I’m Ashamed to Admit but I Have Watched Dallas. The Value Hierarchy of TV Programs

Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 dofinansowane zostało ze środków MNiSW w ramach działalności upowszechniającej naukę

International Trade and Search

The standard model of international trade based on Dixit-Stiglitz theory of monopolistic competition originally developed by Helpman and Krugman is extended to allow for costly search and matching between producers of different varieties and retailers. This extension provides a new way of characterizing how the economy is divided in closed and open sectors. Trade policies will naturally have an effect on this division. The entry and exit of retailers and producers is modeled. It is shown that these (both gross and temporarily also net) flows (and the associated job flows) are affected by policies. Tariffs increase gross flows of retailers relative to producers. Gross flows will also be increased in the sector favored by policies. This provides a potentially fruitful hypothesis for empirical work. In contrast to the standard model, trade policies have also an effect on the scale of output by individual producers. Finally, the welfare effects of tariffs are surprising. Tariffs can improve welfare if they switch enough productive resources from the producers in the matching process relative to producers already matched and producing. This result is new to the literature.

Ahlfors-David regular sets and bilipschitz maps

Given two Ahlfors-David regular sets in metric spaces, we study the question whether one of them has a subset bilipschitz equivalent with the other

Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes

We present strong versions of Marstrand's projection theorems and other related theorems. For example, if E is a plane set of positive and finite s-dimensional Hausdorff measure, there is a set X of directions of Lebesgue measure 0, such that the projection onto any line with direction outside X, of any subset F of E of positive s-dimensional measure, has Hausdorff dimension min(1,s), i.e. the set of exceptional directions is independent of F. Using duality this leads to results on the dimension of sets that intersect families of lines or hyperplanes in positive Lebesgue measure.Comment: 8 page