From 016f553023fa2dc2d384d921588e9757f33df36b Mon Sep 17 00:00:00 2001 From: Jonathan Conning Date: Sat, 27 Jan 2024 16:29:16 -0500 Subject: [PATCH] add image to explanation --- notebooks/kbar.ipynb | 27 +++++++++++++++++++++++---- notebooks/media/kbarfig.png | Bin 0 -> 37928 bytes 2 files changed, 23 insertions(+), 4 deletions(-) create mode 100644 notebooks/media/kbarfig.png diff --git a/notebooks/kbar.ipynb b/notebooks/kbar.ipynb index 4e00625..cb6e48d 100644 --- a/notebooks/kbar.ipynb +++ b/notebooks/kbar.ipynb @@ -79,7 +79,7 @@ "id": "8a30128d", "metadata": {}, "source": [ - "Re-arranging to solve for the $\\kappa=\\bar kappa$ at which this holds as an equality, we find:\n", + "Re-arranging to solve for the $\\kappa=\\bar \\kappa$ at which this holds as an equality, we find:\n", "\n", "Setting $c_{1}^{0} =c_1^F = c_{2}^{0}$ equal to the implied efficient continuation contract into no-renegotiation constraint we can solve for the $\\bar \\kappa$ value of $\\kappa$ that allows this to just hold:\n", "\n", @@ -104,6 +104,17 @@ "For the monopoly case we simply replace the competitive $c_1^F$ term by the analogous $c_1^{mF}$ efficient monopoly contract ters. The monopoly formula for the threshold is thus $\\bar \\kappa^m = c_1^{mF} \\cdot \\Upsilon$" ] }, + { + "cell_type": "markdown", + "id": "241fe6e2", + "metadata": {}, + "source": [ + "This diagram helps to visualize. Zero's first-best commitment smoothing contract at $F$ is not because the $\\kappa =\\bar \\kappa$ renegotiation cost is just high enough to make the bank reject the most favorable renegotiated contract that could be offered to the bank at $R$ .\n", + "\n", + "\n", + "" + ] + }, { "cell_type": "markdown", "id": "20ae35ed-0ed9-4ad6-a94c-cde7fab05407", @@ -261,14 +272,14 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 8, "id": "7279cf5b-f088-4152-b8d2-2d31d686c478", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { - "model_id": "38c24a8cd8324e2697fabb295b069ea0", + "model_id": "db9e21b916cd48458439fbb7c7ef2a23", "version_major": 2, "version_minor": 0 }, @@ -281,8 +292,16 @@ } ], "source": [ - "interact(plotkb, rho=(0.1, 2, 0.101), y0=(50,200,10));" + "interact(plotkb, rho=(0.1, 2, 0.101), y0=(50,300,10));" ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e87f6278", + "metadata": {}, + "outputs": [], + 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