Income elasticity of demand

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<H1 id="firstHeading" class="firstHeading" lang="en">Income elasticity of demand</H1>			<DIV id="bodyContent" class="mw-body-content">
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				<DIV id="mw-content-text" lang="en" dir="ltr" class="mw-content-ltr"><DIV class="mw-parser-output"><P>In economics, <B>income elasticity of demand</B> measures the responsiveness of the quantity demanded for a good or service to a change in the income of the people demanding the good. It is calculated as the ratio of the percentage change in quantity demanded to the percentage change in income. For example, if in response to a 10% increase in income, the quantity demanded for a good increased by 20%, the income elasticity of demand would be 20%/10% = 2.0
</P>
<DIV id="toc" class="toc"><INPUT type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none" /><DIV class="toctitle" lang="en" dir="ltr"><H2>Contents</H2><SPAN class="toctogglespan"><LABEL class="toctogglelabel" for="toctogglecheckbox"></LABEL></SPAN></DIV>
<UL>
<LI class="toclevel-1 tocsection-1"><A href="#Interpretation"><SPAN class="tocnumber">1</SPAN> <SPAN class="toctext">Interpretation</SPAN></A></LI>
<LI class="toclevel-1 tocsection-2"><A href="#Mathematical_definition"><SPAN class="tocnumber">2</SPAN> <SPAN class="toctext">Mathematical definition</SPAN></A></LI>
<LI class="toclevel-1 tocsection-3"><A href="#Types_of_income_elasticity_of_demand"><SPAN class="tocnumber">3</SPAN> <SPAN class="toctext">Types of income elasticity of demand</SPAN></A></LI>
<LI class="toclevel-1 tocsection-4"><A href="#Selected_income_elasticities"><SPAN class="tocnumber">4</SPAN> <SPAN class="toctext">Selected income elasticities</SPAN></A></LI>
<LI class="toclevel-1 tocsection-5"><A href="#See_also"><SPAN class="tocnumber">5</SPAN> <SPAN class="toctext">See also</SPAN></A></LI>
<LI class="toclevel-1 tocsection-6"><A href="#Notes"><SPAN class="tocnumber">6</SPAN> <SPAN class="toctext">Notes</SPAN></A></LI>
<LI class="toclevel-1 tocsection-7"><A href="#References"><SPAN class="tocnumber">7</SPAN> <SPAN class="toctext">References</SPAN></A></LI>
</UL>
</DIV>

<H2><SPAN class="mw-headline" id="Interpretation">Interpretation</SPAN><SPAN class="mw-editsection"><SPAN class="mw-editsection-bracket">[</SPAN><A href="/w/index.php?title=Income_elasticity_of_demand&action=edit&section=1" title="Edit section: Interpretation">edit</A><SPAN class="mw-editsection-bracket">]</SPAN></SPAN></H2>
<DIV class="thumb tright"><DIV class="thumbinner" style="width:222px;"><A href="/wiki/File:Income_elasticity_of_demand_-_inferior_goods.svg" class="image"><IMG alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Income_elasticity_of_demand_-_inferior_goods.svg/220px-Income_elasticity_of_demand_-_inferior_goods.svg.png" width="220" height="148" class="thumbimage" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Income_elasticity_of_demand_-_inferior_goods.svg/330px-Income_elasticity_of_demand_-_inferior_goods.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/Income_elasticity_of_demand_-_inferior_goods.svg/440px-Income_elasticity_of_demand_-_inferior_goods.svg.png 2x" data-file-width="512" data-file-height="344" /></A>  <DIV class="thumbcaption"><DIV class="magnify"><A href="/wiki/File:Income_elasticity_of_demand_-_inferior_goods.svg" class="internal" title="Enlarge"></A></DIV><A href="/wiki/Inferior_good" title="Inferior good">Inferior goods</A>' demand falls as consumer income increases.</DIV></DIV></DIV>
<UL><LI>A negative  income elasticity of demand is associated with <A href="/wiki/Inferior_good" title="Inferior good">inferior goods</A>; an increase in income will lead to a fall in the demand and may lead to changes to more luxurious substitutes.</LI>
<LI>A positive income elasticity of demand is associated with <A href="/wiki/Normal_good" title="Normal good">normal goods</A>; an increase in income will lead to a rise in demand. If income elasticity of demand of a commodity is less than 1, it is a <A href="/wiki/Necessity_good" title="Necessity good">necessity good</A>. If the elasticity of demand is greater than 1, it is a <A href="/wiki/Luxury_good" class="mw-redirect" title="Luxury good">luxury good</A> or a <A href="/wiki/Superior_good" title="Superior good">superior good</A>.</LI>
<LI>A zero income elasticity of demand occurs when an increase in income is not associated with a change in the demand of a good. These would be sticky goods.</LI></UL>
