[求助]关于预算线，没你想象中简单

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<P>关于预算线（<FONT face="Times New Roman">budget line</FONT>）</P>
<P>预算线的含义：</P>
<P>高鸿业版：又称为预算约束线、消费可能线和价格线。预算线表示在消费者的收入和商品的价格给定的条件下，消费者的全部所能购买到的两种商品的各种组合。</P>
<P>平狄克版：代表了消费者用尽其所有收入购买的商品的所有组合。<FONT face="Times New Roman">P<SUB>F</SUB>F+P<SUB>C</SUB>C=I</FONT></P>
<P>萨缪尔森版（英文版·<FONT face="Times New Roman">16</FONT>版）：<FONT face="Times New Roman">When a consumer has fixed money income, all of which she spends, and is confronted with market prices of two goods, she is constrained to move along a straight line called the budget line or budget constraint. The line’s slope will depend on the ratio of the two market prices; how far out it lies will depend on the size of her income.</FONT></P>
<P>周惠中版：消费者的收入和商品的价格决定了消费者的购买力。我们用预算约束或预算曲线来表示消费者的购买力。一般说来，预算约束是线性的，但如果消费者的收入受到税收或补贴的影响，或者价格因购买量的不同，那么，预算约束便可能是非线性的。预算约束的概念可以推延到时间约束、票证约束等。</P>
<P>
<P><FONT face="Times New Roman"></FONT></P>


<P>疑问：（周惠忠的一道题）</P>
<P>教委决定在高校文科师生中普及计算机的应用。目前，一般高校将六十万元教研经费中的二十万元用于计算机普及，而教委希望增加这方面的费用。有关部门提出了几个不同的方案</P>
<P><FONT face="Times New Roman">……</FONT></P>
<P>方案<FONT face="Times New Roman">B</FONT>：给每校增拨十万元，但动用这笔经费的条件是学校在计算机教育方面至少花费十万元。</P>
<P>方案<FONT face="Times New Roman">C</FONT>：给每校增拨十万元，但动用这笔经费的条件是学校在计算机教育方面的开支比目前的水平至少多十万元。</P>
<P><FONT face="Times New Roman">……</FONT></P>
<P>
<P><FONT face="Times New Roman"></FONT></P>
<p>
<P>我的问题一：</P>
<P>我的一位研究生学长说：“因为各教材中给的预算线表达式为：<FONT face="Times New Roman">I=P<SUB>X1</SUB>X<SUB>1</SUB>+P<SUB>X2</SUB>X<SUB>2</SUB>,</FONT>其中变量为<FONT face="Times New Roman">X<SUB>1</SUB></FONT>、<FONT face="Times New Roman">X<SUB>2</SUB>,</FONT>所以该题只能做定性分析，不能做定量分析。”
<p>
<p>
<P>我的疑问是：可否把<FONT face="Times New Roman"><FONT size=1>P<SUB>X1</SUB>X<SUB>1</SUB>、P<SUB>X2</SUB>X<SUB>2</SUB></FONT></FONT>作为变量？
<p>
<p>
<P>那么此题“金钱约束”（按周惠中对预算约束的推延）的斜率为<FONT face="Times New Roman">-1</FONT>，截距为<FONT face="Times New Roman">60</FONT>万，这样就可以定量分析。</P>
<P>
<P><FONT face="Times New Roman"></FONT></P>
<p>
<P>我的问题二：</P>
<P>怎样解释下图</P>
<P><img src="http://pic.pinggu.com/attachments/uploadfile_20082009/2005-10/20051016204839807.jpg" border="0" onload="if(this.width>document.body.clientWidth*0.5) {this.resized=true;this.width=document.body.clientWidth*0.5;this.style.cursor='pointer';} else {this.onclick=null}" alt="" /></P>
<P>解释一：学校在计算机的支出达到十万元时，给予其十万元补贴，且必须全部用于计算机支出</P>
<P>解释二：学校在计算机的支出至少为十万元时，给予其十万元补贴，且必须全部用于计算机支出</P>
<P>
<P><FONT face="Times New Roman"></FONT></P>
<p>
<P>我的解释是解释一，但学长告诉我：“这两个解释是一样的。”“达到”和“至少为”怎么能一样呢？甚为不解，有没有高手能指点一下，还是学长错了。</P>
<P>
<P><FONT face="Times New Roman"></FONT></P>
<p>
<P>我的问题三：</P>
<P>预算线可以画成方案组的么？</P>
<P>（如下图：在承认问题一的“金钱约束”的前提下）</P>
<P>
<img src="http://pic.pinggu.com/attachments/uploadfile_20082009/2005-10/20051016204929538.jpg" border="0" onload="if(this.width>document.body.clientWidth*0.5) {this.resized=true;this.width=document.body.clientWidth*0.5;this.style.cursor='pointer';} else {this.onclick=null}" alt="" />
</P>
<P>望指点，谢谢。</P>

