Question 2: {20 marks) We are in the basic endogenous growth model studied in class. Suppose that the quantity of output is produced according to Y(t) = [A(t)(1 aL)L(t)] . New ideas are produced in this economy according to: A(t) = B[aLL(t)]YA(t)3, B > 0,)! 2 1. Labor evolves according to 130:) = nL(t). a) (4 mark) Find an expression for the growth rate of the growth rate of knowledge [gA(t)/g,q(t)]. Show your working (Hint: write the equation for gAOE) first) . b) (6 marks) Assuming that 9 = 1, find the long-run growth rate of knowledge (gj;1 ) and clearly explain its determinants. b) (10 marks) Explain the evolution of the economy when 9 = 1 and there is a permanent increase in B. In particular, what are the predictions about short-run and long-run growth? Consider the cases when n = 0 and n > 0