History does not matter in Solow Models

Essentially, a fundamental result of Solow is that “history does not matter“; furthermore, it also suggests that “inequality does not matter“. The Solow model predicts convergence in levels of capital stock per capita and also in GDP per capita with no long-run growth (all growth is exogeneous, e.g. due to technological progress etc.).

Inequality does not matter in the long run

To see this, suppose we have two economies with the same aggregate capital stock and all parameters such as savings and population growht and depreciatino are the same. However initially, in economy A, this capital stock is distributed unequally, whereas in economy B it is distirbuted equally.

This implies that initially, economy A with the unequal distribution of capital stock will have a lower GDP per capita as economy B. This is because of diminishing returns,  as each individual faces the same technology to invest their capital, e.g. Cobb-Douglas $$y_{it} = A k^{\alpha}_{it}$$, where the $$i$$ indexes individuals, $$t$$ indexes time.

In economy B, the aggregate returns to capital equal the individual returns to capital, whereas in economy A, the individual returns to capital are lower for the richer and higher for the poorer as the diminishing returns kick in stronger for the richer and less for the poorer.

Without capital markets, individuals will accumulate in simple Solow logic and eventually reach the steady state, which corresponds to the aggregate steady state. So even though, initially inquality had an effect on the variables, in the long run, this dissapears. So history does not matter.