Add lecture on commodity price model#172
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HengchengZhang merged 5 commits intomainfrom Apr 28, 2023
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@HengchengZhang could you please fix the merge conflict? You will need to expand the bib file to include all new references from the open PRs. |
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Hi @jstac, fixed by merging changes from |
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@shlff could you please review? Thanks. |
shlff
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Apr 26, 2023
lectures/commod_price.md
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| 1. can be traded by speculators and | ||
| 1. have intrinsic value to consumers. | ||
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| Total demand is the sum of consumer demand and demand by spectulators. |
lectures/commod_price.md
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| Regarding quantities, | ||
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| * supply is the sum of of carryover by speculators and the current harvest |
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| ## The Model | ||
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| Consider a market for a single commodity, whose price is given at $t$ by |
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is given at $t$ -> is given at time $t$?
lectures/commod_price.md
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| We now know that an equilibrium can be obtained by finding a function $p^*$ | ||
| that satisfies [](eq:dopf). | ||
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| It can be shown that, under mild conditions there is exactly on function on |
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exactly on function on -> exactly one function on
| ax.plot(grid, price, 'k-', alpha=0.5, lw=2, label=r'$p^*$') | ||
| ax.legend() | ||
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| plt.show() |
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Shall we add x and y labels for the plot above?
| error = max(np.abs(new_price - price)) | ||
| price = new_price | ||
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| ax.plot(grid, price, 'k-', alpha=0.5, lw=2, label=r'$p^*$') |
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Shall we say label=r'approximation of $p^*$' instead?
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Thanks @shlff , nice work, much appeciated. |
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Closes #145
Could someone please do a first review. I'm sure there will be typos.
Then I want to discuss adding an exercise. In the exercise, we might change harvests to a Markov process.
It would be good to add in the interest rate and we could make it stochastic.
Still need to add a reference to https://johnstachurski.net/edtc, where a more formal treatment with proofs can be found (in Ch 6).