Consider a Solow model, the economy has the constant saving rate at 0.4. The production technology in this economy follows a standard Cobb-Douglas function, Yₜ = KₜθLₜ¹⁻θ 0 = 0.4, and the population grows at a constant rate gi = 0.05. Be- sides, the depreciate rate & in this economy equals to 0.1. Hint: The economy is growing, so you may convert the model into a stationary one first and then solve for the steady state! It is better for you to solve the model in notations first and then set the parameter values!
(a) Solve for the steady state in this economy, and show the steady state with a diagram analysis.
(b) Please explain how the steady state would change if the population growth rate were larger? how the steady state would change if the saving rate were larger?
(c) Please linearize the model and show that the economy converges to the steady state from any initial capital state.