Quantity and number

Quantity is the first category that Aristotle lists after substance. It has extraordinary epistemological clarity: "2+2=4" is the model of a self-evident and universally known truth. Continuous quantities such as the ratio of circumference to diameter of a circle are as clearly known as discrete ones. The theory that mathematics was "the science of quantity" was once the leading philosophy of mathematics. The article looks at puzzles in the classification and epistemology of quantity

Fluid quantity gaging

A system for measuring the mass of liquid in a tank on orbit with 1 percent accuracy was developed and demonstrated. An extensive tradeoff identified adiabatic compression as the only gaging technique that is independent of gravity or its orientation, and of the size and distribution of bubbles in the tank. This technique is applicable to all Earth-storable and cryogenic liquids of interest for Space Station use, except superfluid helium, and can be applied to tanks of any size, shape, or internal structure. Accuracy of 0.2 percent was demonstrated in the laboratory, and a detailed analytical model was developed and verified by testing. A flight system architecture is presented that allows meeting the needs of a broad range of space fluid systems without custom development for each user

Quality or quantity?

The role of school quality in determining educational outcomes has received much research attention in the United States. However, in developing countries, where a significant part of the school age population never attends school, policymakers must consider both quality and quantity when deciding how to maximize the impact of scarce investments. Acknowledging this difference in the policy environment in developing countries, this paper provides comparative estimates of the impact of quality versus quantity investments in school supply in rural Mozambique, one of the world's poorest countries. Policy simulations show that improving school quality (through the pupil-teacher ratio) increases grade attainment and efficiency by approximately 9 percent with no impact on overall enrollment rates. However, these same results can be generated by increasing starting enrollment probabilities through the establishment of new schools in all rural villages that currently do not have schools. Furthermore, similar rates of increase in school achievement indicators can be achieved by building schools in only 56 percent of all villages currently without schools, provided these schools are placed in those villages that also do not have a school nearby. When cost information is considered, the main policy implication is that the expansion of school quantity through well targeted placement of new schools will provide the greatest increase in educational outcomes for Mozambique at this time.FCND ,School children. ,Education Economic aspects. ,Mozambique. ,

Quality or quantity?

The role of school quality in determining educational outcomes has received much research attention in the United States. However, in developing countries, where a significant part of the school age population never attends school, policymakers must consider both quality and quantity when deciding how to maximize the impact of scarce investments. Acknowledging this difference in the policy environment in developing countries, this paper provides comparative estimates of the impact of quality versus quantity investments in school supply in rural Mozambique, one of the world's poorest countries. Policy simulations show that improving school quality (through the pupil-teacher ratio) increases grade attainment and efficiency by approximately 9 percent with no impact on overall enrollment rates. However, these same results can be generated by increasing starting enrollment probabilities through the establishment of new schools in all rural villages that currently do not have schools. Furthermore, similar rates of increase in school achievement indicators can be achieved by building schools in only 56 percent of all villages currently without schools, provided these schools are placed in those villages that also do not have a school nearby. When cost information is considered, the main policy implication is that the expansion of school quantity through well targeted placement of new schools will provide the greatest increase in educational outcomes for Mozambique at this time.FCND ,School children. ,Education Economic aspects. ,Mozambique. ,

Reconstructing the Quantity Theory (I)

The quantity theory is disjunct to the hard core of general equilibrium theory. It does not relate to the formal foundations of standard economics and, vice versa, from the behavioral axioms of standard economics a rationale for using money cannot be derived. The present paper leaves the standard axioms aside and reconstructs the quantity theory from entirely new structural axiomatic foundations. This gives a coherent view of the interrelations of quantity of money, transaction money, saving–dissaving, liquidity–illiquidity, rates of interest, leverage, allocation, prices, profits, unit of account, and employment

Quantity Tropes and Internal Relations

In this article, we present a new conception of internal relations between quantity tropes falling under determinates and determinables. We begin by providing a novel characterization of the necessary relations between these tropes as basic internal relations. The core ideas here are that the existence of the relata is sufficient for their being internally related, and that their being related does not require the existence of any specific entities distinct from the relata. We argue that quantity tropes are, as determinate particular natures, internally related by certain relations of proportion and order. By being determined by the nature of tropes, the relations of proportion and order remain invariant in conventional choice of unit for any quantity and give rise to natural divisions among tropes. As a consequence, tropes fall under distinct determinables and determinates. Our conception provides an accurate account of quantitative distances between tropes but avoids commitment to determinable universals. In this important respect, it compares favorably with the standard conception taking exact similarity and quantitative distances as primitive internal relations. Moreover, we argue for the superiority of our approach in comparison with two additional recent accounts of the similarity of quantity tropes

Quantity Rationing of Credit

Quantity rationing of credit, when ?firms are denied loans, has greater potential to explain macroeconomics ?fluctuations than borrowing costs. This paper develops a DSGE model with both types of financial frictions. A deterioration in credit market con?fidence leads to a temporary change in the interest rate, but a persistent change in the fraction of ?firms receiving ?financing, which leads to a persistent fall in real activity. Empirical evidence confi?rms that credit market con?fidence, measured by the survey of loan officers, is a signi?cant leading indicator for capacity utilization and output, while borrowing costs, measured by interest rate spreads, is not.Quantity Rationing, Credit, VAR

Quantity Constrained General Equilibrium

In a standard general equilibrium model it is assumed that there are no price restrictions and that prices adjust infinitely fast to their equilibrium values.In case of price restrictions a general equilibrium may not exist and rationing on net demands or supplies is needed to clear the markets.In the mid 1970s it was shown that in case of upper and lower bound restrictions on the prices there exists a quantity constrained equilibrium at which not both demand and supply of a good are rationed simultaneously and there is rationing on the net supply or net demand of a good only if the price of that good is on its lower or upper bound, respectively.For an arbitrary set of admissible prices it was recently proposed to let the rationing schemes be determined by the components of a vector being a direction in which the prices are restricted to move.When the set of restricted prices is convex and compact, it was shown that there exists a connected set of such quantity constrained equilibria, containing two trivial no-trade equilibria without trade opportunities.In this paper we refine the concept of quantity constrained equilibrium and propose a specific quantity constrained equilibrium which may serve as a general equilibrium in case of price restrictions.At this equilibrium demand rationing and supply rationing are in balance with each other, so that trade opportunities are maximal and therefore trivial no-trade and other equilibria with less trade opportunities are excluded.Moreover, in equilibrium only relative prices matter. Any homogenous transformation or normalization of the set of admissible prices yields the same set of quantity constrained general equilibria up to scaling of the price vectors.exchange economy;price restrictions;general equilibrium;rationing

Quantity rationing of credit

Quantity rationing of credit, when firms are denied loans, has greater potential to explain macroeconomic fluctuations than borrowing costs. This paper develops a DSGE model with both types of financial frictions. A deterioration in credit market confidence leads to a temporary change in the interest rate, but a persistent change in the fraction of firms receiving financing, which leads to a persistent fall in real activity. Empirical evidence confirms that credit market confidence, measured by the survey of loan officers, is a significant leading indicator for capacity utilization and output, while borrowing costs, measured by interest rate spreads, is not.quantity rationing; credit; VAR