{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": [
     "remove_cell"
    ]
   },
   "outputs": [],
   "source": [
    "from datascience import *\n",
    "\n",
    "import sympy\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "import matplotlib.patches as patches\n",
    "# plt.style.use('seaborn-muted')\n",
    "mpl.rcParams['figure.dpi'] = 200\n",
    "%matplotlib inline\n",
    "\n",
    "from IPython.display import display\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "solve = lambda x,y: sympy.solve(x-y)[0] if len(sympy.solve(x-y))==1 else \"Not Single Solution\"\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "4f243c01-873e-4eb5-bdfe-451f2a06dfea"
   },
   "source": [
    "# Market Equilibria\n",
    "\n",
    "We will now explore the relationship between price and quantity of oranges produced between 1924 and 1938. Since the data {cite}`01demand-fruits` is from the 1920s and 1930s, it is important to remember that the prices are much lower than what they would be today because of inflation, competition, innovations, and other factors. For example, in 1924, a ton of oranges would have costed \\$6.63; that same amount in 2019 is \\$100.78. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "cell_id": "5a6c6746-bad6-466e-8c18-bc16f5fad344"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Year</th> <th>Pear Price</th> <th>Pear Unloads (Tons)</th> <th>Plum Price</th> <th>Plum Unloads</th> <th>Peach Price</th> <th>Peach Unloads</th> <th>Orange Price</th> <th>Orange Unloads</th> <th>NY Factory Wages</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>1924</td> <td>8.04      </td> <td>18489              </td> <td>8.86      </td> <td>6582        </td> <td>4.96       </td> <td>41880        </td> <td>6.63        </td> <td>21258         </td> <td>27.22           </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1925</td> <td>5.67      </td> <td>21919              </td> <td>7.27      </td> <td>5526        </td> <td>4.87       </td> <td>38772        </td> <td>9.19        </td> <td>15426         </td> <td>28.03           </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1926</td> <td>5.44      </td> <td>29328              </td> <td>6.68      </td> <td>5742        </td> <td>3.35       </td> <td>46516        </td> <td>7.2         </td> <td>24762         </td> <td>28.89           </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1927</td> <td>7.15      </td> <td>17082              </td> <td>8.09      </td> <td>5758        </td> <td>5.7        </td> <td>32500        </td> <td>8.63        </td> <td>22766         </td> <td>29.14           </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1928</td> <td>5.81      </td> <td>20708              </td> <td>7.41      </td> <td>6000        </td> <td>4.13       </td> <td>46820        </td> <td>10.71       </td> <td>18766         </td> <td>29.34           </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1929</td> <td>7.6       </td> <td>13071              </td> <td>10.86     </td> <td>3504        </td> <td>6.7        </td> <td>36990        </td> <td>6.36        </td> <td>35702         </td> <td>29.97           </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1930</td> <td>5.06      </td> <td>22068              </td> <td>6.23      </td> <td>7998        </td> <td>6.35       </td> <td>29680        </td> <td>10.5        </td> <td>23718         </td> <td>28.68           </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1931</td> <td>5.4       </td> <td>19255              </td> <td>6.86      </td> <td>5638        </td> <td>3.91       </td> <td>50940        </td> <td>5.81        </td> <td>39263         </td> <td>26.35           </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1932</td> <td>4.06      </td> <td>17293              </td> <td>6.09      </td> <td>7364        </td> <td>4.57       </td> <td>27642        </td> <td>4.71        </td> <td>38553         </td> <td>21.98           </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1933</td> <td>4.78      </td> <td>11063              </td> <td>5.86      </td> <td>8136        </td> <td>3.57       </td> <td>35560        </td> <td>4.6         </td> <td>36540         </td> <td>22.26           </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (5 rows omitted)</p>"
      ],
      "text/plain": [
       "Year | Pear Price | Pear Unloads (Tons) | Plum Price | Plum Unloads | Peach Price | Peach Unloads | Orange Price | Orange Unloads | NY Factory Wages\n",
       "1924 | 8.04       | 18489               | 8.86       | 6582         | 4.96        | 41880         | 6.63         | 21258          | 27.22\n",
       "1925 | 5.67       | 21919               | 7.27       | 5526         | 4.87        | 38772         | 9.19         | 15426          | 28.03\n",
       "1926 | 5.44       | 29328               | 6.68       | 5742         | 3.35        | 46516         | 7.2          | 24762          | 28.89\n",
       "1927 | 7.15       | 17082               | 8.09       | 5758         | 5.7         | 32500         | 8.63         | 22766          | 29.14\n",
       "1928 | 5.81       | 20708               | 7.41       | 6000         | 4.13        | 46820         | 10.71        | 18766          | 29.34\n",
       "1929 | 7.6        | 13071               | 10.86      | 3504         | 6.7         | 36990         | 6.36         | 35702          | 29.97\n",
       "1930 | 5.06       | 22068               | 6.23       | 7998         | 6.35        | 29680         | 10.5         | 23718          | 28.68\n",
       "1931 | 5.4        | 19255               | 6.86       | 5638         | 3.91        | 50940         | 5.81         | 39263          | 26.35\n",
