Production function

Consider a production function Yt = F(Kt,Lt) = ¯AKα t L1−α t (1) and the resource constraint Yt = Ct + It + Gt and the capital accumulation equation Kt+1 = It + (1 − ¯d)Kt Consumers consume a certain fraction of the output so the consumption equation is Ct = (1 − ¯s)Yt The government spending Gt is a fraction of capital stock, so with the higher capital stock, there is more government spending. Gt = ¯gKt Assume there is no population growth, so Lt = Lt+1 = ¯L a. Derive a Solow-Growth model and describe the intuition of the equation. b. What is the key assumption in this model c. Find the steady state per-worker quantities of capital, output, and consumption d. Draw the Solow model (the x-axis is Capital stock, the y-axis is output) e. Suppose there was a big government spending. Therefore, ¯g increased. What is the new steady state per-worker quantities of capital, output, and consumption?