<P>Income elasticity of demand can be used as an indicator of industry health, future consumption patterns and as a guide to firms investment decisions. For example, the "selected income elasticities" below suggest that an increasing portion of consumer's budgets will be devoted to purchasing automobiles and restaurant meals and a smaller share to tobacco and margarine.<SUP id="cite_ref-1" class="reference"><A href="#cite_note-1">[1]</A></SUP>
</P><P>Income elasticities are closely related to the population income distribution and the fraction of the product's sales attributable to buyers from different <A href="/wiki/Income_bracket" title="Income bracket">income brackets</A>.  Specifically when a buyer in a certain income bracket experiences an income increase,  their purchase of a product changes to match that of individuals  in their new income bracket.  If the income share elasticity is defined as the negative percentage change in individuals given a percentage increase in income bracken the income-elasticity, after some computation, becomes the expected value of the income-share elasticity with respect to the income distribution of purchasers of the product.  When the income distribution is described by a <A href="/wiki/Gamma_distribution" title="Gamma distribution">gamma distribution</A>, the income elasticity is proportional to the percentage difference between the average income of the product's buyers and the average income of the population.<SUP id="cite_ref-2" class="reference"><A href="#cite_note-2">[2]</A></SUP>
</P>
<H2><SPAN class="mw-headline" id="Mathematical_definition">Mathematical definition</SPAN><SPAN class="mw-editsection"><SPAN class="mw-editsection-bracket">[</SPAN><A href="/w/index.php?title=Income_elasticity_of_demand&action=edit&section=2" title="Edit section: Mathematical definition">edit</A><SPAN class="mw-editsection-bracket">]</SPAN></SPAN></H2>
<DL><DD><SPAN class="mwe-math-element"><SPAN class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon _{Y}={\frac {\%\ {\mbox{change in demand}}}{\%\ {\mbox{change in income}}}}}">
  <semantics>
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              <mtext> </mtext>
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                  <mtext>change in demand</mtext>
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              <mi mathvariant="normal">%<!-- % --></mi>
              <mtext> </mtext>
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                <mstyle displaystyle="false" scriptlevel="0">
                  <mtext>change in income</mtext>
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    <annotation encoding="application/x-tex">{\displaystyle \epsilon _{Y}={\frac {\%\ {\mbox{change in demand}}}{\%\ {\mbox{change in income}}}}}</annotation>
  </semantics>
</math></SPAN><IMG src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6198141bf00948d934cfc5b01fc55247175f4053" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:26.965ex; height:6.176ex;" alt="\epsilon _{Y}={\frac  {\%\ {\mbox{change in demand}}}{\%\ {\mbox{change in income}}}}" /></SPAN></DD></DL>
<P>More formally, the income elasticity of demand, <SPAN class="mwe-math-element"><SPAN class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ \epsilon _{d}}">
  <semantics>
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    <annotation encoding="application/x-tex">{\displaystyle \ \epsilon _{d}}</annotation>
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</math></SPAN><IMG src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7249ff2300158a0925632de593f87ced07783d9a" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:2.617ex; height:2.009ex;" alt="\ \epsilon _{d}" /></SPAN>,  for a given <A href="/wiki/Marshallian_demand_function" title="Marshallian demand function">Marshallian demand function</A> <SPAN class="mwe-math-element"><SPAN class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q(I,{\vec {P}})}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi>Q</mi>
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    <annotation encoding="application/x-tex">{\displaystyle Q(I,{\vec {P}})}</annotation>
  </semantics>
</math></SPAN><IMG src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4ad802e0754b98c2fe386af15881d65fa0cf701" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:7.631ex; height:3.343ex;" alt="Q(I,{\vec  {P}})" /></SPAN> for a good is
</P>
<DL><DD><SPAN class="mwe-math-element"><SPAN class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon _{d}={\frac {\partial Q}{\partial I}}{\frac {I}{Q}}}">
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            <mrow>
