Thursday, July 19, 2007

Checkers mathematically solved

Who would have thought such a simple game would take so long to solve. All you need to do is write out the game tree and employ backwards induction. No small task!


Checkers mathematically solved: "David Pescovitz: Checkers has officially been 'solved.' A new computer-generated mathematical proof reveals that a perfectly-played game of checkers (aka draughts) always ends in a draw. University of Alberta computer games researcher Jonathan Schaeffer spent 18 years on the problem, making it 'one of the longest running computations in history,' according to New Scientist:
At its peak, Schaeffer had 200 desktop computers working on the problem full time, although in later years he reduced this to 50 or so. 'The problem is such that if I made a mistake 10 years ago, all the work from then on would be wrong,' says Schaeffer. 'So I've been fanatical about checking for errors.' "



(Via Boing Boing.)

Wednesday, July 18, 2007

A Real World Giffen Good

Mankiw points to a new paper on the existence of the elusive Giffen goods.

A Real World Giffen Good: "Do such goods ever exist? A new study by Robert Jensen and Nolan Miller, economists at Harvard's Kennedy School, answers this question in the affirmative:

we conducted a field experiment in which for five months, randomly selected households were given vouchers that subsidized their purchases of their primary dietary staple. Building on the insights of our earlier analysis, we studied two provinces of China: Hunan in the south, where rice is the staple good, and Gansu in the north, where wheat is the staple. Using consumption surveys gathered before, during and after the subsidy was imposed, we find strong evidence that poor households in Hunan exhibit Giffen behavior with respect to rice. That is, lowering the price of rice via the experimental subsidy caused households to reduce their demand for rice, and removing the subsidy had the opposite effect. This finding is robust to a range of alternative specifications and methods of parsing the data. In Gansu, the evidence is somewhat weaker, and relies to a greater extent on segregating households that are poor from those that are too poor or not poor enough. We attribute the relative weakness of the case for Giffen behavior in Gansu to the partial failure of two of the basic conditions under which Giffen behavior is expected; namely that the staple good have limited substitution possibilities, and that households are not so poor that they consume only staple foods. Focusing our analysis on those whom the theory identifies as most likely to exhibit Giffen behavior, we find stronger evidence of its existence....

To the best of our knowledge, this is the first rigorous empirical evidence of Giffen behavior. It is ironic that despite a long search, in sometimes unusual settings, we found examples in the most widely consumed foods for the most populous nation in the history of humanity."



(Via Greg Mankiw's Blog.)


[AF]

Sunday, July 15, 2007

PGL and Mark Thoma on Greg Mankiw

PGL and Mark Thoma on Greg Mankiw: "Angry Bear: Fair Taxation: Mark Thoma reads a NYTimes oped by Greg Mankiw and has this comment:

Greg's use of the word 'only' in the sentence 'The poorest fifth of the population, with average annual income of $15,400, pays only 4.5 percent' makes it seem as though he does not consider that amount to be much of a burden to the poor, not like a rich taxpayer who 'forks-over' 31.1 percent of their income which seems to imply much more hardship. But remember, 'Fairness is not an economic concept.'"



(Via Brad DeLong's Blog.)


[AF]

Saturday, July 14, 2007

Fair Taxes? Depends What You Mean by ‘Fair’ - New York Times

How progressive are these numbers?

Fair Taxes? Depends What You Mean by ‘Fair’ - New York Times: "The C.B.O.’s most recent calculations of federal tax rates show a highly progressive system. (The numbers are based on 2004 data, but the tax code has not changed much since then.) The poorest fifth of the population, with average annual income of $15,400, pays only 4.5 percent of its income in federal taxes. The middle fifth, with income of $56,200, pays 13.9 percent. And the top fifth, with income of $207,200, pays 25.1 percent."



(Via .)