Advanced microeconomics: Learning materials for Ph.D. students

Introduction    
Chapter 1. Static and dynamic Marshallian demand function and its properties    
1.1. Static Marshallian demand function    
1.2. Dynamic Marshallian demand function    
1.3. Basic concepts    
1.4. Exercises    
Chapter 2. Models of competitive equilibrium    
2.1. Simple model of exchange    
2.2. Static Arrow-Hurwicz model    
2.3. Dynamic Arrow-Hurwicz model    
2.4. Basic concepts    
2.5. Exercises    
Chapter 3. Monopoly – determining the optimal level of product price and optimal output level    
3.1. Static approach    
3.2. Dynamic approach    
3.3. Basic concepts    
3.4. Exercises    
Chapter 4.  Quantity and price competition in duopoly    
4.1. Cournot duopoly model
4.2. Stackelberg duopoly model    
4.3. Bertrand duopoly model    
4.5. Exercises    
Chapter 5. General equilibrium models  in the Walras sense    
5.1. Market model with exogenous functions of supply and demand    
5.2. Arrow-Debreu-McKenzie model    
5.3. Basic concepts    
5.4. Exercises    

Conclusions    
References    
Figures    
Tables   

The content of the learning materials is strongly related to the neoclassical synthesis trend, referring to the research results of the following Nobel laureates in economics: Paul Samuelson (1970), John Hicks, Keyneth Arrow (1972), Gérad Debreu (1983) and others. The authors decided that it is worth providing doctoral students of the Doctoral School at the Poznan University of Economics and Business with knowledge related essentially to competitive and general equilibrium in the sense of Léon Walras.
The study contains elements of the theory of demand, market structures, competitive and general equilibrium in the Walras’s sense. In Chapter 1 the authors focus our attention on Marshallian static and dynamic demand functions. Chapter 2 deals with the simple model of exchange, as well as the static and dynamic Arrow-Hurwicz models (discrete- and continuous-time). In Chapter 3 the authors discuss the static and dynamic models of the monopoly with an exogenous product demand function, which is the basis of quantity and price competition models in the static and dynamic Cournot, Stackelberg and Bertrand duopoly and oligopoly models presented in Chapter 4. The study culminates in Chapter 5 in which the authors synthesize the general equilibrium theory of Léon Walras on the basis of static and dynamic models with exogenously defined demand and supply functions and static and dynamic Arrow-Debreu-McKenzie models with endogenous defined functions of demand and supply for goods and services (in a discrete- and continuous-version).