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Fix emphasis vs definitions in samuelson.md
Changes per #721: - second-order linear difference equation - national output identity - consumption function - accelerator - accelerator coefficient - aggregate demand - aggregate supply - business cycles - stochastic linear difference equation - marginal propensity to consume - steady state - random - stochastic - shocks - disturbances - second-order scalar linear stochastic difference equation - characteristic polynomial - zeros - roots All terms changed from italic to bold as they are definitions per style guide.
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lectures/samuelson.md

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### Samuelson's model
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Samuelson used a *second-order linear difference equation* to
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Samuelson used a **second-order linear difference equation** to
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represent a model of national output based on three components:
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- a *national output identity* asserting that national output or national income is the
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- a **national output identity** asserting that national output or national income is the
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sum of consumption plus investment plus government purchases.
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- a Keynesian *consumption function* asserting that consumption at
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- a Keynesian **consumption function** asserting that consumption at
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time $t$ is equal to a constant times national output at time $t-1$.
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- an investment *accelerator* asserting that investment at time
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$t$ equals a constant called the *accelerator coefficient*
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- an investment **accelerator** asserting that investment at time
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$t$ equals a constant called the **accelerator coefficient**
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times the difference in output between period $t-1$ and
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$t-2$.
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Consumption plus investment plus government purchases
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constitute *aggregate demand,* which automatically calls forth an
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equal amount of *aggregate supply*.
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constitute **aggregate demand,** which automatically calls forth an
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equal amount of **aggregate supply**.
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(To read about linear difference equations see [here](https://en.wikipedia.org/wiki/Linear_difference_equation) or chapter IX of {cite}`Sargent1987`.)
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Samuelson used the model to analyze how particular values of the
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marginal propensity to consume and the accelerator coefficient might
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give rise to transient *business cycles* in national output.
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give rise to transient **business cycles** in national output.
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Possible dynamic properties include
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identity representing random fluctuations in aggregate demand.
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This modification makes national output become governed by a second-order
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*stochastic linear difference equation* that, with appropriate parameter values,
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**stochastic linear difference equation** that, with appropriate parameter values,
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gives rise to recurrent irregular business cycles.
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(To read about stochastic linear difference equations see chapter XI of
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Y_t = C_t + I_t + G_t
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```
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- The parameter $\alpha$ is peoples' *marginal propensity to consume*
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- The parameter $\alpha$ is peoples' **marginal propensity to consume**
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out of income - equation {eq}`consumption` asserts that people consume a fraction of
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$\alpha \in (0,1)$ of each additional dollar of income.
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- The parameter $\beta > 0$ is the investment accelerator coefficient - equation
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We are interested in studying
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- the transient fluctuations in $Y_t$ as it converges to its
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*steady state* level
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**steady state** level
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- the *rate* at which it converges to a steady state level
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The deterministic version of the model described so far --- meaning that
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### Stochastic version of the model
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We create a *random* or *stochastic* version of the model by adding
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a random process of *shocks* or *disturbances*
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We create a **random** or **stochastic** version of the model by adding
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a random process of **shocks** or **disturbances**
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$\{\sigma \epsilon_t \}$ to the right side of equation {eq}`second_order`,
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leading to the *second-order scalar linear stochastic difference equation*:
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leading to the **second-order scalar linear stochastic difference equation**:
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```{math}
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:label: second_stochastic
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```
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To discover the properties of the solution of {eq}`second_stochastic2`,
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it is useful first to form the *characteristic polynomial*
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it is useful first to form the **characteristic polynomial**
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for {eq}`second_stochastic2`:
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```{math}
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where $z$ is possibly a complex number.
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We want to find the two *zeros* (a.k.a. *roots*) -- namely
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We want to find the two **zeros** (a.k.a. **roots**) -- namely
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$\lambda_1, \lambda_2$ -- of the characteristic polynomial.
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These are two special values of $z$, say $z= \lambda_1$ and

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