# 4 Suppose that we have a standard Solow model with a CobbDouglas production function The central equation of

4. Suppose that we have a standard Solow model with a. Cobb—[buglas produc—
tion function. The central equation of the model is as follows: km 2 SAFE? + (l. – {guilt
Consumption per worker is given by: q=[1-5)Akf. {a} Solve for an expression for the steady state capital stock per worker. In
doing so1 assume that the level of productivity is ﬁxed at some value A. {h} Use your answer on the previous part to solve for an expression for steady state consumption per worleer. {c} Use calculus to derive an expression for the a which maximizes steady state consumption per worker.
Macroeconomics