64,495 research outputs found

    Concave consumption function and precautionary wealth accumulation

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    This paper examines the theoretical foundations of precautionary wealth accumulation in a multi-period model where consumers face uninsurable earnings risk and borrowing constraints. We begin by characterizing the consumption function of individual consumers. We show that consumption function is concave when the utility function has strictly positive third derivative and the inverse of absolute prudence is a concave function. These conditions encompass all HARA utility functions with strictly positive third derivative as special cases. We then show that when consumption function is concave, a mean-preserving spread in earnings risk would encourage wealth accumulation at both the individual and aggregate levels.Consumption function, borrowing constraints, precautionary saving

    Concave Consumption Function under Borrowing Constraints

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    This paper analyzes the optimal consumption behavior of a consumer who faces uninsurable labor income risk and borrowing constraints. In particular, it provides conditions under which the decision rule for consumption is a concave function of existing assets. The current study presents two main findings. First, it is shown that the consumption function is concave if the period utility function is drawn from the HARA class and has either strictly positive or zero third derivative. Second, it is shown that the same result can be obtained for certain period utility functions that are not in the HARA class.Consumption function, borrowing constraints, precautionary saving

    Bounding the CRRA Utility Functions

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    The constant-relative-risk-aversion (CRRA) utility function is now predominantly used in quantitative macroeconomic studies. This function, however, is not bounded and thus creates problems when applying the standard tools of dynamic programming. This paper devises a method for "bounding" the CRRA utility functions. The proposed method is based on a set of conditions that can establish boundedness among a broad class of utility functions. These results are then used to construct a bounded utility function that is identical to a CRRA utility function except when consumption is very small or very large. It is shown that the constructed utility function also satisfies the Inada condition and is consistent with balanced growth.Utility Function; Elasticity of Marginal Utility; Boundedness

    Technological Advance and the Growth in Health Care Spending

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    The second half of the twentieth century recorded a rapid growth in health care spending and a significant increase in life expectancy. This paper hypothesizes that the combination of techno-logical progress in medical treatment and rising incomes is the driving force behind these two trends. Using a stochastic, multi-period overlapping-generations model as the analytical vehicle, this paper argues that the rapid growth in medical spending is not driven by factors associated with market structures or insurance opportunities, but instead by factors underlying the production and accumulation of health. According to this model, improvements in medical treatment and rising incomes can explain all of the increase in medical spending and more than 60% of the increase in life expectancy at age 25 during the second half of the twentieth century.Technological progress, life expectancy, medical spending, health

    Ballistic trajectory: parabola, ellipse, or what?

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    Mechanics texts tell us that a particle in a bound orbit under gravitational central force moves on an ellipse, while introductory physics texts approximate the earth as flat, and tell us that the particle moves in a parabola. The uniform-gravity, flat-earth parabola is clearly meant to be an approximation to a small segment of the true central-force/ellipse orbit. To look more deeply into this connection we convert earth-centered polar coordinates to ``flat-earth coordinates'' by treating radial lines as vertical, and by treating lines of constant radial distance as horizontal. With the exact trajectory and dynamics in this system, we consider such questions as whether gravity is purely vertical in this picture, and whether the central force nature of gravity is important only when the height or range of a ballistic trajectory is comparable to the earth radius. Somewhat surprisingly, the answers to both questions is ``no,'' and therein lie some interesting lessons.Comment: 7 pages, 3 figure

    The infra-red spectrum and molecular structure of HNCS

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    From an examination of the microwave spectra of four isotopic species of isothiocyanic acid, Beard and Dailey (1) recently obtained the following values for the molecular parameters in the ground vibrational state

    Bounding the CRRA Utility Functions

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    The constant-relative-risk-aversion (CRRA) utility function is now predominantly used in quantitative macroeconomic studies. This function, however, is not bounded and thus creates problems when applying the standard tools of dynamic programming. This paper devises a method for "bounding" the CRRA utility functions. The proposed method is based on a set of conditions that can establish boundedness among a broad class of utility functions. These results are then used to construct a bounded utility function that is identical to a CRRA utility function except when consumption is very small or very large. It is shown that the constructed utility function also satisfies the Inada condition and is consistent with balanced growth.Utility Function; Elasticity of Marginal Utility; Boundedness

    The Spectrum Characteristic of Hydrogen Bonds

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    It has been observed that in certain substances containing hydroxyl hydrogen the relatively narrow and intense absorption bands which ordinarily are characteristic of the O-H group appear to be absent. Since in these cases it appears very probable that the hydroxyl hydrogen is involved in the formation of the type of linkage known as the "hydrogen bond" it has been suggested that the absence of bands may be taken as a criterion for the presence of such bond (1). On the other hand the O-H fundamental band appears strongly in a number of substances containing hydroxyl groups in which the hydrogens are supposed to be engaged in linkages which Bernal and Megal prefer, in this case, to call "hydroxyl bonds" (2). These substances include ice and a number of minerals examined by Coblentz (3). These observations have left the situation somewhat unclear since they leave the question open as to whether the O-H absorption in the cases first mentioned has merely shifted to some new region where it has not been observed, or whether it has really disappeared. If the latter were true there would appear to be a considerable difference between the hydrogen linkages in the two cases
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