       "1932 | 4.06       | 17293               | 6.09       | 7364         | 4.57        | 27642         | 4.71         | 38553          | 21.98\n",
       "1933 | 4.78       | 11063               | 5.86       | 8136         | 3.57        | 35560         | 4.6          | 36540          | 22.26\n",
       "... (5 rows omitted)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fruitprice = Table.read_table('fruitprice.csv')\n",
    "fruitprice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Finding the Equilibrium\n",
    "\n",
    "An important concept in econmics is the market equilibrium. This is the point at which the demand and supply curves meet and represents the \"optimal\" level of production and price in that market."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{admonition} Definition\n",
    "The **market equilibrium** is the price and quantity at which the demand and supply curves intersect. The price and resulting transaction quantity at the equilibrium is what we would predict to observe in the market.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's walk through how to the market equilibrium using the market for oranges as an example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "61b55ebf-36a4-4ce1-89b7-4b860da25de4"
   },
   "source": [
    "### Data Preprocessing\n",
    "\n",
    "Because we are only examining the relationship between prices and quantity for oranges, we can create a new table with the relevant columns: `Year`, `Orange Price`, and `Orange Unloads`. Here, `Orange Price` is measured in dollars, while `Orange Unloads` is measured in tons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "cell_id": "b75d49b7-7c34-4c8a-a844-e16f26940df7"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Year</th> <th>Orange Price</th> <th>Orange Unloads</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>1924</td> <td>6.63        </td> <td>21258         </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1925</td> <td>9.19        </td> <td>15426         </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1926</td> <td>7.2         </td> <td>24762         </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1927</td> <td>8.63        </td> <td>22766         </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1928</td> <td>10.71       </td> <td>18766         </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1929</td> <td>6.36        </td> <td>35702         </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1930</td> <td>10.5        </td> <td>23718         </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1931</td> <td>5.81        </td> <td>39263         </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1932</td> <td>4.71        </td> <td>38553         </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1933</td> <td>4.6         </td> <td>36540         </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (5 rows omitted)</p>"
      ],
      "text/plain": [
       "Year | Orange Price | Orange Unloads\n",
       "1924 | 6.63         | 21258\n",
       "1925 | 9.19         | 15426\n",
       "1926 | 7.2          | 24762\n",
       "1927 | 8.63         | 22766\n",
       "1928 | 10.71        | 18766\n",
       "1929 | 6.36         | 35702\n",
       "1930 | 10.5         | 23718\n",
       "1931 | 5.81         | 39263\n",
       "1932 | 4.71         | 38553\n",
       "1933 | 4.6          | 36540\n",
       "... (5 rows omitted)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "oranges_raw = fruitprice.select(\"Year\", \"Orange Price\", \"Orange Unloads\")\n",
    "oranges_raw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "8c900ffc-173d-4c91-97c9-e1d8924c8d67"
   },
   "source": [
    "Next, we will rename our columns. In this case, let's rename `Orange Unloads` to `Quantity` and `Orange Price` to `Price` for brevity and understandability. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "cell_id": "254b8839-cf4f-460b-a597-c267ad6ebb84"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Year</th> <th>Price</th> <th>Quantity</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>1924</td> <td>6.63 </td> <td>21258   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1925</td> <td>9.19 </td> <td>15426   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1926</td> <td>7.2  </td> <td>24762   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1927</td> <td>8.63 </td> <td>22766   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1928</td> <td>10.71</td> <td>18766   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1929</td> <td>6.36 </td> <td>35702   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1930</td> <td>10.5 </td> <td>23718   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1931</td> <td>5.81 </td> <td>39263   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1932</td> <td>4.71 </td> <td>38553   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>1933</td> <td>4.6  </td> <td>36540   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (5 rows omitted)</p>"
      ],
      "text/plain": [
       "Year | Price | Quantity\n",
       "1924 | 6.63  | 21258\n",
       "1925 | 9.19  | 15426\n",
       "1926 | 7.2   | 24762\n",
       "1927 | 8.63  | 22766\n",
       "1928 | 10.71 | 18766\n",
       "1929 | 6.36  | 35702\n",
       "1930 | 10.5  | 23718\n",
       "1931 | 5.81  | 39263\n",
       "1932 | 4.71  | 38553\n",
       "1933 | 4.6   | 36540\n",
       "... (5 rows omitted)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "oranges = oranges_raw.relabel(\"Orange Unloads\", \"Quantity\").relabel(\"Orange Price\", \"Price\")\n",
