The real wage, $ \hat{w}_{t} $ , is a function of expected and past real wages and the expected, current, and past inflation rate in which the relative weight depends on the degree of indexation of the nonoptimized wages, $ \gamma_{w} $ . When $ \gamma_{w} = 0 $ , real wages do not depend on the lagged inflation rate. The last term implies a negative effect of the deviation of the actual real wage from the wage that would prevail in a flexible labor market. The size of this effect will be greater, the smaller the degree of wage rigidity, the lower the demand elasticity for labor and the lower the inverse elasticity of labor supply, $ \sigma_{L} $ . The shock to the labor supply, $ u_{t}^{L} $ , follows the AR(1) process, while the shock to the real wage, $ \varepsilon_{t}^{w} $ , is assumed to obey i.i.d.-normal distribution.

The capital accumulation equation is given as:

$$ \hat{K}_{t}=(1-\tau)\hat{K}_{t-1}+\tau\widehat{i n v}_{t-1} $$

Capital, $ \hat{K}_{t} $ , is decreased by the depreciation of capital and increased by investment. Note that $ \tau $ has a double meaning: the depreciation rate of capital and the ratio of investment to capital so that the former is used in the first term of the right-hand-side (RHS) equation and the latter is used in the second term.

### 3.2 Equilibrium Conditions from Corporate Sector

The cost minimization condition is as follows:

$$ \hat{l}_{t}=-\hat{w}_{t}+(1+\psi)\hat{r}_{t}^{k}+\hat{K}_{t-1} $$

where $ \psi = \psi'(1)/\psi''(1) $ is the inverse of elasticity of the capital utilization cost function. For a given installed capital stock, labor demand depends negatively on the real wage, $ \hat{w}_{t} $ , and positively on the rental rate of capital, $ \hat{r}_{t}^{k} $ .

The production function is given by:

$$ \hat{y}_{t}=\phi\hat{u}_{t}^{a}+\phi\alpha\hat{K}_{t-1}+\phi\alpha\psi\hat{r}_{t}^{k}+\phi(1-\alpha)\hat{l}_{t} $$

where $ \phi $ is one plus the share of the fixed cost in production, and $ \hat{u}_{t}^{a} $ is the productivity shock. This equation is derived from the production function.

The inflation law of motion is written as:

$$ \hat{\pi}_{t}=\frac{\beta}{1+\beta\gamma_{p}}E_{t}\hat{\pi}_{t+1}+\frac{\gamma_{p}}{1+\beta\gamma_{p}}\hat{\pi}_{t-1}+\frac{(1-\beta\xi_{p})(1-\xi_{p})}{(1+\beta\gamma_{p})\xi_{p}}\left[\alpha\hat{r}_{t}^{k}+(1-\alpha)\hat{w}_{t}-u_{t}^{a}+\varepsilon_{t}^{p}\right] $$

Inflation, $ \hat{\pi}_{t} $ , depends on past and expected future inflation and the current marginal cost, which itself is a function of the rental rate on capital $ \hat{r}_{t} $ , the real wage $ \hat{w}_{t} $ , and productivity shock $ u_{t}^{a} $ . When $ \gamma_{p}=0 $ , this equation reduces to the standard purely forward-looking Phillips curve. In other words, the degree of indexation, $ \gamma_{p} $ , determines how backward-looking the inflation process is. The elasticity of inflation with respect to changes in the marginal cost, $ \left[\alpha\hat{r}_{t}^{k}+(1-\alpha)\hat{w}_{t}-u_{t}^{a}+\varepsilon_{t}^{p}\right] $ , depends mainly on the degree of price stickiness. When all prices are flexible ( $ \xi_{p}=0 $ ) and the i.i.d-normal price-markup shock, $ \varepsilon_{t}^{p} $ , is zero, this equation reduces to the normal condition that in a flexible price economy the real marginal cost should equal one.