[讨论]是不是教材错了：关于平衡预算乘数

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<p><font size="5">我是自学经济学的。</font></p><p><font size="5">在学习到平衡预算乘数问题时，有一处数学上的问题，就是平</font></p><p><font size="5">衡预算乘数的表达式：</font></p><p><font size="5">许多教材是这样写的：</font></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">平衡预算乘数。平衡预算乘数是指ZF税收净额和ZF购买支出以相同的增量变化时，均衡国民收入的变动对ZF税收或ZF购买支出的变动的比率。</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">
                </span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">特例：平衡预算是指ZF的购买支出和固定税收相等的情况。</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><p></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;"></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">即</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">G<sub>0</sub>=T</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">。这时，均衡国民收入的表达式变成：</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><p></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">Y=[a+bTR+(1-b)G<sub>0</sub>+I<sub>0</sub>]/(1-b)</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">　从而推出平衡预算乘数：</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial;">∂Y/∂G=∂Y/∂T=1</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><p></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;"></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">ZF购买支出增加对收入的影响方式是：</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><p></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;"></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">Y<sub>G</sub>=</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">G+b</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">G+ b<sup>2</sup></span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">G+ b<sup>3</sup></span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">G+</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">……</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">= [ 1/(1-b)] </span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">·</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">
                </span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">G<p></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;"></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">固定税收增加对于收入的影响方式是：</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><p></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;"></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">Y<sub>T</sub>=-b</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">T+ -b<sup>2</sup></span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">T+- b<sup>3</sup></span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">T+</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">……</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">=-[b/(1-b)]</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">·△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">T<p></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;"></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">固定税收增加只能抵消购买支出增加引起的间接影响，而不能抵消直接影响，所以平衡预算乘数等于一。即：</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><p></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;"></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">Y=</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">Y<sub>G</sub>+</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">Y<sub>T</sub>=</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">G+b</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">G+ b<sup>2</sup></span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">G +</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">……</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">-b</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">T-b<sup>2</sup></span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">T-</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">……</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">=</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">G=</span><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">△</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";">T<p></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;"></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 28pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><span style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: 宋体; mso-ascii-font-family: Arial; mso-hansi-font-family: Arial;">这说明，平衡预算乘数等于一。换言之，当ZF的购买支出和固定税收同时增加一单位时，均衡国民收入也增加一单位。在其它条件不变时，固定税收和ZF购买支出等额增加，使ZF预算盈余或赤字保持不变，但是，均衡国民收入提高一个与税收或ZF购买相同的水平。其中的原因和ZF购买支出系数同转移支付系数之间的关系的原因类似。</span><span lang="EN-US" style="FONT-SIZE: 14pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><p></p></span></p><p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 18pt; LINE-HEIGHT: 125%; mso-char-indent-count: 2.0;"><font size="5"><span lang="EN-US" style="FONT-SIZE: 9pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial;"></span><span lang="EN-US" style="FONT-SIZE: 9pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial; mso-bidi-font-family: "Times New Roman";"><p></p></span></font></p><p></p></p><p></p><p></p><p></p><p><font size="5"></font></p><p><font size="5">     我想问的问题是：平衡预算乘数的最后表达式对吗？如果</font></p><p><font size="5">用高等数学来严格要求的话，<span lang="EN-US" style="FONT-SIZE: 9pt; LINE-HEIGHT: 125%; FONT-FAMILY: Arial;">∂Y/∂G真的等于1吗？</span></font></p>

[此贴子已经被作者于2008-3-17 20:43:30编辑过]

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关键词：平衡预算乘数 平衡预算 均衡国民收入 ZF购买 国民收入 国民收入 经济学 表达式 平衡 预算

你的表达式写的这么清楚还不对阿。
还是我没看懂你的意思阿
那三个等式已经证明了。

用高等数学来严格要求的话，∂Y/∂G真的等于1吗？

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     这个 数学表达式以一个有问题的假设条件有为基础，所以值得商讨。在这个平衡式中政府支出只有一次，没有再支出。这就必须规定投资.消

费支出都不会因政府支出而变动。这就有问题了，政府支出不会导致消费和投资变化的假设脱离了实际。导致政府支出的作用被低估。实际

中，政府支出不仅直接增加收入，而且还会带动投资和消费的增加，从而增加更多的收入。以上均衡模型不能很好地反应政府支出和税收变动

对国民收入变动的影响。

     更重要的是，支出和增税对国民收入的作用不会对等。其原理有时间我们再做讨论吧。

若想考虑政府支出的“挤出效应”，再引入一个假设（或条件）就可以了。

（附：“需求管理”政策的前提是：经济中尚未达到“充分就业”状态。若经济中已经没有闲置资源可以利用，从长期看，增加需求也不会增加产出）

我说的是高数的问题，就是偏导数的定义问题。偏Y比上偏G,按照高等数学的要求，并

不会等于1啊。因为根据高数的要求，在求Y对于G的偏导数时，只能有G在变化，即一

个变量在变，T是不能变化的啊。但是Y对于G的偏导数始终是1/（1-b)啊。

Y对于T的偏导数始终是-b/(1-b)啊。只有用Y对G的偏导加上Y对T的偏导数才会等于1啊。

设y=a+b(y-t+tr)+g+x，则y(1-b)=a+b(tr-t)+g+x

既然是“平衡预算”，则tºtr+g，即t不是独立的，而是tr与g的函数。于是有y(1-b)=a+g(1-b)+x，可得g的乘数是1。

这里的关键是，“平衡预算”即给定了一个约束，在该约束下，t并不是独立的，是g的函数。

（附：“乘数原理”并非表达，自发需求增加一个单位，实际产出一定增加多少单位，而是表达，在存在引致需求的情况下，若自发需求增加一个单位，则实际产出增加多少单位，经济才是均衡的）

平衡预算是指**的购买支出和固定税收相等的情况????/

这个好象有问题,而且书上说的平衡预算乘数是指在税收和**支出增量相同时.