Documentation The modelling approach

Stock-flow consistency

The economy is driven by the decentralized actions of agents. The agents are categorized as households, firms, and banks. They interact on markets. The households buy and consume goods, make investments, and provide labor to firms. The firms, on the other hand, hire labor and purchase capital goods in order to produce and sell goods. The banks, finally, act as the financial intermediaries between households and firms. That is, they manage transactions between non-bank agents, they offer saving contracts to households and loan contracts to firms, and they facilitate purchases of equity

In each market transaction a good or service is traded against money. Money therefore always runs from one agent to another. The financial system is thus closed. Each agent has a balance sheet that records his transactions and that reflects his economic situation. The model is therefore stock-flow consistent. Based on the cash flows and the balance sheets of the individual agents national accounting figures can be computed.

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Supply and demand

a) Any market in this model is constituted by a list of offers each of which specifies a quantity and an asked price. An offer can thus be depicted as a horizontal supply curve of a given length. When combined, these supply curves describe the total quantity that is offered in the market and the price spectrum at which this quantity is available.
b) All agents have limited information. Each potential customer who enters a market consults three randomly selected offers and chooses the one with the lowest price. His preferences are described by a demand curve. This curve captures the customer’s reservation price and the fact that purchasing decisions are marginal decisions. A transaction occurs if at least one supply curve intersects with the demand curve.
c,d) After a transaction the seller updates his offer by subtracting the sold quantity from the offered quantity. His supply curve thus becomes shorter and a new state of the market comes into being. This way the model evolves into the future. The fact that the agents enter the markets in a uniformly random order and the fact that all offers in the market have an equal selection probability guarantee that no agent has a systematic advantage over others.

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Physical Capital

Physical capital is represented by a grid in which each node represents one type of good. Each firm specializes in the production of one type of good. The different layers of the grid represent stages of production. There is a variety of different types of goods at each stage which are labeled in alphabetical order. However, only if firms settle at a certain node do goods of the respective type come into existence.
At each node, firms can only use inputs from the next higher stages as intermediate goods. Moreover, they need to employ labor and they may employ machines, which are produced outside of the grid. Labor and machines are non-specific, i.e. they can be allocated anywhere on the grid. Moreover, they are imperfect substitutes. Their use is, however, in any case complementary to the use of intermediate goods.

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Reaction algorithms

Households form their reservation prices based on the principle of diminishing marginal utility while firms and banks apply decision algorithms that are designed to maximize revenue and to minimize costs. An example of such an algorithm is given in the Table on the right. The idea is that, in order to find an estimate of the optimal price-quantity combination, the firms aim to continuously withhold a certain quantity from the market. If there remains an unsold quantity a firm knows that it did not sell its goods below the market value. Conversely, if a firm is unable to withhold quantity from the market this indicates that a higher price may have lead to higher revenues. The prices are adjusted accordingly.

Moreover, a firm that is able to produce its targeted quantity and to sell its entire produce estimates that the marketable quantity is greater than what is currently offered. Thus, more investments are launched. Conversely, a firm that is unable to produce its targeted quantity and which also has weak sales attempts to improve its market position by lowering both quantity and price.

Similar algorithms apply for the setting of wages and interest rates, for the liquidity management, and when making investment decisions.

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Competition

The sales and investment strategy outlined above enables firms to optimize their performance, given the demand for their products and the prices of their inputs. This is illustrated in the figure on the right. At any point in the triangle between the cost curve ac, the demand curve d, and the ordinate can a monopolist sell its entire produce. Given his algorithm, he will thus most likely choose a price that lies considerably above his average costs. If, however, a market is catered by more than one firm then these firms permanently challenge the market positions of one another and the microeconomic structure of the market changes constantly. In a competitive setting the microeconomic market structure changes constantly and prices and average costs approach each other. Competition between firms thus entails a reduction of the price level to the point where cost constraints become binding and an increase in the total quantity supplied to the maximum of what the customers accommodate at that price. Thus, the competition between the agents constantly pushes the economy towards a conceivable equilibrium, but this final state of rest is never reached as new events occur thus upsetting the convergence process.

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