Suppose the production function of the economy takes only capital as input and follows the formula:

Y = zK (5)

With saving rate s, deprectiation rate d and population growth rate n, write down an equation that determines capital stock next period, given capital stock this period.

Convert the equation you have above into per worker form, denoting capital stock per person by k.

Does capital per worker converge to a steady state level? How does it evolve through time?

Now suppose that every period the government taxes income Y at rate t < 1 and simply throw away tax revenue. How does t affect growth rate of the economy? That is, if the government increases t, how does economic growth changes in response?