Changes in the parameters of an $n$-dimensional system of equations induce changes in its solutions. For a class of such systems, we determine the qualitative change in solutions given certain qualitative changes in parameters. Our methods and results are elementary yet useful. They highlight...

We prove that the English auction (with bidders that need not be ex ante identical and may have interdependent valuations) has an efficient ex post equilibrium. We establish this result for environments where it has not been previously obtained. We also prove two versions of the...

We prove that the English auction (with bidders that need not be ex ante identical and may have interdependent valuations) has an efficient ex post equilibrium. We establish this result for environments where it has not been previously obtained. We also prove two versions of the...

Integrating large quantities of variable renewable electricity generation remains a political and operational challenge. One of the main obstacles in Europe to installing at least 200 GWs of power from variable renewable sources is how to deal with the insufficient network capacity and the...

Analyzing price data from sequential German electricity markets, namely the day-ahead and intraday auction, a puzzling but apparently systematic pattern of price premiums can be identified. The price premiums are highly correlated with the underlying demand profile. As there is evidence that...

Analyzing price data from sequential German electricity markets, namely the day-ahead and intraday auction, a puzzling but apparently systematic pattern of price premiums can be identified. The price premiums are highly correlated with the underlying demand profile. As there is evidence that...

The European power grid can be divided into several market areas where the price of electricity is determined in a day-ahead auction. Market participants can provide continuous hourly bid curves and combinatorial bids with associated quantities given the prices. The goal of the auction is to...

We analyze geographic patterns of trade between individuals using transactions data from eBay and MercadoLibre, two large online auction sites. We find that distance continues to be an important deterrent to trade between geographically separated buyers and sellers, though to a lesser extent...

This paper surveys intergenerational altruism in neoclassical growth models. It first examines Barro's approach to intergenerational altruism, whereby successive generations are linked by recursive altruistic preferences. Individuals have an altruistic concern only for their children, who in...

In this paper, we examine an exchange economy with a financial market composed of three assets: a share of a stock, an European call option written on the stock, and a riskless bond.