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2007-11-06
<p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="; FONT-FAMILY: "T11","sans-serif"; mso-bidi-font-family: T11; mso-font-kerning: 0pt;">(6.3 </span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">Mickey is considering buying a tape recorder. His utility function is </span><span lang="EN-US" style="; FONT-FAMILY: "T9","sans-serif"; mso-bidi-font-family: T9; mso-font-kerning: 0pt;">U</span><span lang="EN-US" style="; FONT-FAMILY: "T5","sans-serif"; mso-bidi-font-family: T5; mso-font-kerning: 0pt;">(</span><span lang="EN-US" style="; FONT-FAMILY: "T9","sans-serif"; mso-bidi-font-family: T9; mso-font-kerning: 0pt;">x; y; z</span><span lang="EN-US" style="; FONT-FAMILY: "T5","sans-serif"; mso-bidi-font-family: T5; mso-font-kerning: 0pt;">) = </span><span lang="EN-US" style="; FONT-FAMILY: "T9","sans-serif"; mso-bidi-font-family: T9; mso-font-kerning: 0pt;">x</span><span lang="EN-US" style="; FONT-FAMILY: "T5","sans-serif"; mso-bidi-font-family: T5; mso-font-kerning: 0pt;">+</span><span lang="EN-US" style="; FONT-FAMILY: "T9","sans-serif"; mso-bidi-font-family: T9; mso-font-kerning: 0pt;">f</span><span lang="EN-US" style="; FONT-FAMILY: "T5","sans-serif"; mso-bidi-font-family: T5; mso-font-kerning: 0pt;">(</span><span lang="EN-US" style="; FONT-FAMILY: "T9","sans-serif"; mso-bidi-font-family: T9; mso-font-kerning: 0pt;">y</span><span lang="EN-US" style="; FONT-FAMILY: "T5","sans-serif"; mso-bidi-font-family: T5; mso-font-kerning: 0pt;">)</span><span lang="EN-US" style="; FONT-FAMILY: "T9","sans-serif"; mso-bidi-font-family: T9; mso-font-kerning: 0pt;">z</span><sup><span lang="EN-US" style="; FONT-FAMILY: "T4","sans-serif"; mso-bidi-font-family: T4; mso-font-kerning: 0pt;">5</span></sup><sup><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T8; mso-font-kerning: 0pt; mso-ascii-font-family: T8; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T8;"> </span></sup><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">where </span><span lang="EN-US" style="; FONT-FAMILY: "T9","sans-serif"; mso-bidi-font-family: T9; mso-font-kerning: 0pt;">x </span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">is the amount of money he spends on other goods, </span><span lang="EN-US" style="; FONT-FAMILY: "T9","sans-serif"; mso-bidi-font-family: T9; mso-font-kerning: 0pt;">y </span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">is the number of tape recorders he</span><sup><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T8; mso-font-kerning: 0pt; mso-ascii-font-family: T8; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T8;"> </span></sup><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">buys, and </span><span lang="EN-US" style="; FONT-FAMILY: "T9","sans-serif"; mso-bidi-font-family: T9; mso-font-kerning: 0pt;">z </span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">is the number of tapes he buys. Let </span><span lang="EN-US" style="; FONT-FAMILY: "T9","sans-serif"; mso-bidi-font-family: T9; mso-font-kerning: 0pt;">f</span><span lang="EN-US" style="; FONT-FAMILY: "T5","sans-serif"; mso-bidi-font-family: T5; mso-font-kerning: 0pt;">(</span><span lang="EN-US" style="; FONT-FAMILY: "T9","sans-serif"; mso-bidi-font-family: T9; mso-font-kerning: 0pt;">y</span><span lang="EN-US" style="; FONT-FAMILY: "T5","sans-serif"; mso-bidi-font-family: T5; mso-font-kerning: 0pt;">) = 0 </span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">if </span><span lang="EN-US" style="; FONT-FAMILY: "T9","sans-serif"; mso-bidi-font-family: T9; mso-font-kerning: 0pt;">y < </span><span lang="EN-US" style="; FONT-FAMILY: "T5","sans-serif"; mso-bidi-font-family: T5; mso-font-kerning: 0pt;">1 </span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">and </span><span lang="EN-US" style="; FONT-FAMILY: "T9","sans-serif"; mso-bidi-font-family: T9; mso-font-kerning: 0pt;">f</span><span lang="EN-US" style="; FONT-FAMILY: "T5","sans-serif"; mso-bidi-font-family: T5; mso-font-kerning: 0pt;">(</span><span lang="EN-US" style="; FONT-FAMILY: "T9","sans-serif"; mso-bidi-font-family: T9; mso-font-kerning: 0pt;">y</span><span lang="EN-US" style="; FONT-FAMILY: "T5","sans-serif"; mso-bidi-font-family: T5; mso-font-kerning: 0pt;">) = 8 </span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">if </span><span lang="EN-US" style="; FONT-FAMILY: "T9","sans-serif"; mso-bidi-font-family: T9; mso-font-kerning: 0pt;">y </span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">is greater than</span><sup><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T8; mso-font-kerning: 0pt; mso-ascii-font-family: T8; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T8;"> </span></sup><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">or equal to 1. The price of tape recorders is 20, the price of tapes is 1, and he can easily afford to</span><sup><span lang="EN-US" style="; FONT-FAMILY: "T8","sans-serif"; mso-bidi-font-family: T8; mso-font-kerning: 0pt;"><br/>   </span></sup><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">buy a tape recorder and several tapes. Will he buy a tape recorder?