EC417 Problem Set 2 Review

review

Question 2

(b)

We start from $a_t=\log \tilde{A}$. Since $\rho \in (0,1)$, and $a_{t+1}=\rho a_t+ϵ$, in long run, $a_t\to 0$, Thus $\tilde{A}=1$.

The intuition is to use the guess and verify method. Start by guessing that all variables grow at the same rate $g$. ($G=g+1$)

The key part here is that we have to let $L_t$ and $r_t$ remain unchanged.

Reasons:

1. $L_t\in [0,1]$.
2. $R_t=(1-\alpha )Y_t/K_t$, which is a ratio. Calder effect

(c)

There’s a tricky part about the Taylor Expansion. Recall that:

$$\frac{1}{1+x}\approx 1-x+x^2-x^3\dots$$

when $x$ is small.

We pick the first two terms, that is $\frac{1}{1+x}\approx 1-x$

(d)

When such question, it’s usually three steps:

1. Simplify
2. Guess
3. Verify

Always make it clear that policy function time invariant. Also in (d) and (e), it’s important that when calculating coefficient, every parameter is time-invariant.

The most tricky part for me is that how to use Taylor Expansion to solve such questions.