Eco 0700

1. [8 points] Let the production function be Q (t) = f (t, K(t), L(t)) = exp (gt) K(t ) " L(t ) 1-, (1) where Q is total output, f (.) is the production function, K is capital input, L is labor input, and t is the time which indicates that the production function can shift over time due to technological changes. The notation exp () denotes the exponential function, g > 0 is a constant, and o E (0, 1) is the share of capital in the production function. Derive the expression of the growth rate of Q (t), i.e., dt Q(t) (2) in terms of the growth rates of capital and labor, dL(D) de and K (t) L(t) and two model parameters, o and g.2. [22 points] Consider the following national income model: Y = C+I+G, C = f( Y -T), I = h(r). r = m(M'), where (3) is the macro equilibrium condition, (4) and (5) are the consumption and investment functions, respectively, and (6) is the equation summarizing the demand for money and the money market equilibrium. The variables are defined as follows: Y is national income (or total production), C is consumption, I is investment, G is government spending, 7 is tax revenue, " is the interest rate, and M' is money supply. There are seven variables and four equations so we can potentially solve for 4 endogenous variables (C, Y, I, r) in terms of 3 exogenous variables (G. T, M'). Assume that f (.), h (.), and m (.) are continuously differentiable functions with 0