Consider a problem of choosing the level of capital stock by two firms: A and B....

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Consider a problem of choosing the level of capital stock by two firms: A and B. For simplicity we will assume that production requires capital only. We will follow the convention established at the lecture that in time period t the level of capital Kt is predetermined, but the firm can choose its future level of capital, Kt+1. Firm A does not own its capital stock, but instead rents it at price rk, the rental cost of capital. The problem of maximizing the value of firm A is given by: max {Kt+1)0 1 - + 7jt [F (Kt) – rK Ke] (1+r)² Firm B owns its capital stock, and can adjust its level via investment. The problem of maximizing the value of firm B is given by: 1 (1+r)t [F (K₁) - It] max {K++1)=0 subject to (a) Derive the first order condition of firm A. (b) Derive the first order condition of firm B. (c) What condition has to be satisfied for both firms to choose the same level of Kt+1? (d) Imagine you are the owner of firm C, which rents capital goods to firm A. What would be the maximal level of rk that you could charge this firm? (e) What would happen if you demanded higher rental rate than one found in (d)? t=0 Kt+1 = (1-6) Kt + It Consider a problem of choosing the level of capital stock by two firms: A and B. For simplicity we will assume that production requires capital only. We will follow the convention established at the lecture that in time period t the level of capital Kt is predetermined, but the firm can choose its future level of capital, Kt+1. Firm A does not own its capital stock, but instead rents it at price rk, the rental cost of capital. The problem of maximizing the value of firm A is given by: max {Kt+1)0 1 - + 7jt [F (Kt) – rK Ke] (1+r)² Firm B owns its capital stock, and can adjust its level via investment. The problem of maximizing the value of firm B is given by: 1 (1+r)t [F (K₁) - It] max {K++1)=0 subject to (a) Derive the first order condition of firm A. (b) Derive the first order condition of firm B. (c) What condition has to be satisfied for both firms to choose the same level of Kt+1? (d) Imagine you are the owner of firm C, which rents capital goods to firm A. What would be the maximal level of rk that you could charge this firm? (e) What would happen if you demanded higher rental rate than one found in (d)? t=0 Kt+1 = (1-6) Kt + It

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a The first order condition of firm A is F K t1 rK0 This means that firm A will choose the level of ... View the full answer