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              <mi>Q</mi>
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    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle \epsilon _{d}={\frac {\partial Q}{\partial I}}{\frac {I}{Q}}}</annotation>
  </semantics>
</math></SPAN><IMG src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc27278d80b9a243ad14cefa247b5b0c8b7514e9" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.338ex; width:11.802ex; height:5.843ex;" alt="\epsilon _{d}={\frac  {\partial Q}{\partial I}}{\frac  {I}{Q}}" /></SPAN></DD></DL>
<P>or alternatively:
</P>
<DL><DD><SPAN class="mwe-math-element"><SPAN class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon _{d}={Y_{1}+Y_{2} \over Q_{1}+Q_{2}}\times {\Delta Q \over \Delta Y}}">
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                <mi>Y</mi>
                <mrow class="MJX-TeXAtom-ORD">
                  <mn>1</mn>
                </mrow>
              </msub>
              <mo>+</mo>
              <msub>
                <mi>Y</mi>
                <mrow class="MJX-TeXAtom-ORD">
                  <mn>2</mn>
                </mrow>
              </msub>
            </mrow>
            <mrow>
              <msub>
                <mi>Q</mi>
                <mrow class="MJX-TeXAtom-ORD">
                  <mn>1</mn>
                </mrow>
              </msub>
              <mo>+</mo>
              <msub>
                <mi>Q</mi>
                <mrow class="MJX-TeXAtom-ORD">
                  <mn>2</mn>
                </mrow>
              </msub>
            </mrow>
          </mfrac>
        </mrow>
        <mo>×<!-- × --></mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mfrac>
            <mrow>
              <mi mathvariant="normal">Δ<!-- Δ --></mi>
              <mi>Q</mi>
            </mrow>
            <mrow>
              <mi mathvariant="normal">Δ<!-- Δ --></mi>
              <mi>Y</mi>
            </mrow>
          </mfrac>
        </mrow>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle \epsilon _{d}={Y_{1}+Y_{2} \over Q_{1}+Q_{2}}\times {\Delta Q \over \Delta Y}}</annotation>
  </semantics>
</math></SPAN><IMG src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e3bfa70996fbad10c4dcbabe8f60ae3dd6f59093" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.338ex; width:22.047ex; height:5.843ex;" alt="\epsilon _{d}={Y_{1}+Y_{2} \over Q_{1}+Q_{2}}\times {\Delta Q \over \Delta Y}" /></SPAN></DD></DL>
<P>This can be rewritten in the form:
</P>
<DL><DD><SPAN class="mwe-math-element"><SPAN class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon _{d}={\frac {d\ln Q}{d\ln I}}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <msub>
          <mi>ϵ<!-- ϵ --></mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>d</mi>
          </mrow>
        </msub>
        <mo>=</mo>
        <mrow class="MJX-TeXAtom-ORD">
          <mfrac>
            <mrow>
              <mi>d</mi>
              <mi>ln</mi>
              <mo><!--  --></mo>
              <mi>Q</mi>
            </mrow>
            <mrow>
              <mi>d</mi>
              <mi>ln</mi>
              <mo><!--  --></mo>
              <mi>I</mi>
            </mrow>
          </mfrac>
        </mrow>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle \epsilon _{d}={\frac {d\ln Q}{d\ln I}}}</annotation>
  </semantics>
</math></SPAN><IMG src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5123a04e4c24703bc299ca1f04f8b8ede118cb2b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.005ex; width:11.739ex; height:5.509ex;" alt="\epsilon _{d}={\frac  {d\ln Q}{d\ln I}}" /></SPAN></DD></DL>
<P>With income <SPAN class="mwe-math-element"><SPAN class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mi>I</mi>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle I}</annotation>
  </semantics>
</math></SPAN><IMG src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="I" /></SPAN>, and vector of prices <SPAN class="mwe-math-element"><SPAN class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {P}}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mrow class="MJX-TeXAtom-ORD">
          <mrow class="MJX-TeXAtom-ORD">
            <mover>
              <mi>P</mi>
              <mo stretchy="false">→<!-- → --></mo>
            </mover>
          </mrow>
        </mrow>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle {\vec {P}}}</annotation>
  </semantics>
</math></SPAN><IMG src="https://wikimedia.org/api/rest_v1/media/math/render/svg/765f1dd50e122eb3e565c9bfee85de8f74d47f27" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.778ex; height:2.843ex;" alt="{\vec {P}}" /></SPAN>.
