diff --git a/lectures/intro_supply_demand.md b/lectures/intro_supply_demand.md index 7c5ca42a..5e5a49da 100644 --- a/lectures/intro_supply_demand.md +++ b/lectures/intro_supply_demand.md @@ -18,34 +18,26 @@ the main topics of elementary microeconomics. Throughout the lecture, we focus on models with one good and one price. -({doc}`Later ` we will investigate settings with -many goods.) + +In a {doc}`subsequent lecture ` we will investigate settings with +many goods. Key infrastructure concepts that we'll encounter in this lecture are * inverse demand curves -* marginal utilities of wealth * inverse supply curves * consumer surplus * producer surplus -* social welfare as a sum of consumer and producer surpluses -* competitive equilibrium - - -We will provide a version of the [first fundamental welfare theorem](https://en.wikipedia.org/wiki/Fundamental_theorems_of_welfare_economics), which was formulated by +* social welfare as the sum of consumer and producer surpluses +* relationship between equilibrium quantity and social welfare optimum -* [Leon Walras](https://en.wikipedia.org/wiki/L%C3%A9on_Walras) -* [Francis Ysidro Edgeworth](https://en.wikipedia.org/wiki/Francis_Ysidro_Edgeworth) -* [Vilfredo Pareto](https://en.wikipedia.org/wiki/Vilfredo_Pareto) +Throughout the lectures, we'll assume that inverse demand and supply curves are **affine** functions of output. -Important extensions to the key ideas were obtained by +("Affine" means "linear plus a constant".) -* [Abba Lerner](https://en.wikipedia.org/wiki/Abba_P._Lerner) -* [Harold Hotelling](https://en.wikipedia.org/wiki/Harold_Hotelling) -* [Paul Samuelson](https://en.wikipedia.org/wiki/Paul_Samuelson) -* [Kenneth Arrow](https://en.wikipedia.org/wiki/Kenneth_Arrow) -* [Gerard Debreu](https://en.wikipedia.org/wiki/G%C3%A9rard_Debreu) +We'll also assume affine inverse supply and demand functions when we study models with multiple consumption goods in our {doc}`subsequent lecture `. +We do this in order to simplify the exposition and enable us to use just a few tools from linear algebra, namely, matrix multiplication and matrix inversion. In our exposition we will use the following imports. @@ -98,6 +90,8 @@ class Market: ``` + + Let's create an instance. ```{code-cell} ipython3 @@ -128,7 +122,7 @@ ax.set_ylabel('price') plt.show() ``` - +In the above graph, an **equilibrium** price, quantity pair occurs at the intersection of the supply and demand curves. ### Consumer surplus @@ -175,12 +169,12 @@ plt.show() ``` -Consumer surplus gives a measure of total consumer welfare at quantity $q$. +Consumer surplus provides a measure of total consumer welfare at quantity $q$. -The idea is that the inverse demand curve $d_0 - d_1 q$ shows willingness to -pay at a given quantity $q$. +The idea is that the inverse demand curve $d_0 - d_1 q$ shows a consumer's willingness to +pay for an additional increment of the good at a given quantity $q$. -The difference between willingness to pay and the actual price is the surplus. +The difference between willingness to pay and the actual price is consumer surplus. The value $S_c(q)$ is the "sum" (i.e., integral) of these surpluses when the total quantity purchased is $q$ and the purchase price is $p$. @@ -245,7 +239,7 @@ The idea is similar to that of consumer surplus. The inverse supply curve $s_0 + s_1 q$ shows the price at which producers are prepared to sell, given quantity $q$. -The difference between willingness to sell and the actual price is the surplus. +The difference between willingness to sell and the actual price is producer surplus. The value $S_p(q)$ is the integral of these surpluses. diff --git a/lectures/supply_demand_multiple_goods.md b/lectures/supply_demand_multiple_goods.md index 998b82da..ddea4d32 100644 --- a/lectures/supply_demand_multiple_goods.md +++ b/lectures/supply_demand_multiple_goods.md @@ -17,16 +17,44 @@ kernelspec: ## Overview In a {doc}`previous lecture ` we studied supply, demand -and welfare in a market with just one good. +and welfare in a market with a single consumption good. In this lecture, we study a setting with $n$ goods and $n$ corresponding prices. +Key infrastructure concepts that we'll encounter in this lecture are + +* inverse demand curves +* marginal utilities of wealth +* inverse supply curves +* consumer surplus +* producer surplus +* social welfare as a sum of consumer and producer surpluses +* competitive equilibrium + + +We will provide a version of the [first fundamental welfare theorem](https://en.wikipedia.org/wiki/Fundamental_theorems_of_welfare_economics), which was formulated by + +* [Leon Walras](https://en.wikipedia.org/wiki/L%C3%A9on_Walras) +* [Francis Ysidro Edgeworth](https://en.wikipedia.org/wiki/Francis_Ysidro_Edgeworth) +* [Vilfredo Pareto](https://en.wikipedia.org/wiki/Vilfredo_Pareto) + +Important extensions to the key ideas were obtained by + +* [Abba Lerner](https://en.wikipedia.org/wiki/Abba_P._Lerner) +* [Harold Hotelling](https://en.wikipedia.org/wiki/Harold_Hotelling) +* [Paul Samuelson](https://en.wikipedia.org/wiki/Paul_Samuelson) +* [Kenneth Arrow](https://en.wikipedia.org/wiki/Kenneth_Arrow) +* [Gerard Debreu](https://en.wikipedia.org/wiki/G%C3%A9rard_Debreu) + + We shall describe two classic welfare theorems: * **first welfare theorem:** for a given distribution of wealth among consumers, a competitive equilibrium allocation of goods solves a social planning problem. * **second welfare theorem:** An allocation of goods to consumers that solves a social planning problem can be supported by a competitive equilibrium with an appropriate initial distribution of wealth. +As usual, we start by importing some Python modules. + ```{code-cell} ipython3 # import some packages import numpy as np