
The two sector model of growth which Marx formulated in his 'theory of reproduction' became a basis for development strategies in the Soviet Union and Eastern Europe. The following presentation of this theory builds on the models of simple and expanded reproduction presented earlier but changes the notation and terminology to facilitate understanding of results. Simple algebraic solutions are used and the whole process is illustrated by numerical simulations and graphs. 





It is assumed that capital is the only constraining factor of production. Labor is assumed to be abundant and can be increased without limits. We do not need therefore to bring labor into the model explicitly. 

Further it is assumed that there is no distinction between capital goods and intermediate goods, i.e. capital lasts just one unit of time and it is fully worn out and depreciated at the end of the period. Each period's investment must replace the whole stock of capital worn out during that period and add some additional capital if growth is to occur. The gestation period is one unit of time, i.e. investment of the period t began to produce in the period t+1. 


The main implication of the Marxian 'theory of reproduction' for a centrally planned economy is that planners decide how the net investment are allocated between the producer goods and consumer goods sectors and by doing so control the rate of economic growth. According to this model the preferential allocation of investment to the first sector would speed up the overall rate of economic growth. In the short run some consumption would be sacrificed but the faster growth would increase the consumption in the long run. This can be seen from the following analysis_{:} 


Investment create an increment of capital as indicated by (4a). It follows that capital of the first sector will grow by the rate g and because of fixed coefficients in (1a) the output of producer goods will grow also by the same rate g. According to (2) the growth of X_{1} will result in increased total net_{ }investment and that will  with a lag  lead also to the growth of production of consumer goods. The policy advice to planners is "if you want to improve the standard of living of population in the long run, you must allocate investment preferentially to the production of producer goods and have the sector 1 grow in the short run faster than sector 2. The rate of growth of sector 2 will later catch up with the rate of growth of sector 1". This is the theoretical basis of the quest for industrialization with priorities given to heavy industry. 






Now if g were kept constant the proportion between outputs of the two sectors would also remain constant. In such a case sector 2 would grow by the same rate as sector 1. From that we can derive an expression for a steady (constant) rate of growth in both sectors.

Equation (8) shows that a steady state growth rate, i.e. the growth rate that is equal for both sectors and constant in time depends only on technological coefficients a_{1}, a_{2} and on the proportion of outputs f_{t}. 
Steady State Rates of Growth

We shall now explore three alternative
 