    "oranges"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "d3a20db0-45a5-4ca0-8edf-ae8fe730017c"
   },
   "source": [
    "### Visualize the  Relationship\n",
    "\n",
    "Let's first take a look to see what the relationship between price and quantity is. We would expect to see a downward-sloping relationship between price and quantity; if a product's price increases, consumers will purchase less, and if a product's price decreases, then consumers will purchase more. \n",
    "\n",
    "We will create a scatterplot between the points.\n",
    "\n",
    "[Following image is a scatter plot for demand for oranges]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "cell_id": "b7a2e982-d79e-4094-a295-d8edea5e3c12"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "oranges.scatter(\"Quantity\", \"Price\", width=5, height=5)\n",
    "plt.title(\"Demand Curve for Oranges\", fontsize = 16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "46555368-2878-4561-b1bf-34051f611d06"
   },
   "source": [
    "The visualization shows a negative relationship between quantity and price, which is in line with our expectations: as the price increases, fewer consumers will purchase oranges, so the quantity demanded will decrease. This corresponds to a leftward movement along the demand curve. Alternatively, as the price decreases, the quantity sold will increase because consumers want to maximize their purchasing power and buy more oranges; this is shown by a rightward movement along the curve."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit a Polynomial\n",
    "\n",
    "We will now quantify our demand curve using NumPy's [`np.polyfit` function](https://numpy.org/doc/stable/reference/generated/numpy.polyfit.html). Recall that `np.polyfit` returns an array of size 2, where the first element is the slope and the second is the $y$-intercept.\n",
    "\n",
    "For this exercise, we will be expressing demand and supply as quantities in terms of price. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "cell_id": "42bf023c-0b5a-4f12-8158-dcf58f137185"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -3432.84670093,  53625.8748401 ])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.polyfit(oranges.column(\"Price\"), oranges.column(\"Quantity\"), 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "27c4081e-219e-4dba-a16c-44cd17e8fa5c"
   },
   "source": [
    "This shows that the demand curve is $D(P) = -3433 P+ 53626$. The slope is -3433 and $y$-intercept is 53626. That means that as price increases by 1 unit (in this case, \\$1), quantity decreases by 3433 units (in this case, 3433 tons). \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create the Demand Curve\n",
    "\n",
    "We will now use SymPy to write out this demand curve. To do so, we start by creating a symbol `P` that we can use to create the equation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "cell_id": "d06b28f9-96eb-480c-8a10-3ba4981be472"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 53625.87 - 3432.846 P$"
      ],
      "text/plain": [
       "53625.87 - 3432.846*P"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P = sympy.Symbol(\"P\")\n",
    "demand = -3432.846 * P + 53625.87\n",
    "demand"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "14d44625-4f20-443d-9ce0-304bd60c6c61"
   },
   "source": [
    "### Create the Supply Curve\n",
    "\n",
    "As you've learned, the supply curve is the relationship between the price of a good or service and the quantity of that good or service that the seller is willing to supply. It shows how much of a good suppliers are willing and able to supply at different prices. In this case, as the price of the oranges increases, the quantity of oranges that orange manufacturers are willing to supply increases. They capture the producer's side of market decisions and are upward-sloping.\n",
    "\n",
    "Let's now assume that the supply curve is given by $S(P) = 4348P$. (Note that this supply curve is not based on data.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "cell_id": "f9654557-6972-4ba9-948b-f7ff7a48a61f"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 4348 P$"
      ],
      "text/plain": [
       "4348*P"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "supply = 4348 * P\n",
    "supply"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " This means that as the price of oranges increases by 1, the quantity supplied increases by 4348. At a price of 0, no oranges are supplied."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Find the Price Equilibrium\n",
    "\n",
    "With the supply and demand curves known, we can solve the for equilibrium. \n",
    "The equilibrium is the point where the supply curve and demand curve intersect, and denotes the price and quantity of the good transacted in the market.\n",
    "\n",
    "The equilbrium consists of 2 components: the quantity equilbrium and price equilbrium. \n",
    "The price equilibrium is the price at which the supply curve and demand curve intersect: the price of the good that consumers desire to purchase at is equivalent to the price of the good that producers want to sell at. There is no shortage of surplus of the product at this price.\n",
    "\n",
    "\n",
    "Let's find the price equilibrium. To do this, we will use the provided `solve` function. This is a custom function that leverages some SymPy magic and will be provided to you in assignments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 6.89203590457901$"
      ],
      "text/plain": [
       "6.89203590457901"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P_star = solve(demand, supply)\n",
