2. (i5 III-Lulu) Neoclassical Growth Model: Consider the two main equations for the Neoclassical Growth Model with exogenous labor: BIL/act _ 3f an/act+1 akt-H +(16) f(kta Zt) = Ct + (kt+1 (1 5),\") where Z is exogenous laboraugmenting technological progress. In the steady state, Z and grow at rates of *yz and 7" such that (dZ/dt) /Z = 7; and (d/dt)/ = 7\". Assume that both the production and utility functions take the CES form: 1/7 \"k\" 2.7-.) = ((1 ' \"W + awn-If) \"(Ct'i) = (96%\" + (1 (9)170) 1/\" where 0 0 determines the elasticity of substitution between capital and labor, and where 0 0 determines the elasticity of substitution between consumption and leisure. Finally, households are assumed to have a unitary time endowment. (a) Derive the steady state expressions for capital and output in terms of only exoge nous variables. For parts (b)-(d): If you are unable to obtain an answer to part (a), you may assume_that the steady state_expressions for capital and output take the form of k = qka and f(k, Z) = qbfZ, where 45k and f are exogenous parameters. (b) Use your solutions from part (a) to mathematically show that this model economy exhibits the following long-run properties: i. The output-labor ratio grows at a rate equal to growth in technical progress. ii. The capital-output ratio is constant. (c) Compute the steady state expression for consumption. (d) Suppose that 0 = 1 so leisure is not valued by households. Compute the long-run rate of growth in utility from consumption