Could you help me with this question?

4. Suppose that in the Solow growth model, the production function of a country is given as: Y = zKO'SNO'S. The depreciation rate of capital is d = 0.09, population growth rate is n = 1%, and productivity is z = 2. (a) What is the savings rate that would induce the maximum consumption per capita? (b) Suppose the current savings rate is s = 20%. What are the capital per worker k, output per worker y, and consumption per worker c in the steady state? (c) Suppose the economy in 2007 was in the steady state described in (b). The productivity de- creased to z = l in 2008. Calculate k of 2007 and 2008. . In steady state, the consumption per-capita is: c = (1- s)zf (k*) = zf (k*) - szf (k*) = zf (k*) - (n + d)k* . The golden rule quantity of capital per worker is kar such that c is maximized. zf'(Kgr) = (n + d) . The golden rule savings rate Sar is the savings rate s such that kar is the steady state capital stock: szf (kgr) = (n + d)kgr