Assume an output production function Y (t) = A(t)(1 aL)L(t) and a production function of new ideas A(t) = B[aLL]A^ . Also, assume population grows at rate n. For the simple endogenous growth model, this setup implies gA(t) = ngA(t) + ( 1)gA(t)^2 , where gA(t) is growth rate of knowledge. Assume the initial number of workers is L(0) = 1 for convenience. : 0.25 n: 0.02 B: 0.3 aL:0.4 nnew: 0.01 Bnew: 0.3 a. In your simple endogenous growth economy, what is the steady-state equilibrium growth rate of output (per capita)? b. What value of aL would maximize the current growth rate of output in your economy? How does your answer depend on which case you have for the values of and n? Explain your answer. c. Which parameters changes at time t0 for your simple endogenous growth economy? Show graphically in a plot of lnAt against t what happens in the economy given this change. What happens to output per worker?