{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A simple model of moral hazard with limited liability"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## No monitoring case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from ipywidgets import interact\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Model Parameters**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = 200       #Project returns under success (=0 under failure)\n",
    "p = 0.7       #probability of success if diligent\n",
    "q = 0.5       #probability of success if non-diligent\n",
    "I = 100\n",
    "gamma = 1     # outside lenders' cost of funds\n",
    "B = 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "F = 0        # Fixed cost of loan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Amax = 120"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Amin = p*B/(p-q) -(p*X - gamma*I) + F"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected project return 140.0\n",
      "Expected cost of funds 100\n",
      "LL rent at A=0 is  70.0\n",
      "Min collateral requirement is  30.0\n",
      "LL rent at A= Amin is 40.0\n"
     ]
    }
   ],
   "source": [
    "print('Expected project return {}'.format(p*X))\n",
    "print('Expected cost of funds {}'.format(gamma*I+F))\n",
    "print('LL rent at A=0 is {:5.1f}'.format(p*B/(p-q)))\n",
    "print('Min collateral requirement is {:5.1f}'.format(Amin))\n",
    "print('LL rent at A= Amin is {}'.format(-Amin+p*B/(p-q)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Intermediary fixed cost per borrower **\n",
    "Set to zero in base case."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Monitoring technology:** For simplicity and to fix ideas we assume a linear relationship betweeen more monitoring expense and the extent of moral hazard (the private benefits the client stands to capture from non-diligence)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "B0 = 30\n",
    "alpha = 0.4\n",
    "def B(m): # Private benefit to non-diligence under monitoring intensity m \n",
    "    return B0 - alpha*4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def B(m, B0=30, alpha=0.4):\n",
    "    '''Private benefits as a function of monitoring m'''\n",
    "    return B0 - alpha*m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Minimum collateral requirements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Bank Participation constraint**:\n",
    "$$p(X - s) + (1 - p)A \\ge \\gamma I + F$$\n",
    "\n",
    "**Incentive compatibility** constraint when entrepreneur has pledgeable assets $A$:\n",
    "$$s \\ge  - A + \\frac{B}{\\Delta }$$\n",
    "\n",
    "The **limited liability** constraint is written:\n",
    "$$s \\ge - A$$\n",
    "\n",
    "Actually, a limited liability constraint must hold for each outcome state to make sure that the value of promised repayment in that state does not exceed the value of output plus any pledgeable collateral $A$. In this two-state world the constraints are $(X - s) \\le  A$ and $(0 - s) \\le  A$, but the latter always binds first, so we focus only on this, re-written as stated above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Diagram plots**\n",
    "We want to plot the linear constraints and/or objectives lines in $s_f - s_s$ space. For example a zero profit condition:\n",
    "$$p(X-s_s)+(1-p)(0-s_f) - \\gamma I - FC(N) = 0$$\n",
    "\n",
    "can be rearanged to plot $s_s$ as a function of $s_f$:\n",
    "\n",
    "$$s_s = X - \\frac{\\gamma I + F(N)}{p} -\\frac{1-p}{p} s_f$$\n",
    "\n",
    "Since we'll be illustrating things below with a variety of plots, let's try to economize on code by writing a simple 'function factory' call `line_function(a,b)` that allows to easily create multiple named and parameterized line functions and another `plot_contraints()` function that will plot a variable number of such lines."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def line_function(a, b):\n",
    "    '''return a line function of the form f(x) = a + b*x'''\n",
    "    def f(x):\n",
    "        return a + b*x\n",
    "    return f\n",
    "\n",
    "def plot_constraints(*args, cfmin = -100, cfmax = 200): \n",
    "    '''plot contract constraints\n",
    "    Accepts a variable number of lines/constraint functions to plot\n",
    "    on the same diagram'''\n",
    "    cf = np.linspace(cfmin, cfmax, cfmax-cfmin+1)  # plot range\n",
    "    for count, fn in enumerate(args):              \n",
    "        plt.plot(cf, fn(cf))\n",
    "    plt.axhline(0, linestyle=':', color='black')\n",
    "    plt.axvline(0, linestyle=':', color='black')\n",
    "    plt.ylim(-10,300)                   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x7e45b70>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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w4WZHJRxRVV0Va9LWsOfMHgIeDCDjmQyGu3WuwSaJhBA2hg4dSmxsrNlhiE7KMCA5GVau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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7df8400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "zeroprofit = line_function(X - I/p - F/p, -(1-p)/p)  \n",
    "ic0 = line_function(-0 + B(0)/(p-q), 1)\n",
    "ic100 = line_function(-100 + B(0)/(p-q), 1)\n",
    "\n",
    "plot_constraints(ic0, ic100, zeroprofit)\n",
    "plt.plot(50,150, marker='*')\n",
    "plt.axvline(-50)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}