Schema analysis

The complete schema analysis described here yielded three main findings. First, situational knowledge is sufficient to characterize story problems. Only a small set of situations is required to make the distinctions. This is a key point, because it renders feasible the quest for a basis set of schemas. Second, although situational knowledge may seem so obvious to the experienced researcher and educator as to be almost blatant, in fact, almost no students or teachers appear to be using it in problem solving. Virtually none of the more than 100 individuals in the studies here showed any awareness of situational detail. Third, as one would hope, situational knowledge is relatively easy for students to acquire. Even the mathematically naive students were able to understand and learn about the situations. 

My analytical contribution is to show how the Harrod-Domar model -more specifically, its Domar variant - can be derived from the multisectoral reproduction schema, with the multiplier and the monetary circuit as the key building blocks. These building blocks are defined using Leontief s input-output analysis, a model which has its origins in the Marxian economic tradition. 

A subtext of this analysis is an attempt to address some of the limitations of the reproduction schema. Two main limitations of the schema, as modelled in Chapters 2-6, are the absence of free competition, based on the mobility of capital, and the lack of any room for technical progress. Chapter 7 examines the Grossmann model of how technical progress drives the tendency of the falling rate of profit. And in Chapter 8, free competition is considered by turning to Marx s famous transformation problem a problem that has dominated discussions in Marxian economics. 

This analysis draws on a wide range of economic theory, both within the Marxian economic tradition and further a field in the traditions of Keynes, Kalecki, Domar, Sraffa and Leontief. In the same way that Marx was open to the whole corpus of classical economics in the nineteenth century, this book has as its aim the incorporation of various strands of economic thought in an attempt to understand and clarify the structure of the reproduction schema. 

Whichever interpretation is correct, Kalecki s silence on the labour theory of value leaves open the theoretical possibility that its relevance can be fruitfully explored. To relate Kalecki s model of reproduction to Marx s theory, a reconfiguration is required of the definition of profits. The problem, as we have seen, is that Kalecki s model requires a gross definition of profits that is different from Marx s category of surplus value. The Kalecki principle has not been precisely demonstrated in the context of Marx s reproduction schema, in which surplus value is the key category of analysis. 

What sets this circuit approach apart is its institutionally relevant analysis of the relationship between banks, firms and workers. A model of the circuit of money is developed in which prime importance is placed upon the role of banks in financing industrial activities. Central to this approach is an application of the Kalecki principle, that capitalists earn what they spend the question being how an injection of money can circulate around the economy and return back to the capitalists. Moreover, how is this circuit of money intertwined with the activities of industrial sectors And how much money is required for the circuit to be complete Marx s reproduction schema provides a natural starting point for addressing these questions. 

An emphasis on borrowing, with the multiplier firmly located in Marx s reproduction schema, is provided by the Domar model of economic growth. Instead of providing a snapshot of each period of production, the schema can be developed over an extended number of periods thereby providing a more complete picture of economic growth over time. The contribution of the following analysis will be to derive the model developed by Domar (1947) from foundations that are consistent with Marx s multisectoral schema. Domar s model is particularly suitable for this purpose because it specifies the conditions required for balanced growth. In contrast to Harrod s variant of the model, in which actual investment is determined by an accelerator mechanism, in Domar s model the actual level of investment... 

The Bauer/Grossmann interpretation of Marx s reproduction schema can be contrasted with our alternative perspective in which the role of money provides the focus of analysis. For Kalecki (1991c 241), it is capitalist investment and consumption decisions which determine profits, and not vice versa . In the Grossmann approach, however, capitalist consumption is a residual left over once capitalists have decided their production of surplus value, out of which new constant and variable capital are allocated. The capitalist consumption portion of surplus value is not determined by the amount of money advanced at the start of the production period, but by the portion left once production has been completed. 

Using the formula C, + Vt + S], values can be calculated for each department. In Department 1, for example, the total value of output is 120 in Department 2, the total value is 60. In our previous analysis of Marx s reproduction schema, based on the second volume of Capital, it was assumed that these values are also the total prices of each department. However, in the third volume Marx focuses on the organic composition of capital, which measures the ratio (Ct/Vt) between constant and variable capital.2 These ratios vary between 4 and 0.4 in this example. And it is this variation that leads Marx to argue that values cannot be sustained as indicators of price for each department of production. The problem is that the rate of profit (.SVC, + V) for each department is calculated as a ratio between total surplus value and total capital. Yet, for each department its own mass of surplus value is calculated from the variable capital employed. 

In the final analysis protein folding will be really understood only with the aid of much more extensive, direct experimental evidence. Speculative hypotheses can be useful, however, in suggesting potentially fruitful questions for experimental investigation. Probably the most important idea suggested by the above schema is that there are likely to be considerable systematic differences in the kinetics of folding between the various major structural categories of proteins. 

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Destination choice What forces are at work when people choose a destination, how destinations are imagined and imaged, how these images are built and how they are acted upon in selecting holiday places Multi-attribute destination schema Cognitive maps and image analysis Attitude theory Choice set models Activity augmented destination choice model... 

In the previous chapter I described in some detail how reference is fixed. There are simple sentences associated with each word which are responsible for its reference. Once we know the truth conditions of these sentences, the reference of a word is given by disquotational schemas. The truth conditions of these sentences are identical with their justification conditions. In the final analysis, reference is fixed by justification conditions. However, some justification conditions are inadequate, they are not conducive to truth in other words, they fail as truth conditions. What these inadequate justification conditions determine is relative reference the sort of reference we attribute to users of inadequate conceptual schemes when we give rationalizing explanation of their behavior. As to adequate justification conditions, we cannot do better than to identify them with our current justification conditions. Our current justification conditions may turn out to be inadequate. But we must take what we have. 

Figure 5.8b Principal Component Analysis on the four varietal wines. Representation of the loadings of the variables in PCI and PC2 in the by-plot schema of Figure 5.8a...

From the above analysis we observe that five situations are sufficient to cover the realm of story problems. And, from the evidence presented earlier, we observe that students do not draw on their understanding of these situations. We may conclude that students have not created appropriate schemas that utilize relevant situation knowledge, that is, schemas that build on previous experiences, that contain relevant abstractions, and that facilitate analogical reasoning. We come now to the crux of the matter If situation-based schemas develop, what will they look like ... 

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