1. A model of knowledge accumulation. Consider the model of knowledge accumulation in continuous time defined by the set of equations Y(t) = (1 -aL) A(t) L(t) d.A(t) dt = f(A(t) )aLL(t) where Y(t) is output, L(t) is labour supply, A(t) is the stock of knowledge, 1 > ax > 0 and f is a continous and differentiable real function. We assume that the population growth rate is n. (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 az? 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; (d) Show that if Af'(A) = of(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 agplay a role? Is there a scale effect