Consider the solow model a firm output according to


Consider the Solow model. A firm output according to Cobb-Douglas production function Yt = Kθ(ZtNt)1-θ, where Kt is physical capital stock, and ZtNt is units of effective worker. Labor Nt grows at a rate of gn and efficiency of labor Ztgrows at a rate gz. The household consumes a fixed fraction of its income each period, equal to (1-s). It invests the other fraction of its income, s, in new capital (that is, Itt), with capital accumulating according to: Kt+1 = (1-δ) +It.

  • 1. Now define per effective worker variables as ct= Ct/(ZtNt), it = It/(ZtNt), kt = Kt/(ZtNt), and yt = Yt/(ZtNt). Rewrite the capital accumulation equation in terms of the redefined variable
  • 2. Derive an analytic expression for the steady state per effective worker capital stock, k*
  • 3. What will be the growth rate of Kt in the steady state in which kt is constant at k*. Show the steps in getting your result/answer.
  • 4. Define the Golden Rule saving rate as the saving rate which maximizes steady state consumption per effective worker, ct= Ct/(ZtNt). For the given Cobb-Douglas production function, find an expression for this Golden Rule saving rate.

 

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Microeconomics: Consider the solow model a firm output according to
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