Aggregation problem

<h2 id="aggregate-consumer-demand-curve">Aggregate consumer demand curve</h2>
<p>The aggregate consumer <a href="/facts/Demand_curve/lALNI8BX">demand curve</a> is the summation of the individual consumer demand curves. The aggregation process preserves only two characteristics of individual <a href="/facts/Consumer_choice/Yrpoc6fI">consumer preference theory</a>—continuity and homogeneity. Aggregation introduces three additional non-price determinants of demand:
</p>
<ul><li>Number of consumers</li>
<li>Distribution of tastes among the consumers</li>
<li>Distribution of incomes among consumers of different taste</li></ul>
<p>Thus if the population of consumers increases, <a href="/facts/Ceteris_paribus/x2qc4wC0">ceteris paribus</a> the demand curve will shift out; if the proportion of consumers with a strong preference for a good increases, ceteris paribus the demand for that good will change. Finally, if the <a href="/facts/Distribution_of_income/5ewT5Q6S">distribution of income</a> changes in favor of consumers who prefer the good in question, the demand will shift out. It is important to remember that factors that affect individual demand can also affect aggregate demand. However, net effects must be considered. The most important problem for micro- and macro-economics is the <a href="/facts/Sonnenschein%25E2%2580%2593Mantel%25E2%2580%2593Debreu_theorem/GctbmTRY">Sonnenschein–Mantel–Debreu theorem</a>, which shows that almost no properties of the individual preference are inherited to the aggregate demand functions.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a><a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a><a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a>
</p>
<h3>Difficulties with aggregation</h3>
<h4>Sonnenschein-Mantel-Debreu theorem</h4>
<p><a href="/facts/Sonnenschein-Mantel-Debreu_theorem/GctbmTRY">Sonnenschein-Mantel-Debreu theorem</a> (SMD theorem) is a theorem for exchange economy that can be expressed in the following way:
</p>
<blockquote><p>for a function that is continuous, homogeneous of degree zero, and in accord with Walras's law,there is an economy with at least as many agents as goods such that, for prices bounded away from zero, the function is the aggregate demand
function for this economy.<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a></p></blockquote>
<h4>Independence assumption</h4>
<p>First, to sum the demand functions without other strong assumptions it must be assumed that they are independent – that is, that one consumer's demand decisions are not influenced by the decisions of another consumer.<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> For example, A is asked how many pairs of shoes he would buy at a certain price. A says at that price I would be willing and able to buy two pairs of shoes. B is asked the same question and says four pairs. Questioner goes back to A and says B is willing to buy four pairs of shoes, what do you think about that? A says if B has any interest in those shoes then I have none. Or A, not to be outdone by B, says "then I'll buy five pairs". And on and on. This problem can be eliminated by assuming that the consumers' tastes are fixed in the short run. This assumption can be expressed as assuming that each consumer is an independent idiosyncratic decision maker.
</p>
<h4>No interesting properties</h4>
<p>This second problem is more serious. As <a href="/facts/David_M._Kreps/xAIRlHVk">David M. Kreps</a> notes, “total demand will shift about as a function of how individual incomes are distributed even holding total (societal) income fixed. So it makes no sense to speak of <a href="/facts/Aggregate_demand/LrIyvUMD">aggregate demand</a> as a function of price and societal income".<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a> Since any change in <a href="/facts/Relative_price/FU7GKpjd">relative price</a> brings about a redistribution of real income, there is a separate demand curve for every relative price. Kreps continues, "So what can we say about aggregate demand based on the hypothesis that individuals are preference/utility maximizers? Unless we are able to make strong assumptions about the distribution of preferences or income throughout the economy (everyone has the same <a href="/facts/Homothetic_preferences/Ic0v4lSW">homothetic preferences</a> for example) there is little we can say”.<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a> The strong assumptions are that everyone has the same tastes and that each person's tastes remain the same as income changes so additional income is spent in exactly the same way as before.
</p><p>Microeconomist <a href="/facts/Hal_Varian/D5uEfzBd">Hal Varian</a> reached a more muted conclusion: "The aggregate demand function will in general possess no interesting properties".<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a> However, Varian continued: "the <a href="/facts/Neoclassical_economics/Jw8FAyHm">neoclassical theory</a> of the consumer places no restriction on <a href="/facts/Aggregate_behavior/U18Nalg0">aggregate behavior</a> in general".<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a> This means the preference conditions (with the possible exception of continuity) simply do not apply to the aggregate function.
</p>
<h2 id="see-also">See also</h2>

<ul><li><a href="/facts/Aggregate_demand/LrIyvUMD">Aggregate demand</a></li>
<li><a href="/facts/Aggregate_supply/5HIDYMHa">Aggregate supply</a></li>
<li><a href="/facts/Aggregate_production_function/oKnfDAou">Aggregate production function</a></li>
<li><a href="/facts/Cambridge_capital_controversy/spDGotKA">Cambridge capital controversy</a></li>
<li><a href="/facts/Ecological_fallacy/9Qt3hMA0">Ecological fallacy</a></li>
<li><a href="/facts/Price_index/0okIszGK">Price index</a></li>
<li><a href="/facts/Representative_agent/dWqFI8gx">Representative agent</a></li>
<li><a href="/facts/Methodological_individualism/gzTj1aB9">Methodological individualism</a></li>
<li><a href="/facts/Social_choice_theory/ztMqy1bM">Social choice theory</a></li></ul>