</span><sup><span lang="EN-US" style="; FONT-FAMILY: "T8","sans-serif"; mso-bidi-font-family: T8; mso-font-kerning: 0pt;"><p></p></span></sup></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="; FONT-FAMILY: "T6","sans-serif"; mso-bidi-font-family: T6; mso-font-kerning: 0pt;">(a) </span><span lang="EN-US" style="; FONT-FAMILY: "T5","sans-serif"; mso-bidi-font-family: T5; mso-font-kerning: 0pt;">He should buy a tape recorder at these prices, but if tapes were any more expensive, it would not pay to buy one.<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="; FONT-FAMILY: "T6","sans-serif"; mso-bidi-font-family: T6; mso-font-kerning: 0pt;">(b) </span><span lang="EN-US" style="; FONT-FAMILY: "T5","sans-serif"; mso-bidi-font-family: T5; mso-font-kerning: 0pt;">He should not buy a tape recorder.<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="; FONT-FAMILY: "T6","sans-serif"; mso-bidi-font-family: T6; mso-font-kerning: 0pt;">(c) </span><span lang="EN-US" style="; FONT-FAMILY: "T5","sans-serif"; mso-bidi-font-family: T5; mso-font-kerning: 0pt;">He is indifferent to buying a tape recorder or not.<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="; FONT-FAMILY: "T6","sans-serif"; mso-bidi-font-family: T6; mso-font-kerning: 0pt;">(d) </span><span lang="EN-US" style="; FONT-FAMILY: "T5","sans-serif"; mso-bidi-font-family: T5; mso-font-kerning: 0pt;">There is not enough information here for us to be able to tell.<p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US" style="; FONT-FAMILY: "T6","sans-serif"; mso-bidi-font-family: T6; mso-font-kerning: 0pt;">(e) </span><span lang="EN-US" style="; FONT-FAMILY: "T5","sans-serif"; mso-bidi-font-family: T5; mso-font-kerning: 0pt;">Even if the price of tapes doubled, he should still buy a tape recorder<p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T5; mso-font-kerning: 0pt; mso-ascii-font-family: T5; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T5;">答案:</span><span lang="EN-US" style="; FONT-FAMILY: "T5","sans-serif"; mso-bidi-font-family: T5; mso-font-kerning: 0pt;"><p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="; FONT-FAMILY: "T12","sans-serif"; mso-bidi-font-family: T12; mso-font-kerning: 0pt;">Topic: Demand <span style="mso-tab-count: 1;">      </span><span style="mso-tab-count: 2;">              </span>Difficulty: 2<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="; FONT-FAMILY: "T12","sans-serif"; mso-bidi-font-family: T12; mso-font-kerning: 0pt;">% Correct Responses: 0 <span style="mso-tab-count: 1;">    </span>Discrimination Index: 0<p></p></span></p><p></p><p></p><p class="MsoNormal" align="left" style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: left; mso-layout-grid-align: none;"><span lang="EN-US" style="; FONT-FAMILY: "T12","sans-serif"; mso-bidi-font-family: T12; mso-font-kerning: 0pt;">Correct Answer: B<p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US" style=";"><p><font face="Calibri"> </font></p></span></p><p><font face="Calibri"> </font></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: Calibri; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">为什么?这个应该选</span><span lang="EN-US" style=";"><font face="Calibri">E</font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: Calibri; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">,不是吗?