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Copy file name to clipboardExpand all lines: lectures/intro_supply_demand.md
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@@ -33,7 +33,7 @@ Exports were regarded as good because they brought in bullion (gold flowed into
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Imports were regarded as bad because bullion was required to pay for them (gold flowed out).
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This [zero-sum](https://en.wikipedia.org/wiki/Zero-sum_game) view of economics was eventually overturned by the work of the classical economists such as [Adam Smith](https://en.wikipedia.org/wiki/Adam_Smith) and [David Ricado](https://en.wikipedia.org/wiki/David_Ricardo), who showed how freeing domestic and international trade can enhance welfare.
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This [zero-sum](https://en.wikipedia.org/wiki/Zero-sum_game) view of economics was eventually overturned by the work of the classical economists such as [Adam Smith](https://en.wikipedia.org/wiki/Adam_Smith) and [David Ricardo](https://en.wikipedia.org/wiki/David_Ricardo), who showed how freeing domestic and international trade can enhance welfare.
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There are many different expressions of this idea in economics.
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### A discrete example
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```{prf:example}
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:label: isd_ex_cs
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Regarding consumer surplus, suppose that we have a single good and 10 consumers.
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These 10 consumers have different preferences; in particular, the amount they would be willing to pay for one unit of the good differs.
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(We have ordered consumers by willingness to pay, in descending order.)
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```
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If $p$ is the price of the good and $w_i$ is the amount that consumer $i$ is willing to pay, then $i$ buys when $w_i \geq p$.
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When the price is $p$, producer surplus for producer $i$ is $\max\{p - v_i, 0\}$.
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```{prf:example}
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:label: isd_ex_dc
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For example, a producer willing to sell at \$10 and selling at price \$20 makes a surplus of \$10.
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Total producer surplus is given by
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$$
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The shaded area is the total producer surplus in this continuous model.
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```
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```{code-cell} ipython3
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We will not try to cover these ideas here, partly because the subject is too big, and partly because you only need to know one rule for this lecture, stated below.
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If $f(x) = c + \mathrm{d} x$, then
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If $f(x) = c + dx$, then
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$$
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\int_a^b f(x) \mathrm{d} x = c (b - a) + \frac{d}{2}(b^2 - a^2)
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Observe that the equilibrium quantity equals the same $q$ given by equation {eq}`eq:old1`.
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The outcome that the quantity determined by equation {eq}`eq:old1` equates
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supply to demand brings us a **key finding:**
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supply to demand brings us a *key finding*:
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* a competitive equilibrium quantity maximizes our welfare criterion
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In addition
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* we'll derive **demand curves** from a consumer problem that maximizes a
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**utility function** subject to a **budget constraint**.
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* we'll derive *demand curves* from a consumer problem that maximizes a
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*utility function* subject to a *budget constraint*.
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* we'll derive **supply curves** from the problem of a producer who is price
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taker and maximizes his profits minus total costs that are described by a **cost function**.
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* we'll derive *supply curves* from the problem of a producer who is price
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taker and maximizes his profits minus total costs that are described by a *cost function*.
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