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ID: 1131518 • Letter: #
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<div class="txt-body question-body"><div class="feedback-rating abuse-flag" data-questionid="12254165"></div><div class="ugc-base"><p>The market of natural gas is described by the following supplyand demand equations:</p><p>                                 Qs = 14 + 2 P<sub>G</sub> + .25P<sub>0</sub>          Qd = -5 P<sub>G</sub> + 3.75 P<sub>0</sub></p><p>    where Qs represent the quantities suppliedand demanded of natural gas (in millions <span style="line-height:1.6;">of cubic feet), P</span><sub>G</sub><span style="line-height:1.6;">represents the price of natural gas(per cubic foot) and P</span><sub>0</sub><span style="line-height:1.6;">represents the</span></p><p>    price of oil (per barrel).</p><p>a. If P<sub>0</sub> = 8, find the equilibrium price andquantities of natural gas.</p><p>b. Find the new equilibrium price and quantities ifP<sub>0</sub> doubles (from 8 to 16).</p></div></div>Explanation / Answer
<div class="txt-body answer-body"> <div class="answer-given-body ugc-base"> <p>a. If P0 = 8, then the equations become:<br>Qs = 14 + 2PG + 0.25*8 = 16 + 2PG<br>and Qd = -5PG + 3.75*8 = -5PG + 30</p><p>At equilibrium, Qs = Qd</p><p>16 + 2PG = -5PG + 30<br>2PG + 5PG = 30 - 16 = 14<br>PG = 14/7 = 2</p><p>Qs = 16 + 2*2 = 20</p><p><strong>Equilibrium price of gas is $2 per cubic foot andquantity demanded is 20 million of cubic feet.</strong></p><p>b. If P0 = 16,<br>Qs = 14 + 2PG + 0.25*16 = 18 + 2PG<br>and Qd = -5PG + 3.75*16 = -5PG + 60<br>At equilibrium, Qs = Qd</p><p>18 + 2PG = -5PG + 60<br>7PG = 60 - 18 = 42<br>PG = 42/7 = 6</p><p>and Qs = 18 + 2 *6 = 30</p><p><strong>Equilibrium price of gas becomes $6 per cubic foot andquantity demanded is 30 million of cubic feet.</strong></p> </div> </div>
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