Exercise 2.12. Consider the Solow growth model with constant saving rate s and depreciation rate of capital equal to δ. Assume that population is constant and the aggregate production function is given by the constant returns to scale production function F [AK (t) K (t), AL (t)L(t)] where A˙ L (t) /AL (t) = gL > 0 and A˙ K (t) /AK (t) = gK > 0. (1) Suppose that F is Cobb-Douglas. Determine the steady-state growth rate and the adjustment of the economy to the steady state. (2) Suppose that F is not Cobb-Douglas. Prove that there does not exist a steady state. Explain why this is. (3) For the case in which F is not Cobb-Douglas, determine what happens to the capitallabor ratio and output per capita as t → ∞.