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Copy file name to clipboardExpand all lines: in-work/supply_demand_foundations_v2.md
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@@ -218,7 +218,7 @@ Sometimes a Hicksian demand curve is called a **compensated** demand curve in or
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We'll discuss these distinct demand curves more below.
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## Demand Curve as Constrained Utility Maximization
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## Demand Curve Implied by Constrained Utility Maximization
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For now, we assume that the budget constraint is {eq}`eq:old2`.
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where $p_i$ is the price of one unit of consumption in state $i$.
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The state commodities being traded are often called **Arrow securities**.
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The state-contingent commodities being traded are often called **Arrow securities**.
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Before the random state of the world $i$ is realized, the consumer sells his/her state-contingent endowment bundle and purchases a state-contingent consumption bundle.
We'll see that the monopolist sets a **lower output** $q$ than does either a
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We'll eventually see that a monopolist sets a **lower output** $q$ than does either a
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* planner who chooses $q$ to maximize social welfare
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* a competitive equilibrium
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**Remark:** We can make exercises asking readers to verify the monopolist's supply curve {eq}`eq:qmonop` and the
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**Remark:** We can make exercises asking readers to verify the monopolist's supply curve {eq}`eq:qmonop`.
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(This is another version of the first welfare theorem.)
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We can read the competitive equilbrium price vector off the inverse demand curve or the inverse supply curve.
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We can read a competitive equilbrium price vector from either
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* the inverse demand curve, or
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* the inverse supply curve
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<!-- #endregion -->
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## Initial notes to Jiacheng for coding
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<!-- #region -->
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## Notes about coding strategy
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Hi Jiacheng.
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These are just some suggestions about how to begin writing code.
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Here are some suggestions about how to write our code.
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I sketch some things that are "not even pseudo code". Here goes.
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I sketch some ideas that are "not even pseudo code".
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I recommend that we start "general" and write a Python class that will do "everything".
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Once we get that working with a bunch of fun examples, we can then "work backwards" and make some very simple "baby code" that starts with simple cases (e.g., a scalar case) and graduallly builds up to the class.
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Once we get that working with a bunch of fun examples, we can then "work backwards" and make some very simple "baby code" that starts with a simple cases (e.g., a scalar case) and graduallly adds functions that we'll ultimately assemble as methods that appear in our class.
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The fun thing will be to make some revealing examples.
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@@ -664,8 +669,7 @@ I recommend making a Python class with the following attributes:
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* an $n \times 1$ nonnegative vector $h$
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* an $n \times n$ positive definite matrix $J$
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Along the lines of your great suggestion (now incorporated in the main text in the previous cell)
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the class would do a test to make sure that $b > > \Pi e $ and raise an exception if it is violated
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The class will include a test to make sure that $b > > \Pi e $ and raise an exception if it is violated
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(at some threshold level we'd have to specify).
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* **A Person** in the form of a pair that consists of
@@ -695,7 +699,7 @@ the class would do a test to make sure that $b > > \Pi e $ and raise an excepti
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**Remark:** I don't know whether we want to be simple or fancy in terms of using class inheritance in creating a person or an economy.
To compute a competitive equilibrium for a production economy where demand curve is pinned down by the marginal utility of wealth $\mu$, we first solve for the allocation using equation.
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To compute a competitive equilibrium for a production economy where demand curve is pinned down by the marginal utility of wealth $\mu$, we first compute an allocation by solving a planning problem.
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Then we compute the equilibrium price vector using the inverse demand or supply curve.
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### A Monopolist Supplier
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Let us follow the above digression and consider a monopolist supplier in this economy. We add a method to the `production_economy` class we built above to compute the equilibrium price and allocation when there is a monopolist supplier. Since the supplier now has the price-setting power,
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Let's consider a monopolist supplier.
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We add a method to the `production_economy` class we built above to compute the equilibrium price and allocation when there is a monopolist supplier.
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Since the supplier now has the price-setting power
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- we first compute the optimal quantity that solves the monopolist's profit maximization problem.
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- Then we derive the required price level from the consumer's inverse supply curve.
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- Then we back out an equilibrium price from the consumer's inverse demand curve.
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Next, we use a graph for the single good case to illustrate the difference between a competitive equilibrium and an equilibrium with a monopolist supplier.
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Recall that in a competitive equilibrium of the economy, the price-taking supplier equates the marginal revenue $p$ with the marginal cost $h + Hq$.
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This yields the monopolist's inverse supply curve.
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A monopolist's marginal revenue is not constant but instead is a non-trivial function of the quantity it sets.
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The monopolist's marginal revenue is
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Next, we use a graph for the single good case to illustrate the difference between a competitive equilibrium and an equilibrium with a monopolist supplier. Recall that in a competitive equilibrium of the economy, the price-taking supplier equalizes the marginal revenue $p$ with the marginal cost $h + Hq$. This yields the inverse supply curve. In a monopolist economy, the marginal revenue of the firm is a function of the quantity it chooses:
which the monopolist supplier equalizes with the marginal cost.
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Our plot illustrates the fact that the monopolist supplier's equilibrium output is lower than either the competitive equilibrium or the social optimal level. In a single good case, this equilibrium is associated with a higher price of the good.
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which the monopolist equates to its marginal cost.
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Our plot indicates that the monopolist supplier's equilibrium output is lower than either the competitive equilibrium or the social optimal level.
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In a single good case, this equilibrium is associated with a higher price of the good.
description: This website presents a set of lectures on python programming for economics, designed and written by Thomas J. Sargent and John Stachurski.
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keywords: Python, QuantEcon, Quantitative Economics, Economics, Sloan, Alfred P. Sloan Foundation, Tom J. Sargent, John Stachurski
#description: This website presents a set of lectures on python programming for economics, designed and written by Thomas J. Sargent and John Stachurski.
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#keywords: Python, QuantEcon, Quantitative Economics, Economics, Sloan, Alfred P. Sloan Foundation, Tom J. Sargent, John Stachurski
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