Consider the same economy as in the previous question, with a saving rate of s. Assume that the accumulation of capital depends on investmentIt=sYt minus the depreciation of capital, , as follows:

Kt+1=Kt+1Kt=ItKt

Show that the fundamental equation of the Solow model (for capital accumulation) is the following:

kt+1=skt(+n)kt

Hint: Start by re-expressing the production function and the capital accumulation equation in per-worker terms. Substitute the outcome per-worker in the capital accumulation equation and simplify.