Question

Consider the Solow growth model. Output at time t is given by the production function Yt = AKt3 L3 , where A is total factor productivity, Kt is total capital at time t and L is the labour force. Total factor productivity A and labour force L are constant over time. There is no government or foreign trade and Yt = Ct + It where Ct is consumption and It is investment at time t. Every agent saves s share of his income and consumes the rest. Therefore, Ct = (1 − s)Yt and St = sYt. Each period, savings equal investment: It = St. Capital evolves according the transition equation Kt+1 = (1−d)Kt +It, where d is the depreciation rate.

1. Combine the production function and the transition equation for capital to express Kt+1 as a function of Kt and the parameters of the model.

2. Express the transition equation in per worker terms, letting kt = Kt denote capital per L

   worker. Suppose that A=5,L=1,s=0.2,d=0.1. Furthermore kt =8.

3. Let yt = Yt denote output per worker. Express output per worker in terms of capital per worker using the above production function. Calculate output per worker at time t.

4. Calculate how much capital (per worker) depreciates at time t. Calculate investment (per worker) at time t. Calculate the level of capital per worker in t + 1. Did capital per worker increase?

5. Suppose that kt′ = 64. Calculate how much capital depreciates (per worker) at time t′. Calculate investment (per worker) at time t′. Calculate the level of capital per worker in t′ + 1. Did capital per worker increase? Compare with Q4 and comment on the differences.

Answer 1