</P><P>Many necessities have an income elasticity of demand between zero and one: expenditure on these goods may increase with income, but not as fast as income does, so the proportion of expenditure on these goods falls as income rises.  This observation for food is known as <I><A href="/wiki/Engel%27s_law" title="Engel's law">Engel's law</A></I>.
</P>
<H2><SPAN class="mw-headline" id="Types_of_income_elasticity_of_demand">Types of income elasticity of demand</SPAN><SPAN class="mw-editsection"><SPAN class="mw-editsection-bracket">[</SPAN><A href="/w/index.php?title=Income_elasticity_of_demand&action=edit&section=3" title="Edit section: Types of income elasticity of demand">edit</A><SPAN class="mw-editsection-bracket">]</SPAN></SPAN></H2>
<P><B>There are five possible income demand curves:</B>
</P><P>1. High income elasticity of demand:
</P><P>In this case increase in income is accompanied by relatively larger increase in quantity demanded.
</P><P>2. Unitary income elasticity of demand:
</P><P>In this case increase in income is accompanied by same proportionate increase in quantity demanded.
</P><P>3. Low income elasticity of demand:
</P><P>In this case increase in income is accompanied by less than proportionate increase in quantity demanded.
</P><P>4. Zero income elasticity of demand:
</P><P>This shows that quantity bought is constant regardless of changes in income.
</P><P>5. Negative income elasticity of demand:
</P><P>In this case increase in income is accompanied by decrease in quantity demanded.
</P>
<H2><SPAN class="mw-headline" id="Selected_income_elasticities">Selected income elasticities</SPAN><SPAN class="mw-editsection"><SPAN class="mw-editsection-bracket">[</SPAN><A href="/w/index.php?title=Income_elasticity_of_demand&action=edit&section=4" title="Edit section: Selected income elasticities">edit</A><SPAN class="mw-editsection-bracket">]</SPAN></SPAN></H2>
<UL><LI>Automobiles 2.98<SUP id="cite_ref-3" class="reference"><A href="#cite_note-3">[3]</A></SUP></LI>
<LI>Books 1.44</LI>
<LI>A person's own life (also called <A href="/wiki/Value_of_life" title="Value of life">Value of Statistical Life</A>) 0.50 to 0.60  <SUP id="cite_ref-The_Value_of_a_Statistical_Life:_A_critical_Review_4-0" class="reference"><A href="#cite_note-The_Value_of_a_Statistical_Life:_A_critical_Review-4">[4]</A></SUP></LI>
<LI>Restaurant Meals 1.40</LI>
<LI>Tobacco 0.64</LI>
<LI>Margarine −0.20</LI>
<LI>Public Transportation −0.36<SUP id="cite_ref-5" class="reference"><A href="#cite_note-5">[5]</A></SUP></LI></UL>
<P>Income elasticities are notably stable over time and across countries due to the <A href="/wiki/Law_of_one_price" title="Law of one price">law of one price</A>.<SUP id="cite_ref-6" class="reference"><A href="#cite_note-6">[6]</A></SUP>
</P>
<H2><SPAN class="mw-headline" id="See_also">See also</SPAN><SPAN class="mw-editsection"><SPAN class="mw-editsection-bracket">[</SPAN><A href="/w/index.php?title=Income_elasticity_of_demand&action=edit&section=5" title="Edit section: See also">edit</A><SPAN class="mw-editsection-bracket">]</SPAN></SPAN></H2>
<UL><LI><A href="/wiki/Cross_elasticity_of_demand" title="Cross elasticity of demand">Cross elasticity of demand</A> (CED)</LI>
