(80 points) Prime Minister Osiris has come down with the feline coronavirus (look it up, its actually a thing) and has tasked his second in command, Queen of the Nile, Lord and Savior of the Universe Isis to fill in for him while he is being cared for in a well-staffed medical facility that will be giving him a healthy dose of GS-441524 (very similar to Remdesivir, but more effective in cats... Again, its a thing... Look it up). She is trying to get on board with how you do your economic modeling because she, just like you, want to be able to extend these models to analyzing business cycles, and this is the workhorse model for understanding how business cycles work in a general equilibrium context.

You have the objective function

And the following constraints:

1. yt = ct + it 2. yt = Atkt 3. it =kt+1 (1)kt,

U = tln(ct) t=0

and Isis would like you to solve the model out to be able to predict shocks to the economy. (a) (8 points) Show all three constraints can be combined to yield

(b) (8 points) Formulate the Bellman Equation.

c =Ak k +(1)k tttt+1 t

Money and Banking Problem Set III - Page 3 of 5 10/7/2020 (c) (10 points) What are the first order conditions? Hint: You want V (kt) = 0.

(d) (8 points) Find

(e) (10 points) What is the Euler Equation?

(f) (10 points) What is the economic significance of the Euler Equation?

V (kt+1) kt+1

kt+1

Money and Banking Problem Set III - Page 4 of 5 10/7/2020 (g) (8 points) What is steady state capital?

(h) (8 points) What is steady state output?

(i) (10 points) What is steady state investment?

(j) (8 points) What is steady state consumption?