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...when Engels Law, backed by a good amount empirical evidence, demonstrates that overall consumer preferences are not homothetic.

See for example, Jorgenson (1997)

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    $\begingroup$ This question would be improved by linking to a few examples of the good amount of empirical evidence. $\endgroup$ – Giskard Feb 11 '16 at 12:31
  • $\begingroup$ Basically any household survey will show that as income of household's increases the share of their income that is dedicated to, say, food goods decreases, rather than remains constant. A.Deaton touches on this subject briefly (although by talking about international, rather than national comparisons) on p8 link $\endgroup$ – StatsScared Feb 11 '16 at 15:39
  • $\begingroup$ These are links to references of empirical evidence. I agree that your claim is true, but it would be nice to have a link to an empirical study. $\endgroup$ – Giskard Feb 11 '16 at 16:20
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    $\begingroup$ I am not very well versed with microeconomic theory and studies related to it, so I actually do not know of any particular study that proves this. However, I have explored household level income and consumption data myself and I was intrigued by the fact that the Engel's Law is pretty self-evident. It was because of this that I decided to post the question since I recall many models assume homothetic preferences. Perhaps the error is the the premise that many models actually assume homothetic preferences? $\endgroup$ – StatsScared Feb 11 '16 at 19:45
  • $\begingroup$ I think it is mainly used to teach basic theory but I am not well versed. $\endgroup$ – Giskard Feb 11 '16 at 22:26
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Let me answer the question by following @HRSE's explanation and recommending a good reading. Eaton and Kortum (Ecta, 2002) use homothetic preferences, a convenient assumption to get a tractable general equilibrium Ricardian model of trade. However, there is exhaustive evidence that the income elasticity of demand varies across goods and that this variation is economically significant.

Fieler (Ecta, 2011) follows Eaton and Kortum (2002) and makes substantial theoretical progress by introducing non-homothetic preferences. High income elasticity goods have a higher dispersion and are produced in high income countries. This higher dispersion leads to more trade among the high-income countries relative to low-income countries. The production side still assumes perfect competition.

  • Eaton, Jonathan, Kortum, Samuel, 2002. Technology, geography, and trade. Econometrica 70, 1741–1779.
  • Fieler, Ana Cecília, 2011. Non-homotheticity and bilateral trade: evidence and a quantitative explanation. Econometrica 79, 1069–1101.
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Here a short answer: Homothetic, identical preferences have the modelling advantage that the distribution of income across individuals does not matter for aggregate demand. That is, if you want to study, let's say, monetary policy where you do not expect changes in the distribution of income to affect your policy recommendations, then this is a reasonable assumption to make. If you want to study questions where changes in the distribution of income have large impact on policy recommendation (e.g., optimal taxation) this may be a bad assumption.

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  • $\begingroup$ This is great, thanks. Some questions: a) are identical preferences the same as homothetic preferences? b) Is assuming homothetic preferences the same as assuming that the relative distribution of income or expenditure will be unchanged? c) any resources that elaborates more on this topic. I've gone through several online classroom notes and book on consumer choice theory but couldn't find intuitive real-world examples $\endgroup$ – StatsScared Feb 12 '16 at 18:31
  • $\begingroup$ a) No, identical preferences mean that all individuals have utility functions that are monotone transformations of each other and homothetic preferences is a special class of utility function. b) No, it only means that changes in the relative distribution of income does not affect what happens to aggregate demand. Productivity shocks for example may still affect the distribution of income. $\endgroup$ – HRSE Feb 13 '16 at 2:36
  • $\begingroup$ Regarding c) I actually think if you carefully read the math of an intermediate microeconomics book, the concept of homothetic preferences will be quite clear to you. For a real world example, consider the demand for left and right shoes. Clearly, if my income increases, I will not start to buy more left shoes than right shoes. $\endgroup$ – HRSE Feb 13 '16 at 2:41

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