</span><span lang="EN-US" style=";"><p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: Calibri; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">比如收入为</span><span lang="EN-US" style=";"><font face="Calibri">M</font></span><span style="; FONT-FAMILY: 宋体; mso-ascii-font-family: Calibri; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">(</span><span lang="EN-US" style=";"><font face="Calibri">big enough</font></span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;"> to</span><sup><span lang="EN-US" style="; FONT-FAMILY: "T8","sans-serif"; mso-bidi-font-family: T8; mso-font-kerning: 0pt;"><br/>   </span></sup><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">buy a tape recorder and several tapes</span><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T10; mso-font-kerning: 0pt; mso-ascii-font-family: T10; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T10;">)</span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">,<p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T10; mso-font-kerning: 0pt; mso-ascii-font-family: T10; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T10;">不买时,</span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">U</span><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T10; mso-font-kerning: 0pt; mso-ascii-font-family: T10; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T10;">=</span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">M<p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T10; mso-font-kerning: 0pt; mso-ascii-font-family: T10; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T10;">买</span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">1</span><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T10; mso-font-kerning: 0pt; mso-ascii-font-family: T10; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T10;">个</span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">recorder</span><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T10; mso-font-kerning: 0pt; mso-ascii-font-family: T10; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T10;">和</span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">2</span><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T10; mso-font-kerning: 0pt; mso-ascii-font-family: T10; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T10;">个</span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">tape,</span><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T10; mso-font-kerning: 0pt; mso-ascii-font-family: T10; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T10;">则</span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">U</span><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T10; mso-font-kerning: 0pt; mso-ascii-font-family: T10; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T10;">=</span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">M-20-2+8*2<sup>5</sup>=M+234<p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T10; mso-font-kerning: 0pt; mso-ascii-font-family: T10; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T10;">显然买比较划算啊。</span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;"><p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T10; mso-font-kerning: 0pt; mso-ascii-font-family: T10; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T10;">即使</span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">tape</span><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T10; mso-font-kerning: 0pt; mso-ascii-font-family: T10; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T10;">的价格翻倍变成了</span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">2,</span><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T10; mso-font-kerning: 0pt; mso-ascii-font-family: T10; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T10;">买的效用也是</span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;">U=M+230>M</span><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T10; mso-font-kerning: 0pt; mso-ascii-font-family: T10; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T10;">啊</span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;"><p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;"><p> </p></span></p><p> </p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T10; mso-font-kerning: 0pt; mso-ascii-font-family: T10; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T10;">是不是答案错了?还是我哪里没弄清?</span><span lang="EN-US" style="; FONT-FAMILY: "T10","sans-serif"; mso-bidi-font-family: T10; mso-font-kerning: 0pt;"><p></p></span></p><p></p><p></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="; FONT-FAMILY: 宋体; mso-bidi-font-family: T10; mso-font-kerning: 0pt; mso-ascii-font-family: T10; mso-fareast-font-family: 宋体; mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: T10;">谢谢</span><span lang="EN-US" style=";"><p></p></span></p><p></p><p></p>

[此贴子已经被作者于2007-11-6 17:55:17编辑过]

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2007-11-6 17:34:00
原题是x+f(y)*z^0.5吧?
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2007-11-6 17:54:00
以下是引用sungmoo在2007-11-6 17:34:00的发言:
原题是x+f(y)*z^0.5吧?

果然....这个电子版的字极不清楚,而且0.5都写成.5。我说这个人怎么会这么喜欢tape呢....这样就没有问题了。

谢谢~~

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