# 经济代写|微观经济学代写Microeconomics代考|ECON106

## 经济代写|微观经济学代写Microeconomics代考|Survival Again and Subsistence

The three possible assumptions that surmount the zero-income problem do not avoid the survival problem: they ensure that the income of each consumer will not be zero, but not that it will be sufficient for survival.

On the other hand, the assumption that each consumer has an endowment sufficient for survival does not suffice to avoid discontinuities, because another form of the zero-income problem, again a discontinuity of demand when a price becomes zero, can arise.

Consider a consumer with strongly monotonic preferences, who has an endowment of two units of good 1 and one unit of good 2 and needs one unit of both goods for survival. Figure $6.7$ shows the consumption set defined as excluding non-survival baskets and the endowment $\omega=(2,1)$ of the representative consumer. At any positive $p_1 / p_2$ the consumer demands possibly less but never more than two units of good 1 because that would mean to consume less than one unit of good 2; when $\mathrm{p}_1=0$ she jumps to demanding an infinite amount of good 1.

Note that monotonic preferences are not sufficient to avoid this problem, unless there are consumers who have an income in excess of what they need for survival and therefore can have a demand for good 1 in excess of their subsistence needs when $\mathrm{p}_1$ approaches zero.

So some assumption ensuring no discontinuity at a zero price is needed in addition to something guaranteeing survival. There is no possibility here to illustrate the details of the literature on this issue (see Bryant 2010, Chap. 2), but it seems possible to say that, apart from a blunt assumption that each consumer’s income is always above what is needed to purchase a survival level of consumption but without indication of what is required to ensure this, the two assumptions which surmount this more general minimum-income problem are as follows:
Interiority Beyond Survival $\quad\left(\mathrm{B}^{\prime}\right)$ Each consumer has an endowment where all goods are in excess of survival needs ${ }^{10}$; this guarantees that the consumer, after setting aside enough of her endowment to ensure survival, remains with a strictly positive residual endowment of all goods and is therefore in the same condition relative to market interactions as she would be under condition B if she had zero survival necds;

## 经济代写|微观经济学代写Microeconomics代考|Existence of General Equilibrium of Exchange

We have already seen ( Sect. 4.7) that in the case of only two commodities at least one equilibrium certainly exists if:

1. $\mathbf{z}(\mathbf{p})$ is a continuous function on the interior of the price simplex $\mathrm{S}^{\mathrm{n}-1}:=\left{\mathbf{p} \in \mathrm{R}^{\mathrm{n}}{ }{+}: \Sigma{\mathrm{i}} \mathrm{p}_{\mathrm{i}}=1\right}$
2. some $z_i(\mathbf{p}) \rightarrow+\infty$ when some $p_j \rightarrow 0$, where it can be but it need not be $i=j$.
The proof that an equilibrium exists for a higher (but finite) number of commodities can be obtained, but the less restrictive the assumptions, the longer the proof and the more complex the mathematical tools. To go over the several possible proofs at different degrees of generality and with different methods would take an entire book. I present one very simple proof under restrictive assumptions and a less simple one to get a feeling of the kind of proof methods used in this area.
In all existence proofs it is assumed that of all goods of which a price is quoted there is a positive aggregate endowment. ${ }^{13}$

## 经济代写|微观经济学代写微观经济学代考|交换一般均衡的存在

1. $\mathbf{z}(\mathbf{p})$是价格单纯形内部的一个连续函数$\mathrm{S}^{\mathrm{n}-1}:=\left{\mathbf{p} \in \mathrm{R}^{\mathrm{n}}{ }{+}: \Sigma{\mathrm{i}} \mathrm{p}_{\mathrm{i}}=1\right}$
2. some $z_i(\mathbf{p}) \rightarrow+\infty$当some $p_j \rightarrow 0$，它可以是，但不一定是$i=j$
可以得到对较高(但有限)数量的商品存在均衡的证明，但假设的限制性越小，证明就越长，数学工具就越复杂。要用不同程度的普遍性和不同的方法来复习这几种可能的证明，就要花上整整一本书。我在限制性假设下提出了一个非常简单的证明和一个不那么简单的证明，以了解在这个领域中使用的证明方法。在所有的存在证明中，都假设所有报价的商品的总禀赋都是正的。${ }^{13}$

myassignments-help数学代考价格说明

1、客户需提供物理代考的网址，相关账户，以及课程名称，Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明，让您清楚的知道您的钱花在什么地方。

2、数学代写一般每篇报价约为600—1000rmb，费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵)，报价后价格觉得合适，可以先付一周的款，我们帮你试做，满意后再继续，遇到Fail全额退款。

3、myassignments-help公司所有MATH作业代写服务支持付半款，全款，周付款，周付款一方面方便大家查阅自己的分数，一方面也方便大家资金周转，注意:每周固定周一时先预付下周的定金，不付定金不予继续做。物理代写一次性付清打9.5折。

Math作业代写、数学代写常见问题

myassignments-help擅长领域包含但不是全部: