## 3 Model Overview
### Work Motivation
#### 3.2.2 Firms  
Production Capacity  
Firms adjust their output and prices each period according to the sales of the products they produce. As indicated in Equation (5), the production volume is determined by the Cobb-Douglas type function, where the upper limit \(Q_{i_{t}}^{f\_lim}\) of the inventory that firm \(f\) can hold for product variety \(i\) is determined by its number of facilities \(K\), the labor force \(L\), and the coefficient \(a\). \[Q_{i_{t}}^{f\_lim}=a^{f}\ K_{t}^{f\beta}L_{t}^{f^{\dagger-\beta}} \tag{5}\]  
In this case, \(K\) is the number of facilities owned and \(L\) is the labor force of employed workers. \(\beta\) is a parameter of the distribution ratio, with the assumption that the sum of the \(K\) and \(L\) exponents is 1. In addition, \(a\) is the value of technical skill given to each firm by a random number. Furthermore, \(L\) varies with the work ethic \(M_{t}^{th}\) of the worker (household) fh belonging to firm f in the relevant period, as indicated in Equation (6). \[L_{t}=\sum M_{t}^{fh} \tag{6}\]  
Production Volume Determination  
Firms determine the target production number \(Q_{i_{t}}^{f\_lim}\) for each period using the periodic ordering method, with \(Q_{i_{t}}^{f\_elim}\) as the actual upper production limit and the number of sales of the product up to the previous period. In this case, the forecast demand during the \(ti\) forecasting period is the average number of sales during the \(ti\) period. The safety stock is determined by the formula shown in Equation (7), assuming that the ordering interval is 1 and the procurement period is 0. \[Q_{i_{t}}^{f\_elim}=\frac{1}{ti}\sum_{j=t-ti}^{t-1}Q_{i_{j}}^{f\_sel}+\left\{ sa\sqrt{\frac{1}{ti}\sum_{j=t-ti}^{t-1}\left(Q_{i_{j}}^{f\_sel}-\frac{1}{ti} \sum_{j=t-ti}^{t-1}Q_{i_{j}}^{f\_sel}\right)^{2}}\right\}-ST_{i_{t}}^{f} \tag{7}\]  
Here, \(Q_{i_{j}}^{f\_sel}\) is the sales volume of product i in period j, sa is the safety factor, and ST is the amount of inventory prior to production. As \(Q_{i_{t}}^{f\_lim}\) is the upper production limit, the sum of \(Q_{i_{t}}^{f\_\_\emph{sim}}\) and ST will be \(Q_{i_{t}}^{f\_\_\emph{sim}}=Q_{i_{t}}^{f\_\_\emph{sim}}-ST_{i_{t}}^{f}\) if it exceeds \(Q_{i_{t}}^{f\_\_\emph{sim}}\). Pricing Determination  
Prices are raised or lowered if the ratio of the previous period's inventory to the production ceiling exceeds a threshold value. In this study, the price is raised by 2% when the inventory ratio is 20% and is lowered by 2% when it is 80%. However, the price is set so that it does not fall below the total cost of the product, which is calculated from the labor cost, depreciation cost, and interest on the borrowing incurred during the investment period. Capital investment is made to strengthen production capacity when inventory shortages persist for a certain period of time. Capital investment will increase K in Equation (5) to augment production capacity. The capital investment decisions are made by adding the investment flag variable in the period when \(Q_{i_{t}}^{f\_ aim}\) exceeds \(Q_{i_{t}}^{f\_ aim}\) in the production plan and subtracting the investment flag variable in the period when \(Q_{i_{t}}^{f\_ aim}\) falls below the current inventory of \(ST_{i_{t}}^{f}\). In this paper, capital investment is made when the investment flag variable exceeds the investment decision threshold of 20. Half of the capital investment is financed by the firm's own funds and half by long-term loans from banks. Wages  
The wage \(W^{th}\) that a firm pays to each of its workers \(\beta t\) consists of a fixed salary \(W_{f}\) and a bonus. The amount of the fixed salary is randomly assigned to each household at the beginning of the simulation. However, the value of the fixed salary varies depending on work motivation. Bonuses are determined by the profit \(E_{t}\) derived from the previous period's sales multiplied by the bonus rate \(r_{b}\).