Week 2 Class Example (elasticity and revenue maximization).ipynb

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    "Firm's revenue is $$R = P*Q$$"
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   "source": [
    "Consider firm's decision to raise price $P$ slightly, what is the marginal revenue in response to the increase in price?"
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    "\\begin{align}\n",
    "MR &= \\frac{d [P*Q]}{dP} \\\\\n",
    "&= \\frac{dP}{dP}*Q + \\frac{dQ}{dP}*P \\\\\n",
    "&= Q + \\frac{dQ}{dP}*P\n",
    "\\end{align}"
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   "source": [
    "we stated that to max R, we want $MR = 0$, which means\n",
    "$$Q + \\frac{dQ}{dP}*P = 0$$"
   ]
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   "source": [
    "recall, the price elasticity of demand is\n",
    "$$ \\epsilon = \\frac{dQ}{dP}\\frac{P}{Q}$$"
   ]
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    "**Argument**: to max R, we need $\\epsilon = -1$"
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   "source": [
    "max R requires\n",
    "\\begin{align}\n",
    "Q + \\frac{dQ}{dP}*P &= 0 \\\\\n",
    "\\frac{dQ}{dP}*P &= -Q \\\\\n",
    "\\frac{dQ}{dP}*\\frac{P}{Q} &= -1 \\\\\n",
    "\\epsilon &= -1\n",
    "\\end{align}"
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