01 May Question: Consider the Solow growth model. Output at time t is given by the production function Yt = AKt3 L…
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.
- 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.
- 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.
- 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.
- 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?
- 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.
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