Microeconomics_temp.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "7330f20a",
   "metadata": {},
   "source": [
    "## Econ 401A Homework 1\n",
    "\n",
    "### 1.a) Suppose an agent uses a central heater. What indoor temperature t do they choose if they use a central heater? What is their utility?\n",
    "$U(t,x)=-(t-70)^2-x$\n",
    "\n",
    "\n",
    "$x=28+4(t-70)$\n",
    "\n",
    "\n",
    "$U(t,x)=-(t-70)^2-28-4(t-70)$\n",
    "\n",
    "\n",
    "$\\frac{dU}{dt}=-2(t-70)-4=0$\n",
    "\n",
    "$t=68$\n",
    "\n",
    "\n",
    "### t=68 U="
   ]
  },
  {
   "attachments": {
    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "b0b52408",
   "metadata": {},
   "source": [
    "### 2.a) Draw the consumer's budget set\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "### This is the budget constrain for m=20"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f88cf87",
   "metadata": {},
   "source": [
    "### 2B) Assume that $U(x_1, x_2) = x_1x_2$ and $m = 20$. Solve for the agent's optimal choices $x_1^*(p, m), x_2^*(p, m)$.\n",
    "\n",
    "\n",
    "$U(x_1, x_2) = x_1x_2$\n",
    "\n",
    "\n",
    "$x_1+x_2=m$ \n",
    "\n",
    "$\\frac{MU_1}{MU_2}=MRS=\\frac{p_1}{p_2}$\n",
    "\n",
    "$\\frac{x_2}{x_1}=1$\n",
    "\n",
    "$x_1^*=x_2^*$\n",
    "\n",
    "$x_1^*=\\frac{m}{2}$\n",
    "  $x_2^*=\\frac{m}{2}$\n",
    "  \n",
    "#### If $x>=8$ $m=22$\n",
    "\n",
    "$x_1^*=11$\n",
    "  $x_2^*=11$\n",
    "  \n",
    "$U^*=121$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3dafdb8",
   "metadata": {},
   "source": [
    "### 2C) Assume that $U(x_1, x_2) = x_1x_2$ and $m = 10$. Solve for the agent's optimal choices $x_1^*(p, m), x_2^*(p, m)$.\n",
    "\n",
    "#### If we solve in the same way as the previous point we will obtain that $x_1^*=5$ $x_2^*=5$ $U^*=25$, however there is a more optimal solution regarding the constrain budget where m=m+2\n",
    "\n",
    "$U(x_1, x_2) = x_1x_2$\n",
    "\n",
    "\n",
    "$x_1+x_2=m$ \n",
    "\n",
    "\n",
    "$x_1>=8$\n",
    "\n",
    "$m=12$\n",
    "\n",
    "$L=x_1x_2+B_1(m-x_1-x_2)+B_2(x_1-8)$\n",
    "\n",
    "$\\frac{dL}{dx_1}=x_2-B_1+B_2=0$\n",
    "\n",
    "$\\frac{dL}{dx_2}=x_1-B_1=0$\n",
    "\n",
    "$\\frac{dL}{B_1}=12-x_1-x_2=0$\n",
    "\n",
    "$\\frac{dL}{B_2}=x_1-8=0$\n",
    "\n",
    "$x_1^*=8$\n",
    "\n",
    "$x_2^*=4$\n",
    "\n",
    "$B_1^*=8$\n",
    "\n",
    "$B_2^*=4$\n",
    "\n",
    "$U^*=32$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a05448c",
   "metadata": {},
   "source": [
    "### 3.A) Solve for the agent's optimal consumption bundle $x^*(p, m) = (x_1^*(p, m), x_2^*(p, m))$ and her indirect utility $v(p, m)$ under the original prices."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90168376",
   "metadata": {},
   "source": [
    "$U(x_1, x_2) = x_1x_2$\n",
    "\n",
    "\n",
    "$x_1+x_2=m$ \n",
    "\n",
    "$\\frac{MU_1}{MU_2}=MRS=\\frac{p_1}{p_2}$\n",
    "\n",
    "$\\frac{x_2}{x_1}=1$\n",
    "\n",
    "$x_1^*=x_2^*$\n",
    "\n",
    "$x_1^*=\\frac{m}{2}$\n",
    "  $x_2^*=\\frac{m}{2}$\n",
    "    \n",
    "$v(p,m)=\\frac{m^2}{4}$\n",
    "\n",
    "$m=24$\n",
    "\n",
    "$x_1^*=12$\n",
    "  $x_2^*=12$\n",
    "  \n",
    "$U^*=144$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46b463da",
   "metadata": {},
   "source": [
    "### 3,B)\n",
    "\n",
    "$U(x_1, x_2) = x_1x_2$\n",
    "\n",
    "\n",
    "$x_1+2x_2=m'$ \n",
    "\n",
    "$\\frac{MU_1}{MU_2}=MRS=\\frac{p_1}{p_2}$\n",
    "\n",
    "$\\frac{x_2}{x_1}=\\frac{1}{2}$\n",
    "\n",
    "$x_1^*=2x_2$\n",
    "\n",
    "$x_1^*=\\frac{m'}{2}$\n",
    "  $x_2^*=\\frac{m'}{4}$\n",
    "    \n",
    "$v(p,m)=\\frac{m^2}{8}$\n",
    "\n",
    "$m=24$\n",
    "\n",
    "$x_1^*=12$\n",
    "  $x_2^*=6$\n",
    "  \n",
    "$U^*=72$\n",
    "\n",
    "$v(p,m)=\\frac{m^2}{8}$\n",
    "\n",
    "$144=\\frac{m^2}{8}$\n",
    "\n",
    "$m^*(p,p',m)=\\sqrt{144*8}=33,94$\n",
    "\n",
    "$iCV=\\frac{33,94}{24}=1,41$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb7fa33d",
   "metadata": {},
   "source": [
    "### 3.C)\n",
    "\n",
    "$iL=\\frac{36}{24}=1,5$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "324ec60f",
   "metadata": {},
   "source": [
    "### 3.D)\n",
    "\n",
    "$iP=\\frac{24}{18}=1,33$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4aa2e32",
   "metadata": {},
   "source": [
    "### 3.E) \n",
    "### It is true that $iL>iCV>iP$ since $1,5>1,41>1,33$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d02b30d6",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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