Práctica 0

Sub intento

El problema del hogar

\[ V_t = E_t [\sum_{k=0}^{\infty} \beta^{k}(\frac{C_{t+k}^{1-\sigma}}{1 - \sigma} - \frac{N_{t+k}^{1+v}}{1 + v})] \]

\[ C_t + B_t = W_t \times N_t + \pi_t - T_t + (1 + r_{t-1}) \times B_{t-1} \]

Condiciones de primer orden del hogar

\[ C_t^{-\theta} = \beta \times E_t \times [C_{t+1}^{-\theta} \times (1 + r_t)] \]

\[ C_t^{-\theta} \times W_t = N_t^v \]

El problema de las firmas

\[ \Omega_t = E_t \times [\sum_{k=0}^\infty \beta^k (\frac{C_{t+k}}{C_t})^{-\sigma}](Y_{t+k} - W_{t+k} \times H_{t+k} - I_{t+k}) \]

\[ Y_{t+k} = A_{t+k} \times K_{t-1+k}^\alpha \times H_{t+k}^{1 - \alpha} \]

\[ K_{t+k} = I_{t+k} + (1 - \delta) \times K_{t-1+k} \]

\[ ln(A_{t+k}) = \rho ln (A_{t-1+k}) + \xi_{t+k} \]

\[ (1 - \alpha) \frac{Y_t}{H_t} = W_t \]

\[ 1 = \beta \times E_t \times [(\frac{C_{t+1}}{C_t})^{-\sigma}\times(\alpha \times \frac{Y_{t+1}}{K_t} + 1 - \delta)] \]

Condiciones de equilibrio

\[ B_t = 0 \]

\[ Y_t = C_t + I_t + G_t \]

\[ N_t = H_t \]