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2 changes: 1 addition & 1 deletion lectures/ak2.md
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Expand Up @@ -226,7 +226,7 @@ r_t & = \alpha K_t^\alpha L_t^{1-\alpha}
\end{aligned}
$$ (eq:firmfonc)

Output can be consumed either by old people or young people; or sold to young people who use it to augment the capital stock; or sold to the government for uses that do not generate utility for the people in the model (i.e., ``it is thrown into the ocean'').
Output can be consumed either by old people or young people; or sold to young people who use it to augment the capital stock; or sold to the government for uses that do not generate utility for the people in the model (i.e., "it is thrown into the ocean").


The firm thus sells output to old people, young people, and the government.
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2 changes: 1 addition & 1 deletion lectures/ar1_turningpts.md
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Expand Up @@ -276,7 +276,7 @@ $$

This is designed to express the event

- ``after one or two decrease(s), $Y$ will grow for two consecutive quarters''
- "after one or two decrease(s), $Y$ will grow for two consecutive quarters"

Following {cite}`wecker1979predicting`, we can use simulations to calculate probabilities of $P_t$ and $N_t$ for each period $t$.

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2 changes: 1 addition & 1 deletion lectures/exchangeable.md
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Expand Up @@ -262,7 +262,7 @@ So there is something to learn from the past about the future.
## Exchangeability

While the sequence $W_0, W_1, \ldots$ is not IID, it can be verified that it is
**exchangeable**, which means that the joint distributions $h(W_0, W_1)$ and $h(W_1, W_0)$ of the ''re-ordered'' sequences
**exchangeable**, which means that the joint distributions $h(W_0, W_1)$ and $h(W_1, W_0)$ of the "re-ordered" sequences
satisfy

$$
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2 changes: 1 addition & 1 deletion lectures/likelihood_ratio_process.md
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Expand Up @@ -1725,7 +1725,7 @@ markov_results = analyze_markov_chains(P_f, P_g)
Likelihood processes play an important role in Bayesian learning, as described in {doc}`likelihood_bayes`
and as applied in {doc}`odu`.

Likelihood ratio processes are central to Lawrence Blume and David Easley's answer to their question ''If you're so smart, why aren't you rich?'' {cite}`blume2006if`, the subject of the lecture{doc}`likelihood_ratio_process_2`.
Likelihood ratio processes are central to Lawrence Blume and David Easley's answer to their question "If you're so smart, why aren't you rich?" {cite}`blume2006if`, the subject of the lecture{doc}`likelihood_ratio_process_2`.

Likelihood ratio processes also appear in {doc}`advanced:additive_functionals`, which contains another illustration of the **peculiar property** of likelihood ratio processes described above.

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6 changes: 3 additions & 3 deletions lectures/likelihood_ratio_process_2.md
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Expand Up @@ -29,7 +29,7 @@ kernelspec:
## Overview

A likelihood ratio process lies behind Lawrence Blume and David Easley's answer to their question
''If you're so smart, why aren't you rich?'' {cite}`blume2006if`.
"If you're so smart, why aren't you rich?" {cite}`blume2006if`.

Blume and Easley constructed formal models to study how differences of opinions about probabilities governing risky income processes would influence outcomes and be reflected in prices of stocks, bonds, and insurance policies that individuals use to share and hedge risks.

Expand Down Expand Up @@ -294,7 +294,7 @@ $$ (eq:welfareW)

where $\lambda \in [0,1]$ is a Pareto weight that tells how much the planner likes agent $1$ and $1 - \lambda$ is a Pareto weight that tells how much the social planner likes agent $2$.

Setting $\lambda = .5$ expresses ''egalitarian'' social preferences.
Setting $\lambda = .5$ expresses "egalitarian" social preferences.

Notice how social welfare criterion {eq}`eq:welfareW` takes into account both agents' preferences as represented by formula {eq}`eq:objectiveagenti`.

Expand Down Expand Up @@ -369,7 +369,7 @@ values of the likelihood ratio process $l_t(s^t)$:

$$l_\infty (s^\infty) = 0; \quad c_\infty^1 = 0$$

* In the above case, agent 2 is ''smarter'' than agent 1, and agent 1's share of the aggregate endowment converges to zero.
* In the above case, agent 2 is "smarter" than agent 1, and agent 1's share of the aggregate endowment converges to zero.



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