In the typical bathtub, the flow of water into the tub is controlled by a faucet independently of the quantity of water in the tub

How is the bathtub analogy of the steady state in the Solow model different? How does this difference relate to the phenomenon of convergence?

In the Solow model, the flow of investment is determined by the fixed rate of saving and the variable level of output, which depends on the stock of capital, the labor input, and the available technology. It is as if the faucet on the tub were controlled by the level of water in the tub. The convergence phenomenon is that economies with low per capita income have relatively high growth rates. But for economies to converge, all of the determinants of output must be similar. Thus, it is not surprising that convergence is not found among large groups of countries. Among suitably similar economies, evidence of convergence is striking testimony of the importance of diminishing returns. Despite the low level of investment that is feasible in a low-income economy, the growth impact of new capital there is greater than occurs in an otherwise similar high-income economy in which the level of investment is higher.