<h2 id="notes">Notes</h2>

<ul><li><a href="/facts/Franklin_M._Fisher/CpHnXg0y">Franklin M. Fisher</a> (1987).  "aggregation problem," <i><a href="/facts/The_New_Palgrave%3a_A_Dictionary_of_Economics/3VDv8Bdp">The New Palgrave: A Dictionary of Economics</a></i>, v. 1, pp. 53–55.</li>
<li>Jesus Felipe and  Franklin M. Fisher (2008).  "aggregation (production)," <i><a href="/facts/The_New_Palgrave_Dictionary_of_Economics/3VDv8Bdp">The New Palgrave Dictionary of Economics</a>, 2nd Edition</i>. <a href="http://www.dictionaryofeconomics.com/article?id=pde2008_A000059&q=aggregation%20(production)&topicid=&result_number=1">Abstract.</a></li>
<li><a href="/facts/John_Hicks/8AgpsS4F">John R. Hicks</a> (1939, 2nd ed. 1946). <i><a href="/facts/Value_and_Capital/d6PVzvkH">Value and Capital</a></i>.</li>
<li><a href="/facts/Werner_Hildenbrand/GLK6ufpR">Werner Hildenbrand</a> (2008). "aggregation (theory),"   <i>The New Palgrave Dictionary of Economics</i>, 2nd Edition.  <a href="http://www.dictionaryofeconomics.com/article?id=pde2008_A000247&q=aggregation&topicid=&result_number=4">Abstract.</a></li>
<li>Thomas M. Stoker (2008).  "aggregation (econometrics)," <i>The New Palgrave Dictionary of Economics</i>, 2nd Edition.  <a href="http://www.dictionaryofeconomics.com/article?id=pde2008_A000234&q=aggregation&topicid=&result_number=2">Abstract.</a></li>
<li>Douglas W. Blackburn and Andrey D. Ukhov (2008) "Individual vs. Aggregate Preferences: The Case of a Small Fish in a Big Pond," <a href="http://ssrn.com/abstract=941126">Abstract.</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Franklin M. Fisher  (1987).  "aggregation problem," The New Palgrave: A Dictionary of Economics, v. 1, pp.53-55 <a href="/wiki/The_New_Palgrave:_A_Dictionary_of_Economics" target="_blank">/wiki/The_New_Palgrave:_A_Dictionary_of_Economics</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Franklin M. Fisher  (1987).  "aggregation problem," The New Palgrave: A Dictionary of Economics, v. 1, pp.53-55 <a href="/wiki/The_New_Palgrave:_A_Dictionary_of_Economics" target="_blank">/wiki/The_New_Palgrave:_A_Dictionary_of_Economics</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>J. Felipe & J.S.L. McCombie (2014) The Aggregate Production Function: 'Not Even Wrong.' Review of Political Economy 26(1): 60-84. <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>"Disaggregation". UNESCWA. Disaggregation is the breakdown of observations, usually within a common branch of a hierarchy, to a more detailed level to that at which detailed observations are taken. <a href="https://archive.unescwa.org/sd-glossary/disaggregation" target="_blank">https://archive.unescwa.org/sd-glossary/disaggregation</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Franklin M. Fisher  (1987).  "aggregation problem," The New Palgrave: A Dictionary of Economics, v. 1, pp.53-55 <a href="/wiki/The_New_Palgrave:_A_Dictionary_of_Economics" target="_blank">/wiki/The_New_Palgrave:_A_Dictionary_of_Economics</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>S. Abu Turab Rizvi (1994) The microfoundations project in general equilibrium theory. Cambridge Journal of Economics 18(4) : 357-377. <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
<li id="fn:7"><p>A. Abu Turab Rizivi (2006) "The Sonnenschein-Matel-Dereu Results after Thirty Years." History of Political Economy 38 (Suppl_1): 228–245. http://ebour.com.ar/pdfs/Rizvi%20The%20Sonnenschein%20Mantel%20Debreu%20Results%20after%20Thirty%20Years.pdf" <a href="http://ebour.com.ar/pdfs/Rizvi%20The%20Sonnenschein%20Mantel%20Debreu%20Results%20after%20Thirty%20Years.pdf" target="_blank">http://ebour.com.ar/pdfs/Rizvi%20The%20Sonnenschein%20Mantel%20Debreu%20Results%20after%20Thirty%20Years.pdf</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li>
<li id="fn:8"><p>Alan Kirman (1989) "The Intrinsic Limits of Modern Economic Theory: The Emperor has No Clothes." Economic Journal 99 (395) Supplement: Conference Papers: 126-139. <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li>
<li id="fn:9"><p>A. Abu Turab Rizivi (2006) "The Sonnenschein-Matel-Dereu Results after Thirty Years." History of Political Economy 38 (Suppl_1): 228–245. http://ebour.com.ar/pdfs/Rizvi%20The%20Sonnenschein%20Mantel%20Debreu%20Results%20after%20Thirty%20Years.pdf" <a href="http://ebour.com.ar/pdfs/Rizvi%20The%20Sonnenschein%20Mantel%20Debreu%20Results%20after%20Thirty%20Years.pdf" target="_blank">http://ebour.com.ar/pdfs/Rizvi%20The%20Sonnenschein%20Mantel%20Debreu%20Results%20after%20Thirty%20Years.pdf</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li>
<li id="fn:10"><p>Besanko and Braeutigam, (2005) p. 169 <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li>
<li id="fn:11"><p>Kreps (1990) p. 63. <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li>
<li id="fn:12"><p>Kreps (1990) p. 63. <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li>
<li id="fn:13"><p>Varian (1992) p. 153. <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li>
<li id="fn:14"><p>Varian (1992) p. 153. <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li>
</ol>

Aggregation problem open-in-new

Aggregation problem