Stock and flow

Economics, business, accounting, and related fields often distinguish between quantities that are stocks and those that are flows. These differ in their units of measurement. A stock is measured at one specific time, and represents a quantity existing at that point in time (say, December 31, 2004), which may have accumulated in the past. A flow variable is measured over an interval of time. Therefore, a flow would be measured per unit of time (say a year). Flow is roughly analogous to rate or speed in this sense. For example, U.S. nominal gross domestic product refers to a total number of dollars spent over a time period, such as a year. Therefore, it is a flow variable, and has units of dollars/year. In contrast, the U.S. nominal capital stock is the total value, in dollars, of equipment, buildings, and other real productive assets in the U.S. economy, and has units of dollars. The diagram provides an intuitive illustration of how the stock of capital currently available is increased by the flow of new investment and depleted by the flow of depreciation. Thus, a stock refers to the value of an asset at a balance date (or point in time), while a flow refers to the total value of transactions (sales or purchases, incomes or expenditures) during an accounting period. If the flow value of an economic activity is divided by the average stock value during an accounting period, we obtain a measure of the number of turnovers (or rotations) of a stock in that accounting period. Some accounting entries are normally always represented as a flow (e.g. profit or income), while others may be represented both as a stock or as a flow (e.g. capital). A person or country might have stocks of money, financial assets, liabilities, wealth, real means of production, capital, inventories, and human capital (or labor power). Flow magnitudes include income, spending, saving, debt repayment, fixed investment, inventory investment, and labor utilization. These differ in their units of measurement. Capital is a stock concept which yields a periodic income which is a flow concept.

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Flow Time Scheduling and Prefix Beck-Fiala

Ola Nils Anders Svensson, Lars Rohwedder

We relate discrepancy theory with the classic scheduling problems of minimizing max flow time and total flow time on unrelated machines. Specifically, we give a general reduction that allows us to transfer discrepancy bounds in the prefix Beck-Fiala (bounded iota 1-norm) setting to bounds on the flow time of an optimal schedule. Combining our reduction with a deep result proved by Banaszczyk via convex geometry, give guarantees of O(root logn) and O( root logn logp) for max flow time and total flow time, respectively, improving upon the previous best guarantees of O(logn) and O( log n log p). Apart from the improved guarantees, the reduction motivates seemingly easy versions of prefix discrepancy questions: any constant bound on prefix Beck-Fiala where vectors have sparsity two (sparsity one being trivial) would already yield tight guarantees for both max flow time and total flow time. While known techniques solve this case when the entries take values in {-1, 0, 1}, we show that they are unlikely to transfer to the more general 2-sparse case of bounded iota 1-norm.

ASSOC COMPUTING MACHINERY2022

Fixed investment

Fixed investment in economics is the purchasing of newly produced fixed capital. It is measured as a flow variable – that is, as an amount per unit of time. Thus, fixed investment is the accumulation of physical assets such as machinery, land, buildings, installations, vehicles, or technology. Normally, a company balance sheet will state both the amount of expenditure on fixed assets during the quarter or year, and the total value of the stock of fixed assets owned.

Plus-value (marxisme)

La plus-value (ou parfois survaleur) est un concept forgé par Proudhon, puis repris et développé par Karl Marx dans sa critique de l'économie politique et de l'exploitation capitaliste, et ensuite détaillé dans Le Capital. Karl Marx reprend et complète la théorie de la valeur des économistes classiques (Adam Smith, David Ricardo, etc.), et développe l'idée que la source de la valeur d’échange d’une marchandise est la quantité de travail (socialement nécessaire) qui y est incorporée.

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