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",
+    "<img src=\"media/kbarfig.png\" width=\"500\"/>\n",
+    "</div>"
+   ]
+  },
   {
    "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": [],
+   "source": []
   }
  ],
  "metadata": {
diff --git a/notebooks/media/kbarfig.png b/notebooks/media/kbarfig.png
new file mode 100644
index 0000000..f9f8626
Binary files /dev/null and b/notebooks/media/kbarfig.png differ