挑战书：市场均衡问题

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<p>请证明：</p><p>          一个有N种商品的经济，如果N-1个商品市场上已经实现了均衡，则第N个市场必定均衡！</p><p>最好有数学证明，请赐教！！！</p>

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关键词：市场均衡 挑战书 商品市场 数学 最好 挑战书

看微观经济学一般均衡那章

好像是基于一个瓦尔拉定理好像，你自己看看书就有了。

反证法：若否，则违反Warlas' Law。

In an exchange economy with

Two persons (A and B)

Two goods (1 and 2)

Where

p denotes price

x(p) denotes demand function

w denots endownment

e(p) denotes net demand function for each individual

z(p) denotes excess demand function for the market

Here goes the prove for Walras's Law for 2 market case (Varian Intermediate Microeconomics)

First consider two identities:

p1 * xA1(p1,p2) + p2 * xA2(p1,p2) = p1 * wA1 + p2 * wA2 (A's budget constraint)

p1 * xB1(p1,p2) + p2 * xB2(p1,p2) = p1 * wB1 + p2 * wB2 (B's budget constraint)

Rearrange:

p1 [xA1 - wA1] + p2 [xA2 - wA2] =0 => p1 * eA1(p1,p2) + p2 * eA2(p1,p2) = 0

p1 [xB1 - wB1] + p2 [xB2 - wB2] =0 => p1 * eB1(p1,p2) + p2 * eB2(p1,p2) = 0

Adding two equation together:

p1 [eA1 + eB1] + p2 [eA2 + eB2] = 0 =>

p1 * z1(p1,p2) + p2 * z2(p1,p2) = 0

Therefore, if N-1 market (in this case where N=2) is in equilibrium:

z1(p1,p2) = 0

Then the remaining market must in equilibrium:

z2(p1,p2) = 0

很难

哦