1. Capital stock dynamics and specific production functions [4 marks] Consider the Solow model with depreciation (6) set to zero. The total capital stock (K) then evolves according to K = sY, where Y denotes total output, and s E (0, 1) is the rate of saving (and investment). Output is given by the Neoclassical production function Y = F(K, AL), where A and L denote labor-augmenting productivity, and the size of the labor force, which grow at rates g and n, respectively. Note that s, n, and g, are all strictly positive, exogenous, and constant over time, while Y, K, A and L are functions of time, although we suppress the time argument. Lower-case letters denote units per effective worker, so that k = K/(AL), and y = Y/(AL). The real interest rate, denoted r, equals the marginal product of capital: T = OF(K, AL) For (a) and (b) below, let Y = K(AL)1-a, where a (0,1). (a) Find an expression for k in terms of (some or all of) k, s, n, a, and g (and possibly numbers). [1 mark] (b) Find an expression for in terms of (some or all of) r, s, n, a, and g (and possibly numbers). [1 mark] For (c) and (d) below, Y = [(1-8)K+B(AL)], where Be (0, 1), p <1, nd p0. (c) Find an expression for the steady-state level of y, denoted y" (assuming it exists). Your answer should be in terms of (some or all of) s, n, , p, and g (and possibly numbers). [1 mark] (d) Find an expression for the steady-state level of r, denoted r' (assuming it exists). Your answer should be in terms of (some or all of) s, n, B. p, and g (and possibly numbers). [1 mark]