    "P_star"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This means that the price of oranges that consumers want to purchase at and producers want to provide is about \\$6.89. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "571c23b2-4d84-4173-9ff4-bbe1da039e5f",
    "tags": []
   },
   "source": [
    "### Find the Quantity Equilibrium\n",
    "\n",
    "Similarly, the quantity equilibrium is the quantity of the good that consumers desire to purchase is equivalent to the quantity of the good that producers supply; there is no shortage or surplus of the good at this quantity. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "cell_id": "6e28af89-0a83-465e-bb24-d7e66c9b978e"
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 29966.5721131095$"
      ],
      "text/plain": [
       "29966.5721131095"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "demand.subs(P, P_star)\n",
    "supply.subs(P, P_star)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "35482561-c903-4cc5-a072-7e7b50e586c8"
   },
   "source": [
    "This means that the number of tons of oranges that consumers want to purchase and producers want to provide in this market is about 29,967 tons of oranges. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualize the Market Equilibrium \n",
    "\n",
    "Now that we have our demand and supply curves and price and quantity equilibria, we can visualize them on a graph to see what they look like. \n",
    "\n",
    "There are 2 pre-made functions we will use: `plot_equation` and `plot_intercept`.\n",
    "- `plot_equation`: It takes in the equation we made previously (either demand or supply) and visualizes the equations between the different prices we give it\n",
    "- `plot_intercept`: It takes in two different equations (demand and supply), finds the point at which the two intersect, and creates a scatter plot of the result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_equation(equation, price_start, price_end, label=None, color=None, linestyle=None):\n",
    "    plot_prices = [price_start, price_end]\n",
    "    plot_quantities = [equation.subs(list(equation.free_symbols)[0], c) for c in plot_prices]\n",
    "    plt.plot(plot_quantities, plot_prices, label=label, color=color, linestyle=linestyle)\n",
    "    \n",
    "def plot_intercept(eq1, eq2):\n",
    "    ex = sympy.solve(eq1-eq2)[0]\n",
    "    why = eq1.subs(list(eq1.free_symbols)[0], ex)\n",
    "    plt.scatter([why], [ex], zorder=10, color=\"black\")\n",
    "    return (ex, why)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can leverage these functions and the equations we made earlier to create a graph that shows the market equilibrium.\n",
    "\n",
    "[Following image is a scatter plot for supply and demand for oranges]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "cell_id": "f5d296fd-a13d-4b0b-a22d-a22806cb498c",
    "tags": [
     "remove_input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mpl.rcParams['figure.dpi'] = 150\n",
    "plot_equation(demand, 2, 10, label = \"Demand\")\n",
    "plot_equation(supply, 2, 10, label = \"Supply\", color=\"#CB7432\", linestyle=\"dashed\")\n",
    "plt.ylim(0,13)\n",
    "plt.title(\"Orange Supply and Demand in 1920's and 1930's\", fontsize = 15)\n",
    "plt.xlabel(\"Quantity (Tons)\", fontsize = 14)\n",
    "plt.ylabel(\"Price ($)\", fontsize = 14)\n",
    "plot_intercept(supply, demand)\n",
    "plt.legend(loc = \"upper right\", fontsize = 12)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_id": "feb1ae9b-936c-49da-be36-2a6847d8486e"
   },
   "source": [
    "You can also practice on your own and download additional data sets [here](http://users.stat.ufl.edu/~winner/datasets.html), courtesy of the University of Flordia's Statistics Department. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Movements Away from Equilibrium\n",
    "\n",
    "What happens to market equilibrium when either supply or demand shifts due to an exogenous shock?\n",
    "\n",
    "Let's assume that consumers now prefer Green Tea as their hot beverage of choice moreso than before. We have an outward shift of the demand curve - quantity demanded is greater at every price. The market is no longer in equilibrium.\n",
    "\n",
    "[Following image is a hand drawn diagram of a shift in demand]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{figure} fig1-demand.png\n",
    "---\n",
    "width: 500px\n",
    "name: demand-shift\n",
    "---\n",
    "A shift in the demand curve\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove_cell"
    ]
   },
   "source": [
    "![title](fig1-demand.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At the same price level (the former equilibrium price), there is a shortage of Green Tea. The amount demanded by consumers exceeds that supplied by producers: $Q_D > Q_S$. This is a seller's market, as the excess quantity demanded gives producers leverage (or market power) over consumers. They are able to increase the price of Green Tea to clear the shortage. As prices increase, consumers who were willing and able to purchase tea at the previous equilibrium price would leave the market, reducing quantity demanded. $Q_S$ and $Q_D$ move up along their respective curves until the new equilibrium is achieved where $Q_S = Q_D$. \n",
    "\n",
    "This dual effect of increasing $Q_S$ and $Q_D$ is sometimes referred to as the \"invisible hand\". Sans government intervention, it clears out the shortage or surplus in the market, resulting in the eventual convergence to a new equilibrium level of quantity $Q^*$ and price $P^*$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
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}