1. The problem of the firm in the two-period model with investment is where and max V = + {N,N',I} ' 1+r = 2KN - wN-I, = 'K'N' -w'N' + (1 -d) K' K'=(1-d) K+I. Parameters a and are both positive and sum to less than 1, i.e. a > 0, 3 > 0 and (a + 3) < 1. (a) Write down the first-order conditions for the firm's optimization problem (3 points) and solve them to derive algebraic expressions for optimal N (2 points), N' (2 points) and I (5 points). (b) The elasticity of labor demand is defined as N aN w w N Use the expression for optimal labor demand from part (a) to derive an expression for N (2 points). What is the range for n? (1 point) If 8 = 1/3, what is ny? (1 point) Interpret your answer. (1 point)