Wikipedia:Reference desk/Archives/Mathematics/2009 August 7

= August 7 =

Inferior goods and recessions
Is it normal for the price of inferior goods to rise during a recession? In May of this year, I noticed that since last summer the price of house-brand macaroni-and-cheese dinner had risen from $0.49 to $0.69 per box, and the price of the cheapest beers at the local beer store had gone from $24 to $25.60 per 24-pack. I doubt inflation alone is responsible. (All figures in Canadian dollars.) -- Neon Merlin  05:50, 7 August 2009 (UTC)


 * Food prices have increased in the past few years because of a run-up in the prices of the underlying commodities. See for example 2007–2008 world food price crisis.  Among other things the food vs. fuel debate has intensified because of the run-up.  The recession is probably a separate issue. 70.90.174.101 (talk) 05:57, 7 August 2009 (UTC)


 * I agree that it may just be general rising food prices. If it's just the inferior good rising, though, then it could be the recession. As people's income reduces they switch to cheaper alternatives, so the demand for inferior goods increases which will increase the price. It may well be a combination of the two. Of course, if your sample if just two items then it could just be complete coincidence. --Tango (talk) 19:21, 7 August 2009 (UTC)
 * Giffen good may be relevant, though this seems to be that effect in reverse. AndrewWTaylor (talk) 20:28, 8 August 2009 (UTC)

Line -> Triangle -> Pyramid -> ?
I was thinking today about how the centre of mass is 1/2 the way up a line, 1/3 the way up a triangle, 1/4 the way up a pyramid, and i was trying to describe the corresponding 4-D object it would be 1/5 the way up of. I can visualise it: clearly it would be any 4-dimensional shape with a cross-sectional volume which is uniformly shrinking in the 4th dimension. My friend said a 'pentachoron', but it's my understanding that this is more specific a term than I desire in that it restricts the number of vertices (sort of how tetrahedron is to triangle). What is the object I'm describing called? —Preceding unsigned comment added by 82.35.84.214 (talk) 18:32, 7 August 2009 (UTC)


 * Pentachoron is the word you want. You need to specify the number of vertices otherwise you haven't specified the shape. A line has 2 vertices, a triangle has 3, a tetrahedron (which is a type of pyramid and the one you want) has 4 and a pentachoron has 5. A general term for all those kind of shapes is a simplex. --Tango (talk) 18:59, 7 August 2009 (UTC)
 * But the centre of mass of any pyramid (or cone, to use a more common term) is 1/4 of the way from the base to the apex, whatever manner of pyramid/cone it may be. Algebraist 19:02, 7 August 2009 (UTC)
 * Is it? Ok. Then the desired term is a "4 dimensional cone" or a "cone over a 3 dimensional shape", I don't know of a shorter word (I guess "4-cone" would work). --Tango (talk) 19:17, 7 August 2009 (UTC)
 * We have a hypercone article, which is concerned with hypercones of spherical base volume (just like Cone (geometry) is mostly concerned with cones of circular base area), but it also hints that the word (just like the word "cone") has a wider meaning too. — JAO • T • C 19:19, 7 August 2009 (UTC)
 * The "hyper-" prefix is ambiguous - it sometimes means one dimension higher than usual and it sometimes means any number of dimensions higher (and sometimes is used as a general term for any number of dimensions). --Tango (talk) 19:24, 7 August 2009 (UTC)