[此贴子已经被作者于2005-10-16 21:35:43编辑过]

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关键词：预算线 Constrained Constraint constrain Consumer 萨缪尔森 budget called income market

你最好把题给完整的写一下

你这样抽取其中一部分写不太好懂

只有你的问题二，我懂了，那两个解释是一样的（提醒一下：不要在字眼上扣，关键是这两句话的实质是否一样，即画出的图有没有本质的区别，达到10万和至少为10万都是说，只要你的支出在10万以上就可以获得10万的拨款）

以下是引用xntm在2005-10-16 21:13:09的发言：

你最好把题给完整的写一下

你这样抽取其中一部分写不太好懂

只有你的问题二，我懂了，那两个解释是一样的（提醒一下：不要在字眼上扣，关键是这两句话的实质是否一样，即画出的图有没有本质的区别，达到10万和至少为10万都是说，只要你的支出在10万以上就可以获得10万的拨款）

问题是：我认为如果用至少的话可以画很多图，那一幅只是其中之一（等于十万元），十万元以上（如二十万），他们在逻辑上是“或”的关系

原题：（范里安习题集的第五章答案）

5.10 (0) Central High School has $60,000 to spend on computers and other stu, so its budget equation is C + X = 60; 000, where C is ex- penditure on computers and X is expenditures on other things. C.H.S. currently plans to spend $20,000 on computers. The State Education Commission wants to encourage \computer lit- eracy" in the high schools under its jurisdiction. The following plans have been proposed. Plan A: This plan would give a grant of $10,000 to each high school in the state that the school could spend as it wished. Plan B: This plan would give a $10,000 grant to any high school, so long as the school spent at least $10,000 more than it currently spends on computers. Any high school can choose not to participate, in which case it does not receive the grant, but it doesn't have to increase its expenditure on computers. Plan C: Plan C is a \matching grant." For every dollar's worth of computers that a high school orders, the state will give the school 50 cents. Plan D: This plan is like plan C, except that the maximum amount of matching funds that any high school could get from the state would be limited to $10,000. (a) Write an equation for Central High School's budget if plan A is adopted. C + X = 70; 000. Use black ink to draw the bud- get line for Central High School if plan A is adopted. (b) If plan B is adopted, the boundary of Central High School's budget set has two separate downward-sloping line segments. One of these segments describes the cases where C.H.S. spends at least $30,000 on computers. This line segment runs from the point (C; X) =(70; 000; 0) to the point (C; X) = (30,000, 40,000). (c) Another line segment corresponds to the cases where C.H.S. spends less than $30,000 on computers. This line segment runs from (C; X) = (30,000,30,000) to the point (C; X) =(0; 60; 000). Use red ink to draw these two line segments.ഊ62 CHOICE (Ch. 5) (d) If plan C is adopted and Central High School spends C dollars on com- puters, then it will have X = 60; 000 − :5C dollars left to spend on other things. Therefore its budget line has the equation .5C+X=60,000. Use blue ink to draw this budget line. (e) If plan D is adopted, the school district's budget consists of two line segments that intersect at the point where expenditure on comput- ers is 20,000 and expenditure on other instructional materials is 50,000. (f ) The slope of the atter line segment is − :5. The slope of the steeper segment is − 1. Use pencil to draw this budget line.

好复杂啊，确实不简单