<LI><A href="/wiki/Price_elasticity_of_demand" title="Price elasticity of demand">Price elasticity of demand</A> (PED)</LI>
<LI><A href="/wiki/Price_elasticity_of_supply" title="Price elasticity of supply">Price elasticity of supply</A> (PES)</LI></UL>
<H2><SPAN class="mw-headline" id="Notes">Notes</SPAN><SPAN class="mw-editsection"><SPAN class="mw-editsection-bracket">[</SPAN><A href="/w/index.php?title=Income_elasticity_of_demand&action=edit&section=6" title="Edit section: Notes">edit</A><SPAN class="mw-editsection-bracket">]</SPAN></SPAN></H2>
<DIV class="reflist" style="list-style-type: decimal;">
<DIV class="mw-references-wrap"><OL class="references">
<LI id="cite_note-1"><SPAN class="mw-cite-backlink"><B><A href="#cite_ref-1"><SPAN class="cite-accessibility-label">Jump up </SPAN>^</A></B></SPAN> <SPAN class="reference-text">Frank, Robert (2008). p. 125</SPAN>
</LI>
<LI id="cite_note-2"><SPAN class="mw-cite-backlink"><B><A href="#cite_ref-2"><SPAN class="cite-accessibility-label">Jump up </SPAN>^</A></B></SPAN> <SPAN class="reference-text">Bordley and McDonald.</SPAN>
</LI>
<LI id="cite_note-3"><SPAN class="mw-cite-backlink"><B><A href="#cite_ref-3"><SPAN class="cite-accessibility-label">Jump up </SPAN>^</A></B></SPAN> <SPAN class="reference-text">Samuelson; Nordhaus (2001). p.94.</SPAN>
</LI>
<LI id="cite_note-The_Value_of_a_Statistical_Life:_A_critical_Review-4"><SPAN class="mw-cite-backlink"><B><A href="#cite_ref-The_Value_of_a_Statistical_Life:_A_critical_Review_4-0"><SPAN class="cite-accessibility-label">Jump up </SPAN>^</A></B></SPAN> <SPAN class="reference-text"><CITE class="citation journal">WK Viscusi (2003). <A rel="nofollow" class="external text" href="http://lsr.nellco.org/cgi/viewcontent.cgi?article=1180&context=harvard_olin&sei-redir=1&referer=http%3A%2F%2Fscholar.google.com%2Fscholar%3Fq%3Dvalue%2Bof%2Ba%2Blife%2Bto%2Bsociety#search=%22value%20life%20society%22">"The value of a statistical life: a critical review of market estimates throughout the world"</A>. <I>Journal of risk and uncertainty</I>.</CITE><SPAN title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+risk+and+uncertainty&rft.atitle=The+value+of+a+statistical+life%3A+a+critical+review+of+market+estimates+throughout+the+world&rft.date=2003&rft.au=WK+Viscusi&rft_id=http%3A%2F%2Flsr.nellco.org%2Fcgi%2Fviewcontent.cgi%3Farticle%3D1180%26context%3Dharvard_olin%26sei-redir%3D1%26referer%3Dhttp%253A%252F%252Fscholar.google.com%252Fscholar%253Fq%253Dvalue%252Bof%252Ba%252Blife%252Bto%252Bsociety%23search%3D%2522value%2520life%2520society%2522&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIncome+elasticity+of+demand" class="Z3988"><SPAN style="display:none;"> </SPAN></SPAN></SPAN>
</LI>
<LI id="cite_note-5"><SPAN class="mw-cite-backlink"><B><A href="#cite_ref-5"><SPAN class="cite-accessibility-label">Jump up </SPAN>^</A></B></SPAN> <SPAN class="reference-text">Frank (2008) 125.</SPAN>
</LI>
<LI id="cite_note-6"><SPAN class="mw-cite-backlink"><B><A href="#cite_ref-6"><SPAN class="cite-accessibility-label">Jump up </SPAN>^</A></B></SPAN> <SPAN class="reference-text">Perloff, J. (2008). p.105.</SPAN>
</LI>
</OL></DIV></DIV>
