Gaps in Protoplanetary Disks as Signatures of Planets: I. Methodology and Validation

We examine the observational consequences of partial gaps being opened by planets in protoplanetary disks. We model the disk using a static alpha-disk model with detailed radiative transfer, parametrizing the shape and size of the partially cleared gaps based on the results of hydrodynamic simulations. Shadowing and illumination by stellar irradiation at the surface of the gap leads to increased contrast as the gap trough is deepened by shadowing and cooling and the far gap wall is puffed up by illumination and heating. In calculating observables, we find that multiple scattering is important and derive an approximation to include these effects. A gap produced by a 200 M_Earth (70 M_Earth) planet at 10 AU can lower/raise the midplane temperature of the disk by up to ~-25/+29% (~-11/+19%) by shadowing in the gap trough and illumination on the far shoulder of the gap. At the distance of Taurus, this gap would be resolvable with ~0.01" angular resolution. The gap contrast is most significant in scattered light and at thermal continuum wavelengths characteristic of the surface temperature, reducing or raising the surface brightness by up to order of magnitude. Since gaps sizes are correlated to planet mass, this is a promising way of finding and determining the masses of planets embedded in protoplanetary disks.Comment: 11 pages, 9 figures. Accepted to Ap

The influence of line tension on the formation of liquid bridges

The formation of liquid bridges between a planar and conical substrates is analyzed macroscopically taking into account the line tension. Depending on the value of the line tension coefficient \tau and geometric parameters of the system one observes two different scenarios of liquid bridge formation upon changing the fluid state along the bulk liquid-vapor coexistence. For \tau > \tau * (\tau * < 0) there is a first-order transition to a state with infinitely thick liquid bridge. For \tau < \tau * the scenario consists of two steps: first there is a first-order transition to a state with liquid bridge of finite thickness which upon further increase of temperature is followed by continuous growth of the thickness of the bridge to infinity. In addition to constructing the relevant phase diagram we examine the dependence of the width of the bridge on thermodynamic and geometric parameters of the system.Comment: 4 pages, 5 figure

Capital-Labor Substitution, Equilibrium Indeterminacy, and the Cyclical Behavior of Labor Income

This paper examines the quantitative relationship between the elasticity of capital-labor substitution and the conditions needed for equilibrium indeterminacy (and belief-driven áuctuations) in a one-sector growth model. Our analysis employs a ìnormalizedîversion of the CES production function so that all steady-state allocations and factor income shares are held constant as the elasticity of substitution is varied. We demonstrate numerically that higher elasticities cause the threshold degree of increasing returns for indeterminacy to decline monotonically, albeit very gradually. When the elasticity of substitution is unity (the Cobb-Douglas case), our model requires increasing returns to scale of around 1.08 for indeterminacy. When the elasticity of substitution is raised to 5, which far exceeds any empirical estimate, the threshold degree of increasing returns reduces to around 1.05. We also demonstrate analytically that laborís share of income becomes pro-cyclical as the elasticity of substitution increases above unity, whereas laborís share in postwar U.S. data is countercyclical. This observation, together with other empirical evidence, indicates that the elasticity of capital-labor substitution in the U.S. economy is actually below unity.Capital-Labor Substitution, Equilibrium Indeterminacy, Capital Utilization, Real Business Cycles, Labor Income

Indeterminacy and stabilization policy

A demonstration of how an income tax schedule that exhibits a progressivity feature can ensure saddle-path stability in a one-sector, real business-cycle model with sufficient increasing returns in production, thereby shielding the economy against sunspot fluctuations.Economic stabilization ; Business cycles

Tax structure, welfare, and the stability of equilibrium in a model of dynamic optimal fiscal policy

A demonstration that the assumed structure of taxation can have dramatic effects on economic welfare and on the stability of the steady state in a dynamic general-equilibrium model of optimal fiscal policy. The authors find that household welfare is highest under a structure that includes separate tax rates on labor and capital incomes, double taxation of dividends, and tax-deductible depreciation.Taxation ; Fiscal policy

The welfare effects of tax simplification: a general-equilibrium analysis

An analysis of various schemes for simplifying the U.S. tax system, which finds that a uniform tax system performs almost as well as a system with separate taxes on labor and capital incomes, provided that a depreciation allowance is maintained.Taxation

Capital-labor substitution, equilibrium indeterminacy, and the cyclical behavior of labor income

This paper examines the quantitative relationship between the elasticity of capital-labor substitution and the conditions needed for equilibrium indeterminacy (and belief-driven fluctuations) in a one-sector neoclassical growth model. Our analysis employs a “normalized” version of the CES production function so that all steady-state allocations and factor income shares are held constant as the elasticity of substitution is varied. We demonstrate numerically that higher elasticities cause the threshold degree of increasing returns for indeterminacy to decline monotonically, albeit very gradually. When the elasticity of substitution is unity (the Cobb-Douglas case), our model requires increasing returns to scale of around 1.08 for indeterminacy. When the elasticity of substitution is raised to 5, which far exceeds any empirical estimate, the threshold degree of increasing returns reduces to around 1.05. We also demonstrate analytically that labor’s share of income becomes procyclical as the elasticity of substitution increases above unity, whereas labor’s share in postwar U.S. data is countercyclical. This observation, together with other empirical evidence, indicates that the elasticity of capital-labor substitution in the U.S. economy is actually below unity.Capital ; Labor supply

Optimal taxation of capital income in a growth model with monopoly profits

An extension of the standard neoclassical growth model, demonstrating that the optimal steady-state tax on capital income can be positive, negative, or zero, depending on the level of monopoly profits and the degree to which profits can be taxed.Taxation ; Dividends

Tax structure, optimal fiscal policy, and the business cycle

The development of a real business cycle model in which government fiscal variables such as tax rates and public expenditures are endogenous. The authors characterize the "optimal" behavior of these policy variables over the business cycle and relate this behavior to movements in private-sector variables like output, consumption, labor hours, and investment.Business cycles ; Taxation ; Fiscal policy