=US.{\frac {Y}{K}}=SV}$ which expresses the same thing in three forms namely the contribution which capital accumulation makes to the growth rate of the final output. Hence the basic relationship between the growth rate of real income per head and its three basic determinants can be expressed as:

${\displaystyle y-l=Uk-(1-Q)l+r}$

${\displaystyle y-l=US.{\frac {Y}{K}}-(1-Q)l+r}$

${\displaystyle y-l=SV-(1-Q)l+r}$

Meade explains the application of these equations by taking a simple numerical example. Suppose the people save one tenth of their income such that ${\displaystyle S=}$ and that the marginal product of real capital goods or the market profit rate is 5 percent per annum. Hence ${\displaystyle V=5}$ percent per annum. The contribution of capital accumulation to the growth of output, ${\displaystyle SV}$ would be one tenth of 5 percent per annum. Hence ½ percent per annum. The explanation of this is, out of a year's income of 1000, if people save 100 units of product and if a once-for-all addition of 100 units to the stock of machines increases annual output in every future year by 5 units, then the initial annual income of 1000 will be raised by this year's capital accumulation to 1005 or by ½ percent during the course of the year. Assuming initial annual income to be 1000 and the initial machinery stock to be 2000 ${\displaystyle Y=1000}$ and ${\displaystyle K=2000}$. Similarly, the same thing can be expressed by saying that the stock of machines had increased from 2000 to 2100 or by 5 percent per annum. Then ${\displaystyle U={\frac {VK}{Y}}={\frac {(5/100)\times 2000}{1000}}={\frac {1}{10}}}$ and ${\displaystyle Uk={\frac {1}{10}}\times 5={\frac {1}{2}}}$ per annum.

Thus the contribution of capital accumulation to growth rate of the final output was one tenth of 5 percent per year or ½ percent per annum.

The same result can be obtained by multiplying the proportion of the national income going to profits ${\displaystyle U}$, the proportion of the national income which is saved ${\displaystyle S}$ and the annual income to capital stock ratio ${\displaystyle {\frac {Y}{K}}}$ Our numerical example is: ${\displaystyle US.{\frac {Y}{K}}={\frac {1}{10}}\times {\frac {1}{10}}\times {\frac {1}{2}}={\frac {1}{2}}}$ percent per annum.

The growth theory provided by Meade is neo-Classical in nature. It is simple and attractive as it promises a state of steady economic growth. However it suffers from a few drawbacks First, for a steady state of economic growth to exist, the technological progress should be assumed to be entirely labour-augmenting. This is the special case of Harrod-neutral technological progress. However this does not seem to exist in the model.

Second, the neo-Classical adjustment mechanism depends on the flexibility of factor prices. But if they are not flexible a lot of difficulty is established. For example, in the Keynesian liquidity trap, the interest rate may fail to go down beyond a minimum level hence preventing the capital-output ratio to be high enough to reach growth equilibrium.

Third, there is no mention about investment function in the model. It is assumed to be solely determined by savings. Hence entrepreneurial expectations about the future are not taken into account.

Fourth, in the neo-Classical models capital is assumed to be jelly-like, homogeneous and malleable. This assumption is truly unrealistic, but without it present, it becomes very difficult to reach a stage of steady growth.

Finally, the technological progress is considered to be totally exogenous which is again extremely unrealistic and has been pointed out by many economists. To sum up, the neo-Classical growth model of Meade is based on certain restrictive and unrealistic assumptions. Hence applying this model in the case of under developed nations is almost impossible since the assumptions of perfect competition, full employment of labour and machinery and constant returns to scale do not fit in their economic realities.