Acemoglu ch23 — RICH 프리뷰: 결산 — 다재다능 정치경제학

$$A_m \geq \varphi\, \alpha^{\alpha/(1-\alpha)}\, A_e\, \theta_e/\theta_m$$

$$y_i(t) = \frac{1}{\alpha}\, k_i(t)^{\alpha}\, (a_i(t)\, l_i(t))^{1-\alpha}$$

$$a_i(t+1) = \begin{cases} A_H & \text{w/p } \sigma_H\ \text{if } a_i(t) = A_H \\ A_H & \text{w/p } \sigma_L\ \text{if } a_i(t) = A_L \\ A_L & \text{else} \end{cases}$$

$$M \equiv \frac{\sigma_L}{1 - \sigma_H + \sigma_L} \in (0, 1)$$

$$w_H(t) \equiv \max\!\left\{\frac{1-\alpha}{\alpha}\, \beta^{\alpha/(1-\alpha)}\, (1-\tau)^{1/(1-\alpha)}\, A_H - b(t) + \beta(CV^H - CW^H)\, \bar L\right\}$$

$$\mu(t) = \begin{cases} \sigma_H\, \mu(t-1) + \sigma_L(1 - \mu(t-1)) & \text{if (23.17) does not hold} \\ 1 & \text{if (23.17) holds} \end{cases}$$

$$b(t) = b^E \equiv \frac{1}{1-\beta}\, \frac{(1-\beta(1-\sigma_L))\, A_H + \beta(1-\sigma_H)\, A_L}{1 - \beta(\sigma_H - \sigma_L)}\, \cdots$$

$$Y^E(t) = \frac{1}{\alpha}\, \beta^{\alpha/(1-\alpha)}\, [\mu(t)\, A_H + (1 - \mu(t))\, A_L]\, \bar L$$

$$\lim_{t\to\infty} Y^E(t) = Y^E_{\infty} \equiv \frac{1}{\alpha}\, \beta^{\alpha/(1-\alpha)}\, [A_L + M(A_H - A_L)]$$