Bắt đầu từ trạng thái ổn định của Vn = 1 trường hợp, hiển thị các ảnh hưởng của trợ cấp 50% đầu tư (để Vn là giảm một nửa). Thảo luận về động lực đầu tư tối ưu nếu tại thời điểm t = 0, khi Vn là giảm đi một nửa, nó cũng thông báo rằng tại một số thời gian T 0 trong tương lai lãi suất sẽ được tăng gấp ba lần, r (t) = 0,75 t ≥ T. | LABOR MARKET 127 general not relevant for the probability of xt i xg from the viewpoint of t 1. From the viewpoint of period t the probabilities of the same event can be written as Pt t i Pf 1 f i lxt 1 xb P xt 1 xb 11 Pt 1 t i xt 1 xg P xt 1 xg lit where P xt 1 xg lIt 1 p if xt xg and so forth . This allows us to verify the validity of the law of iterative expectations in this context. For i 2 we write Et 1 xt i xb xg xb Pt 1 t i . At date t 1 the probability on the right-hand side of is given while at time t it is not possible to evaluate this probability with certainty it could be Pt 1 t i xt 1 xb or Pt 1 t i xt 1 xg depending on the realization of xt 1. Given the uncertainty associated with this realization from the point of view of time t the conditional expectation Et 1 xt 1 i is itself a random variable and we can therefore calculate its expected value Et Et 1 xt i P xt 1 xb lit Et 1 xt i xt 1 xb P xt 1 xg lit Et 1 xt i xf 1 xg . Inserting using and recalling it follows that Et xt i xb xg xb Pt t 1 Et E t 1 xt i . EXERCISES Exercise 30 Consider the production function F k l a k l a Él2 k2. 22 a Suppose a firm with that production function has given capital k 1 can hire l costlessly pays given wage w 1 and must pay F 1 for each unit of l fired. If at takes the values 4 or 2 with equal probability p and future cashflows are discounted at rate r 1 what is the optimal dynamic employment policy b Suppose capital depreciates at rate s 1 and can be costlessly adjusted to ensure that its marginal product is equal to the cost of funds r s. Does capital adjustment change the optimal employment pattern What are the optimal levels of capital when at 4 and when at 2 Exercise 31 Consider a labor market in which firms have a linear demand curve for labor subject to parallel oscillations p N Z Z N. As in the main text Z can take two values Zb and Zg Zb and oscillates between these values with transition probability p. Also the wage .
