Acemoglu ch19 — RICH 프리뷰: 무역과 성장

$$Y_j(t) = F_j(K_j(t), L_j(t), A_j(t))$$

$$\dot k_j(t) = f(k_j(t)) - \tilde c_j(t) + b_j(t) - (n+g+\delta)\, k_j(t)$$

$$\dot A_j(t) = r(t)\, A_j(t) - B_j(t)$$

$$\dot a_j(t) = (r(t) - g - n)\, a_j(t) - b_j(t)$$

$$p_H(t)\, MP_{L,H}(t) = p_F(t)\, MP_{L,F}(t)$$

$$\sum_{j=1}^{J} A_j\, b_j(t) = 0$$

$$Y_j(t) = F(X^K_j(t), X^L_j(t))$$

$$Y^L_j(t) = A_j\, L_j(t)$$

$$Y^K_j(t) = K_j(t)$$

$$\frac{a_{Lj}}{a_{Hj}} > \frac{a_{Lk}}{a_{Hk}} \Rightarrow j \text{ specializes in } L\text{-good}$$

$$p_K(t)\, [X^K_j - Y^K_j] + p_L(t)\, [X^L_j - Y^L_j] = 0$$

$$\dot K_j(t) = F(X^K_j, X^L_j) - \delta\, K_j(t) - C_j(t)$$

$$\sum_j X^L_j(t) = \sum_j Y^L_j(t),\ \sum_j X^K_j(t) = \sum_j Y^K_j(t)$$

$$U_j = \int_0^{\infty} e^{-(\rho-n) t}\, \frac{c_j(t)^{1-\theta} - 1}{1-\theta}\, dt$$

$$\dot A_j(t) = \sigma_j\, T_j(t) + \lambda_j A_j(t)$$

$$x_j(t) \equiv \frac{X^K_j(t)}{X^L_j(t)},\ Y_j = X^L_j\, f(x_j)$$

$$x^*_j = x^* = \frac{\sum_j K_j(t)}{L(t) \sum_j A_j},\ k^* = \frac{\sum_j K_j(t)}{J\, L(t)}$$

$$p_K^* = \rho + \delta$$

$$\int_0^{\infty} e^{-\rho_j t}\, \log C_j(t)\, dt$$

$$p_I^j(t)\, \dot K_j(t) + p_C^j(t)\, C_j(t) = Y_j(t)$$

$$\sum_{j=1}^{J} \mu_j = N$$

$$p_j(t) = r_j(t)$$

$$T_{ij} = G\, \frac{Y_i\, Y_j}{D_{ij}^{\theta}}$$

$$K^C_j(t) + K^I_j(t) + K^{\mu}_j(t) \leq K_j(t)$$

$$B^C_j(r_j, [p(\nu)]) = r_j^{1-\tau}\, \int_0^N p(t, \nu)^{1-\varepsilon}\, d\nu$$

$$B^I_j(r_j, [p(\nu)]) = \zeta_j\, r_j^{1-\tau}\, \int_0^N p(t, \nu)^{1-\varepsilon}\, d\nu$$

$$r_j(t) + \frac{\dot p^I_j}{p^I_j} - \frac{\dot p^C_j}{p^C_j} = \rho_j + \frac{\dot C_j}{C_j}$$

$$\lim_{t\to\infty} e^{-\rho_j t}\, \frac{p^I_j(t)\, K_j(t)}{p^C_j(t)\, C_j(t)} = 0$$

$$\left(\int_0^N p(t, \nu)^{1-\varepsilon}\, d\nu\right)^{1/(1-\varepsilon)} = 1$$

$$p^C_j(t) = r_j(t)^{1-\tau},\ p^I_j(t) = \zeta_j\, r_j(t)^{1-\tau}$$

$$Y_j(t) = \mu_j\, r_j(t)^{1-\varepsilon}\, Y(t)$$

$$r_j(t)\, K_j(t) = \mu_j\, r_j(t)^{1-\varepsilon}\, \sum_{i=1}^{J} r_i(t)\, K_i(t)$$

$$\frac{\dot K_j}{K_j} = \frac{\dot Y_j}{Y_j} = g^*$$

$$r^*_j = p^*_j = [\zeta_j(\rho_j + g^*)]^{1/\tau}$$

$$y^*_j = A_j\, s_j\, (g^*)^{\alpha/(1-\alpha)}$$

$$\Pr(y > y_0) = \left(\frac{y_0}{y_{\min}}\right)^{-\alpha}$$

$$B^C_j(w_j, r_j, [p(\nu)]) = w_j^{(1-\tau)(1-\gamma)}\, \cdots$$

$$p^C_j(t)\, C_j(t) = \rho_j\, p^I_j(t)\, K_j(t) + \int_t^{\infty} \exp\!\left(-\int_t^z (r_j + \dot p^I_j/p^I_j - \rho_j)\right)\, dz \cdot w_j(t)$$

$$(1-\gamma)(1-\tau)\ \text{of consumption expenditure on goods}$$

$$r_j(t)\, K_j(t) + w_j(t) = \mu_j\, r_j(t)^{1-\varepsilon}\, \sum_i [r_i(t) K_i(t) + w_i(t)]$$

$$\frac{w_j(t)}{r_j(t) K_j(t) + w_j(t)} = \frac{(1-\gamma)(1-\tau) \rho_j}{[\gamma + (1-\gamma)\tau]\, \zeta_j}$$

$$p_n(t) = w_n(t),\ p_o(t) = w_s(t)$$

$$\frac{c_n(t)}{c_o(t)} = \left(\frac{p_n}{p_o}\right)^{-\varepsilon}$$

$$c_n(t) = \frac{L_n}{N_n(t)},\ c_o(t) = \frac{L_s}{N_o(t)}$$

$$\frac{w_n(t)}{w_s(t)} = \max\!\left\{\frac{\eta}{\iota}\, \left(\frac{L_s}{L_n}\right)^{1/\varepsilon},\, 1\right\}$$

$$\eta\, \beta > \rho,\ 2(1-\theta)\, \eta\, \beta < \rho$$

$$g_A = \frac{1}{\theta}\, (\eta\, \beta - \rho)$$

$$\frac{\dot A_j(t)}{A_j(t)} = \eta\, L^1_j(t)$$

$$A_n(0) = 1,\ A_s(0) = 1 - \delta$$

$$p^1_j(t)\, A_j(t) = p^2_j(t)$$

$$\frac{p^1_j(t)}{p^2_j(t)} = \frac{X^1_j(t)}{X^2_j(t)}$$