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@shlff shlff commented Jun 3, 2023

Hi @jstac this PR updates the lecture supply_demand_heterogeneity.md, along with

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jstac commented Jun 3, 2023

At the start of the lecture, add the following.

"""

Overview

In the previous lecture, we studied competitive equilibria in an economy with many goods.

While the results of the study were informative, we used a strong simplifying assumption: all of the agents in the economy are identical.

In the real world, households, firms and other economic agents differ from one another along many dimensions.

In this lecture, we introduce heterogeneity across consumers by allowing their preferences and endownments to differ.

We will examine competitive equilibrium in this setting.

We will also show how a "representative consumer" can be constructed.

"""

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jstac commented Jun 3, 2023

Take the dot point "A Production Economy will consist of" and shift it to the previous lecture, before the production economy class.

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shlff commented Jun 4, 2023

Thanks @jstac. I've made your suggested changes.

Also I made some other changes to make the lecture run more smoothly by restructuring the contexts, fixing some typos and unify math symbols (for example, use $\Pi$ instead of Pi) here.

This PR is ready for review. Here's a preview:

Looking forward to your comments and further advice.


Here we tudy how competitive equilibrium $p, c^1, c^2$ respond to different $b^i$ and $e^i$, $i \in \{1, 2\}.
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Here we study

$i \in {1, 2}$

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(The final dollar sign is missing.)

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jstac commented Jun 4, 2023

Great job @shlff . Please see the minor requests above.

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shlff commented Jun 4, 2023

Great job @shlff . Please see the minor requests above.

Thanks @jstac . I've made the changes as you suggested and also corrected some typos regarding the subscripts and superscripts.

Looking forward to your comments.

p=\tilde{\mu}^{-1}(\Pi^{\top}b-\Pi^{\top}\Pi e)
$$
* an equilibrium price vector $p$ (normalized somehow)
* an equilibrium allocation $c_1, c_2, \ldots, c_m$ -- a collection of $m$ vectors of dimension $n \times 1$
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Chang from $c^1, c^2, \ldots, c^m$ to $c_1, c_2, \ldots, c_m$ aligned with math notations above.

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Good catch @shlff


Here we study how competitive equilibrium $p, c_1, c_2$ respond to different $b_i$ and $e_i$, $i \in \{1, 2\}$.
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Change $c^1, c^2$ and $b^i$ and $e^i$ to $c_1, c_2$ and $b_i$ and $e_i$ aligned with math notations used above.

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jstac commented Jun 4, 2023

Excellent work with this PR and the multi good equilibrium lecture @shlff

@jstac jstac merged commit 9c1c076 into main Jun 4, 2023
@jstac jstac deleted the sdh_update branch June 4, 2023 22:25
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