We are in the basic endogenous growth model studied in class' Suppose that the quantity ofoutput is produced according to Y(t) : [A(t)(1 Egg\" . New ideas are produced in this economy according to: AH] : B[aLL(t)]rA(t)'9, B > 0, l' 2 1. Labor evolves according to [.(t) : nL(t). a) {4 mark) Find an expression for the growth rate ofthe growth rate of knowledge [gA(t)/g,q([)]. Show your working (Hint: write the equation for 9.43) first): b) Assuming that 6' = 1, find the long-run growth rate of knowledge (9; and ,4 clearly explain its determinants. b) Explain the evolution of the economy when 9 = 1 and there is a permanent increase in B. In particular, what are the predictions about shorterun and longerun growtn?Consider the cases when n = 0 and n > O