This section of the model appendix, authored by Frank Smets and Raf Wouters, focuses on the decision problems of firms and households and the equilibrium conditions in an economy. It is divided into four main parts: Final Goods Producers, Intermediate Goods Producers, Households, and the Intermediate Labour Union Sector. Final goods producers maximize profits by buying intermediate goods, packaging them into final goods, and selling them in a perfectly competitive market. The profit maximization problem includes a demand function that reflects the elasticity of demand and markup. The first-order conditions (FOCs) derived from this problem determine the optimal quantities of final and intermediate goods. Intermediate goods producers use a production function that includes capital services, labor input, and fixed costs. They minimize costs to maximize profits, leading to cost minimization conditions. The optimal price set by firms is determined by an optimization problem that considers the Calvo pricing mechanism and partial indexation. Households optimize their consumption, hours worked, bond holdings, investment, and capital utilization to maximize their utility, subject to budget constraints and capital accumulation equations. The model includes external habit formation and stochastic shocks to investment prices. The FOCs for these decisions are derived, and the Lagrange multipliers are used to solve the optimization problem. The intermediate labor union sector differentiates labor services and sets wages subject to a Calvo scheme. Labor packers buy labor from unions and resell it to intermediate goods producers. The unions have market power and can choose wages based on labor demand. The household's budget constraint includes dividends from the union, and the labor supply decision is derived from the FOCs. Unions are subject to nominal rigidities, with the ability to adjust wages probabilistically. The appendix provides a detailed mathematical framework for the decision-making processes of firms and households, along with the equilibrium conditions that govern the economy. It uses a combination of optimization problems, cost minimization, and stochastic processes to model the interactions between different economic agents.This section of the model appendix, authored by Frank Smets and Raf Wouters, focuses on the decision problems of firms and households and the equilibrium conditions in an economy. It is divided into four main parts: Final Goods Producers, Intermediate Goods Producers, Households, and the Intermediate Labour Union Sector. Final goods producers maximize profits by buying intermediate goods, packaging them into final goods, and selling them in a perfectly competitive market. The profit maximization problem includes a demand function that reflects the elasticity of demand and markup. The first-order conditions (FOCs) derived from this problem determine the optimal quantities of final and intermediate goods. Intermediate goods producers use a production function that includes capital services, labor input, and fixed costs. They minimize costs to maximize profits, leading to cost minimization conditions. The optimal price set by firms is determined by an optimization problem that considers the Calvo pricing mechanism and partial indexation. Households optimize their consumption, hours worked, bond holdings, investment, and capital utilization to maximize their utility, subject to budget constraints and capital accumulation equations. The model includes external habit formation and stochastic shocks to investment prices. The FOCs for these decisions are derived, and the Lagrange multipliers are used to solve the optimization problem. The intermediate labor union sector differentiates labor services and sets wages subject to a Calvo scheme. Labor packers buy labor from unions and resell it to intermediate goods producers. The unions have market power and can choose wages based on labor demand. The household's budget constraint includes dividends from the union, and the labor supply decision is derived from the FOCs. Unions are subject to nominal rigidities, with the ability to adjust wages probabilistically. The appendix provides a detailed mathematical framework for the decision-making processes of firms and households, along with the equilibrium conditions that govern the economy. It uses a combination of optimization problems, cost minimization, and stochastic processes to model the interactions between different economic agents.