### 1(a)¶

Here we simply jump up onto the new stable arm and follow that to steady state.

### 1(b)¶

This requires solving for an intersection. One way is to choose the consumption level that we jump to on announcement so that we end up on the new stable arm after one year. Another, potentially more stable way, is to choose the capital level after one year so that when we go backwards in time one year, we are at the original capital level. Here we use the second approach.

### 1(c)¶

Because the state valuation $\mu$ should be continuous in time, we must have the following conditions immediately before and after the policy change ($t=1$)

$$u^{\prime}(c_-) = \mu \qquad \text{and} \qquad u^{\prime}(c_+) = (1+\tau) \mu$$

Combining these and noting that we have $\log$ utility, we arrive at an equation characterizing the consumption jump that occurs at $t=1$

$$\frac{c_+}{c_-} = \frac{1}{1+\tau}$$

Thus we want to choose the capital level after one year ($k_1$) so that when we go backwards in time from $(k_1, (1+\tau) c^{\ast}(k_1))$, we end up at our initial capital level. After that point, we simply follow the same stable arm back to the original steady state.

### 1(d)¶

This is a bit funky. But we basically start from a slightly perturbed steady state and go backwards in time. We want to end up at the original steady state at time zero. But there aren't any real values to solve for. The only wiggle room we have is when to start the simulation (I use $t=20$ below) and how much to perturb it by initially, which we solve for.