Joan Robinson's growth model

Joan Robinson's Growth Model is a simple model of economic growth, reflecting the working of a pure capitalist economy, expounded by Joan Robinson in her 1956 book The Accumulation of Capital. However, The Accumulation of Capital was a terse book. In a later book, Essays in the theory of Economic Growth, she tried to lower the degree of abstraction. Robinson presented her growth model in verbal terms. A mathematical formalization was later provided by Kenneth K. Kurihara.

Assumptions:


 * 1) There is a laissez-faire closed economy.
 * 2) The factors of production are capital and labour only.
 * 3) There is neutral technical progress.
 * 4) There are only two classes: workers and capitalists, among whom the national income is distributed.
 * 5) Workers save nothing and spend their wage income on consumption.
 * 6) Capitalists consume nothing, but save and invest their entire income for capital formation.
 * 7) There is no change in the price level.
 * 8) Saving is a function of profit.

The model
The entrepreneurs’ total profit and the workers’ total wage bill constitute the net national income. It can be mathematically expressed as

$$p Y = w N +\pi p K$$

where Y is the net national income, w is the money wage rate, N is the number of workers employed, K is the amount of capital utilized, p is the average price of output as well as of capital and π is the gross profit rate.The above equation indicates that the profit rate is a functional of labour productivity (p)and real wage rate(w/p)and capital ratio.