diff --git a/docs/book/content/theory/equilibrium.md b/docs/book/content/theory/equilibrium.md index 402873047..06310320a 100644 --- a/docs/book/content/theory/equilibrium.md +++ b/docs/book/content/theory/equilibrium.md @@ -130,7 +130,7 @@ The computational algorithm for solving for the steady-state follows the steps b ``` 6. Find $\pi(\bar{K}_m, \bar{K}^{\tau}_m, \bar{L}_m)$ using the steady-state version of {eq}`EqFirmsProfit` 7. Find the value of the firm in steady-state as: $\bar{V}_{m} = \frac{\pi(\bar{K}_m, \bar{K}^{\tau}_m, \bar{L}_m)}{(1+\bar{r})}$ - 8. Use the steady-state world interest rate $\bar{r}^*$ and labor demand $\bar{L}_m$ to solve for the value of the firm the world interest rate $\bar{V}_m^{r^*}$: + 8. Use the steady-state world interest rate $\bar{r}^*$ and labor demand $\bar{L}_m$ to solve for the value of the firm at the world interest rate $\bar{V}_m^{r^*}$: 1. Use $\bar{Y}_{m}$, $\bar{r}^*$, and $\bar{L}_m$ in {eq}`EqStnrzFOC_K` to solve for $\bar{K}_m^{r^*}$. 2. Solve for $\bar{K}_m^{\tau, r^*} = \frac{(1-\tau^{inv})\delta_m \bar{K}^{r^*}_{m}}{\delta^{\tau}_m}$ 3. Find $\pi(\bar{K}^{r^*}_m, \bar{K}^{\tau, r^*}_m, \bar{L}_m)$ using the steady-state version of {eq}`EqFirmsProfit` @@ -141,7 +141,7 @@ The computational algorithm for solving for the steady-state follows the steps b 3. Use the production function to find $\bar{Y}_M$. 4. Solve for $\bar{K}_M^{\tau} = \frac{(1-\tau^{inv})\delta_M \bar{K}_{M}}{\delta^{\tau}_M}$ 5. Find $\pi(\bar{K}_M, \bar{K}^{\tau}_M, \bar{L}_M)$ using the steady-state version of {eq}`EqFirmsProfit` - 6. Use the steady-state world interest rate $\bar{r}^*$ and labor demand $\bar{L}_M$ to solve for the value of the firm the world interest rate $\bar{V}_M^{r^*}$: + 6. Use the steady-state world interest rate $\bar{r}^*$ and labor demand $\bar{L}_M$ to solve for the value of the firm at the world interest rate $\bar{V}_M^{r^*}$: 1. Use $\bar{L}_{M}$ and $\bar{r}^*$ {eq}`EqStnrzFOC_K` to solve for $\bar{K}_M^{r^*}$. NOTE: may not be an analytical solution here so might have to use a root finder... 2. Solve for $\bar{K}_M^{\tau, r^*} = \frac{(1-\tau^{inv})\delta_M \bar{K}^{r^*}_{M}}{\delta^{\tau}_M}$ 3. Find $\bar{pi}_M^{i'}=\pi(\bar{K}^{r^*}_M, \bar{K}^{\tau, r^*}_M, \bar{L}_M)$ using the steady-state version of {eq}`EqFirmsProfit`