tag:blogger.com,1999:blog-26706564.post115718051691161830..comments2024-03-25T07:51:47.758-04:00Comments on Thoughts On Economics: Contradiction In Arrow-Debreu Model Of Intertemporal Equilibrium?Robert Vienneauhttp://www.blogger.com/profile/14748118392842775431noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-26706564.post-1158601904077894882006-09-18T13:51:00.000-04:002006-09-18T13:51:00.000-04:00«The data of the Arrow-Debreu model of intertempor...«<I>The data of the Arrow-Debreu model of intertemporal equilibrium include the initial quantities, that is, the endowments of all commodities. This specification includes the distribution of these endowments, a statement of who owns what. Some of these endowments are unproduced natural resources which yield services over future time periods in the model. Other endowments can be conceptualized as capital goods, as produced means of production. In the model, markets clear once, at the beginning of time.</I>»<BR/><BR/>The purpose of this is to prove that the distribution of income for <I>factors</I> is uniquely determined by factor productivity, because that is the <B>verity</B> by which Economics gauges the validity of models.<BR/><BR/>There is no contradiction, because assumptions don't matter, only reaching the correct conclusion does.<BR/><BR/>Assuming initial endowments is absolutely vital to this purpose of the model.<BR/><BR/>The reason is that in order to prove the verity it is <I>essential</I> that factor demand must depend on their <I>price</I> instead of their <I>profitability</I> (because that involves the rate of interest).<BR/><BR/>That factor demand depends on price and not profitability is crucial to other tenets mainstream Economics, for example to prove Say's Law, without which it is phenomenally hard :-) to prove the existence and unicity of equilibrium; because if factor demand depends on profitability we get into Sraffian situations.<BR/><BR/>Unicity requires another assumption, convexity, which is assured only if demand (and supply) schedules are smoothly sloping downwards wrt to price.Anonymousnoreply@blogger.com