This paper first appeared as a working paper of the UAB in 1992.This paper sets out a Marxian model that is based on the one by Stephen Marglin with one sector and continuous substitution. It is extended by adding technical progress and land as a factor of production. It is then shown that capital accumulation causes the preconditions for the breakdown of capitalism to emerge; that is, it causes the organic composition of capital to rise, the rate of profit to fall and the rate of exploitation to rise. A compressed history of the idea of the breakdown of capitalism is then set out and an explanation is given as to how the model relates to this and how it may serve as the basis for further research.Financial support from DGCYT grants PB95-0130-C02-01 and PB96-1160-C02-02 is acknowledged.