Price Discrimination between Retailers with and without Market Power

Some retail markets are more competitive than others. A manufacturer with market power in the wholesale market who sells his product to competing retailers in cities and monopolistic ones in each of various towns must set the wholesale price difference between towns and cities to be smaller than the transportation cost to prevent “grey market” arbitrage. If he uses linear pricing, the town retail price will be even higher than under single-retailer double marginalization. Two-part tariffs do not solve the problem as they would if there were a single retailer, because the wholesale unit price must be higher than marginal cost to prevent arbitrage to the cities. If transportation costs are low, price discrimination is difficult and two- part tariffs come to resemble inefficient linear monopoly pricing. High transportation costs allow greater efficiency in contracting, and this can outweigh the negative direct effect on welfare.price discrimination, double marginalization, retail network, transportation costs, two-part tariffs, vertical restraints

What Has Financed Government Debt?

Equilibrium models imply that the real value of debt in the hands of the public must equal the expected present-value of surpluses. Empirical models of fiscal policy typically do not impose this condition and often do not even include debt. Absence of debt from empirical models can produce non-invertible representations, obscuring the true present-value relation, even if it holds in the data. First, we show that small VAR models of fiscal policy may not be invertible and that expanding the information set to include government debt has quantitatively important implications. Then we impose the present-value condition on an identified VAR and characterize the way in which the present-value support of debt varies across types of fiscal shocks. The role of expected primary surpluses in supporting innovations to debt depends on the nature of the shock. Debt is supported almost entirely by changes in the present-value of surpluses for some fiscal shocks, but for other fiscal shocks surpluses fail to adjust, leaving a large role for expected changes in discount rates. Horizons over which debt innovations are financed are long---on the order of 50 years or more.fiscal policy, present-value restriction, taxes, government spending

An adaptive GMsFEM for high-contrast flow problems

In this paper, we derive an a-posteriori error indicator for the Generalized Multiscale Finite Element Method (GMsFEM) framework. This error indicator is further used to develop an adaptive enrichment algorithm for the linear elliptic equation with multiscale high-contrast coefficients. The GMsFEM, which has recently been introduced in [12], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space, (2) the construction of the offline space, and (3) the construction of the online space (the latter for parameter-dependent problems). In [12], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we study an adaptive enrichment procedure and derive an a-posteriori error indicator which gives an estimate of the local error over coarse grid regions. We consider two kinds of error indicators where one is based on the $L^2$-norm of the local residual and the other is based on the weighted $H^{-1}$-norm of the local residual where the weight is related to the coefficient of the elliptic equation. We show that the use of weighted $H^{-1}$-norm residual gives a more robust error indicator which works well for cases with high contrast media. The convergence analysis of the method is given. In our analysis, we do not consider the error due to the fine-grid discretization of local problems and only study the errors due to the enrichment. Numerical results are presented that demonstrate the robustness of the proposed error indicators.Comment: 26 page

What Has Financed Government Debt?

Dynamic rational expectations models imply that the real value of debt in the hands of the public must be equal to the expected present-value of surpluses. We impose this equilibrium condition on an identified VAR and characterize the way in which the present-value support of debt varies across various types of fiscal policy shocks and between fiscal and non-fiscal shocks. The role of expected primary surpluses in supporting innovations to debt depends on the nature of the shock. For some fiscal policy shocks, debt is supported almost entirely by changes in the present-value of surpluses, however, in the case of other fiscal policy shocks, surpluses fail to adjust and instead leave a large role for expected changes in discount rates. Horizons over which debt innovations are financed are long – on the order of fifty years – while present-values calculated up to any finite horizon up to then fluctuate wildly, particularly following government spending and transfer shocks.

Generalized Multiscale Finite Element Method for Elasticity Equations

In this paper, we discuss the application of Generalized Multiscale Finite Element Method (GMsFEM) to elasticity equation in heterogeneous media. Our applications are motivated by elastic wave propagation in subsurface where the subsurface properties can be highly heterogeneous and have high contrast. We present the construction of main ingredients for GMsFEM such as the snapshot space and offline spaces. The latter is constructed using local spectral decomposition in the snapshot space. The spectral decomposition is based on the analysis which is provided in the paper. We consider both continuous Galerkin and discontinuous Galerkin coupling of basis functions. Both approaches have their cons and pros. Continuous Galerkin methods allow avoiding penalty parameters though they involve partition of unity functions which can alter the properties of multiscale basis functions. On the other hand, discontinuous Galerkin techniques allow gluing multiscale basis functions without any modifications. Because basis functions are constructed independently from each other, this approach provides an advantage. We discuss the use of oversampling techniques that use snapshots in larger regions to construct the offline space. We provide numerical results to show that one can accurately approximate the solution using reduced number of degrees of freedom