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Macroeconomic Analysis (Econ 7040)

Tutorial 4: Endogenous Growth model

1. Let’s now make the evolution of technology endogenous. Assume that Y (t) = A(t)(1 — aL )L(t),


A˙ (t) = B[aLL(t)]V A(t)e,    B > 0,V  0

where A˙ (t) =  is the time derivative of A or the rate of change of A.

(a) Assume that a = 1.  Is there a long-run growth rate of knowledge (A) in this economy (balanced growth path)? under what conditions?

(b) Use the condition derived before for the exitence of a balanced growth path and derive the long-run growth rate of knowledge (A) and GDP per-capita (y).

(c) Analyze the efect of an increase in aL (assume that the condition for the existence of balanced growth path is met).  What is the new long-run equilibrium?  how does the the economy transit (converge) to the new balanced growth path?

(d) Answer the previous question but now assuming that a < 1.  What is the new long-run equilibrium (with higher aL )?   how does the economy evolves in the short run?