A basic Kaleckian model is enriched by three simple, intuitive assumptions. First, there is a redistributive system of the wage bill between employed and unemployed workers, the latter receiving subsistence income. Second, only individuals with an income above the subsistence level build savings. The combination of these two assumptions gives rise to an autonomous consumption component whose rate of growth depends on population growth. Consequently, the rate of capital accumulation spontaneously converges towards the rate of population growth (the supermultiplier effect), a dynamic that offers a solution to one of the two Harrodian instability problems. The third assumption corresponds to entrepreneurs’ attempts to adjust investments to restore the normal rate of capacity utilisation. Although this assumption usually generates knife-edge instability, we show here that the stabilising properties of the supermultiplier, provided that the accelerator effect is not overly strong, help overcome this instability and realise the normal rate of capacity utilisation. Therefore, the model may offer a simple, simultaneous solution to the two Harrodian instability problems.