<H2><SPAN class="mw-headline" id="References">References</SPAN><SPAN class="mw-editsection"><SPAN class="mw-editsection-bracket">[</SPAN><A href="/w/index.php?title=Income_elasticity_of_demand&action=edit&section=7" title="Edit section: References">edit</A><SPAN class="mw-editsection-bracket">]</SPAN></SPAN></H2>
<STYLE data-mw-deduplicate="TemplateStyles:r852805940">.mw-parser-output .refbegin{font-size:90%;margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{list-style-type:none;margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li,.mw-parser-output .refbegin-hanging-indents>dl>dd{margin-left:0;padding-left:3.2em;text-indent:-3.2em;list-style:none}.mw-parser-output .refbegin-100{font-size:100%}</STYLE><DIV class="refbegin" style="">
<UL><LI><CITE class="citation journal">Bordley; McDonald. "Estimating Income Elasticities from the Average Income of a Product's Buyers and the Population Income Distribution". <I>Journal of Business and Economic Statistics</I>.</CITE><SPAN title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Business+and+Economic+Statistics&rft.atitle=Estimating+Income+Elasticities+from+the+Average+Income+of+a+Product%27s+Buyers+and+the+Population+Income+Distribution&rft.au=Bordley&rft.au=McDonald&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIncome+elasticity+of+demand" class="Z3988"><SPAN style="display:none;"> </SPAN></SPAN></LI>
<LI><CITE class="citation book">Perloff, J. (2008). <I>Microeconomics Theory & Applications with Calculus</I>. Pearson. <A href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</A> <A href="/wiki/Special:BookSources/978-0-321-27794-7" title="Special:BookSources/978-0-321-27794-7">978-0-321-27794-7</A>.</CITE><SPAN title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Microeconomics+Theory+%26+Applications+with+Calculus&rft.pub=Pearson&rft.date=2008&rft.isbn=978-0-321-27794-7&rft.aulast=Perloff&rft.aufirst=J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIncome+elasticity+of+demand" class="Z3988"><SPAN style="display:none;"> </SPAN></SPAN></LI>
<LI><CITE class="citation book">Samuelson; Nordhaus (2001). <I>Microeconomics</I> (17th ed.). McGraw-Hill.</CITE><SPAN title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Microeconomics&rft.edition=17th&rft.pub=McGraw-Hill&rft.date=2001&rft.au=Samuelson&rft.au=Nordhaus&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIncome+elasticity+of+demand" class="Z3988"><SPAN style="display:none;"> </SPAN></SPAN></LI>
<LI><CITE class="citation book">Frank, Robert (2008). <I>Microeconomics and Behavior</I> (7th ed.). McGraw-Hill. <A href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</A> <A href="/wiki/Special:BookSources/978-0-07-126349-8" title="Special:BookSources/978-0-07-126349-8">978-0-07-126349-8</A>.</CITE><SPAN title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Microeconomics+and+Behavior&rft.edition=7th&rft.pub=McGraw-Hill&rft.date=2008&rft.isbn=978-0-07-126349-8&rft.aulast=Frank&rft.aufirst=Robert&rfr_id=info%3Asid%2Fen.wikipedia.org%3AIncome+elasticity+of+demand" class="Z3988"><SPAN style="display:none;"> </SPAN></SPAN></LI></UL>
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