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    "**Balanced-Budget MUltiplier**:\n",
    "\n",
    "$ Y^* = Y = AD = \\frac{(c_o + I_o + G) + (x_fY^f + x_\\epsilon\\epsilon_rr^f) - (I_r + x_\\epsilon\\epsilon_r)r}{1-c_y(1-t) + im_y} $ :: sticky-price\n",
    "\n",
    "$ {\\Delta}Y = \\frac{{\\Delta}G}{1-c_y(1-t) + im_y} - \\frac{Yc_y{\\Delta}t}{1-c_y(1-t) + im_y} $\n",
    "\n",
    "$ {\\Delta}t = \\frac{{\\Delta}G}{Y} $\n",
    "\n",
    "$ {\\Delta}Y = \\frac{(1-c_y){\\Delta}G}{1-c_y(1-t) + im_y} = \\left(1 - \\frac{c_yt + im_y}{1-c_y(1-t) + im_y}\\right){\\Delta}G $\n",
    "\n"
   ]
  }
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