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## Inhaltsverzeichnis

### 1. Introduction

Abstract
A central concept in (neo-)classical economics is a general equilibrium known as a “Walras Equilibrium”. This equilibrium is characterized by the equality of demand and supply for all goods. Such an equality may be reached, if the prices are fully flexible. On the other hand, Keynes and the “(neo—)keynesian” economists have introduced models, in which rigid prices cause an inequality between demand and supply. Following a recent interpretation, some agents perceive quantity constraints. An equilibrium of these models is often called a “Non-Walrasian Equilibrium”.
Paul van den Heuvel

### 2. Mathematical Results in Optimization and Stability

Abstract
The purpose of this chapter is to provide the mathematical background for the rest of the thesis. We are especially interested in two fields of mathematics: optimization and the theory of differential systems. Section 2.2 contains, in addition to some necessary analytic concepts, a theorem on the differentiability of a solution of a maximization problem with regard to the parameters of the problem.
Paul van den Heuvel

### 3. Static Model

Abstract
In this chapter a short run macromodel is considered with three commodities. This model is similar to the ones of Barro and Grossman (1971, 1976), Malinvaud (1977), Böhm (1978,1980), Muellbauer and Portes (1978) and Gepts (1977) (cf. Chapter 1). In the model there is a consumption sector and a production sector. The two sectors take into account the future. The preferences of the consumption sector are represented by a utility function. The preferences concerning the future are supposed to be worked up in the utility function via a money variable as one of the arguments. The utility for money reflects the preferences and expectations of the consumption sector with respect to future expenditure and income. Nevertheless, for sake of simplicity, the utility function is assumed to be independent of present prices and quantity constraints.
Paul van den Heuvel

### 4. Dynamic Model

Abstract
In the preceding chapter the models covered a period, during which the price of goods and the wage rate were fixed. The present chapter contains an analysis of a somewhat longer term, in which prices are variable (capital and investments, however, are still neglected). A continuous time is introduced. Stocks and prices adjust over time in the following way.
Paul van den Heuvel

### 5. Stability Properties of the Different Types of Equilibria

Abstract
In this chapter some stability properties of equilibria of the models from the preceding section will be investigated. The system
$$\left\{ {\matrix{ {\mathop m\limits^ \circ = M(m,w,y)} \hfill & {(m,w,y)' \in X} \hfill \cr {\mathop w\limits^\circ = W(m,w,y)} \hfill & {} \hfill \cr {\mathop y\limits^ \circ = Y(m,w,y)} \hfill & {} \hfill \cr } } \right.$$
(4.20)
has several types of equilibria. As already pointed out in Section 4.5, for any element of the sets C and u the inequality$$\mathop w\limits^ \circ \ne 0$$ holds. So, equilibria of system (4.20) within these sets are impossible. There may be equilibria in the sets cl K and cl I. Equilibria in the sets K and I will be called Keynesian and Inflation equilibria, respectively. In an Inflation equilibrium the price of the good, the nominal wage rate wn and the nominal money stocks mn grow at the same rate. This inflation, however, does not affect the traded quantities of labour ℓ̂ and goods r̂, that are constant over time. In a Keynesian equilibrium the variables p, wn and mn decrease proportionally, so that there is a constant deflation and the quantities ℓ̂and r̂ are constant again.
Paul van den Heuvel

### 6. Conclusions

Abstract
In the models introduced in this thesis Non-Walrasian Equilibria appear. The conditions for Non-Walrasian Equilibria can be summarized as “optimality”, “voluntariness” and “rationing on the long side only” (see Subsection 1.4.2). We have investigated the Non-Walrasian Equilibria of the Barro and Grossman/Malinvaud model (see Barro and Grossman (1971) and Malinvaud (1977)) extended with the possibility of an inventory change in the production sector.
Paul van den Heuvel

### Backmatter

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