Learning Goal: I’m working on a macro economics exercise and need guidance to he

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Learning Goal: I’m working on a macro economics exercise and need guidance to help me learn.Y (t) = (1 − aL)A(t)L(t)dA(t)/dt = f(A(t))aLL(t)where Y(t) is output, L(t) is labour supply, A(t) is the stock of knowledge, and f is a continous and differentiable real function. We assume that the population growth rate is n. 1 > aL > 0(a) Is the technology for the production of output characterized by constant returns to scale in respect to the rival factor(s)? What is the interpretation for aL? Is knowledge a rival good?(b) Obtain the expression for the growth rate of knowledge, gA.(c) Find the time derivative of the growth rate of knowledge, dga/dt .(d) Show that if Af′(A) = cf(A) with c being a constant such that a > c > 0, then a stable balanced growth path exists. Find the corresponding value of gA.(e) Obtain A(t) and Y(t) along the balanced growth path. Does aL play a role? Is there a scale effect?

 

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