document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189902>Question 1189902</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5. At $1.40 per pound, the daily supply of tobacco is 1075 pounds, and the daily<BR>\n" );
document.write( "demand is 580 pounds. When the price falls to $1.20 per pound, the daily<BR>\n" );
document.write( "supply decreases to 575 pounds and the daily demand increases to 980 pounds.<BR>\n" );
document.write( "Assume that the supply and demand equations are linear.<BR>\n" );
document.write( "a) Find the supply equations.<BR>\n" );
document.write( "b) Find the demand equations.<BR>\n" );
document.write( "c) Find the equilibrium price and quantity. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821409 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821409\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part A\r<BR>\n" );
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document.write( "x = price in dollars<BR>\n" );
document.write( "y = amount supplied in pounds\r<BR>\n" );
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document.write( "\"At $1.40 per pound, the daily supply of tobacco is 1075 pounds\" gives the point (1.40,1075)\r<BR>\n" );
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document.write( "\" When the price falls to $1.20 per pound, the daily<BR>\n" );
document.write( "supply decreases to 575 pounds \" means we have another point (1.20,575)\r<BR>\n" );
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document.write( "Slope through those points<BR>\n" );
document.write( "m = (y2-y1)/(x2-x1)<BR>\n" );
document.write( "m = (575-1075)/(1.20-1.40)<BR>\n" );
document.write( "m = (-500)/(-0.20)<BR>\n" );
document.write( "m = 2500<BR>\n" );
document.write( "The slope of 2500 means that for every price increase of $1, the amount supplied goes up by 2500 units.\r<BR>\n" );
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document.write( "Let's find the y intercept using the slope and the first point mentioned<BR>\n" );
document.write( "y = mx+b<BR>\n" );
document.write( "1075 = 2500*(1.40)+b<BR>\n" );
document.write( "1075 = 3500+b<BR>\n" );
document.write( "1075-3500 = b<BR>\n" );
document.write( "-2425 = b<BR>\n" );
document.write( "b = -2425<BR>\n" );
document.write( "Admittedly, the y intercept doesn't make much sense. It's not possible to have a negative amount supplied. However, this is useful to help set up the equation y = 2500x-2425. The key thing to keep in mind is that there's a certain domain to stick to. It only makes sense to have x > 0 and y > 0.\r<BR>\n" );
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document.write( "To check this, we plug in x = 1.40 and should get y = 1075. Also, plugging in x = 1.20 should lead to y = 575. I'll let you do those checks.\r<BR>\n" );
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document.write( "Answer:<BR>\n" );
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document.write( "The supply equation is <BR>\n" );
document.write( "y = 2500x-2425<BR>\n" );
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document.write( "Part B\r<BR>\n" );
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document.write( "x = price in dollars<BR>\n" );
document.write( "y = amount demanded in pounds\r<BR>\n" );
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document.write( "We'll do similar steps for the demand equation<BR>\n" );
document.write( "\"At $1.40 per pound... the daily<BR>\n" );
document.write( "demand is 580 pounds.\"<BR>\n" );
document.write( "We have the point (1.40,580)\r<BR>\n" );
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document.write( "Also, <BR>\n" );
document.write( "\"the price falls to $1.20 per pound...the daily demand increases to 980 pounds.\"<BR>\n" );
document.write( "So we have the other point (1.20, 980)\r<BR>\n" );
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document.write( "Slope:<BR>\n" );
document.write( "m = (y2-y1)/(x2-x1)<BR>\n" );
document.write( "m = (980-580)/(1.20-1.40)<BR>\n" );
document.write( "m = 400/(-0.20)<BR>\n" );
document.write( "m = -2000<BR>\n" );
document.write( "A negative slope tells us that each time the price (x) goes up, the demand (y) goes down. <BR>\n" );
document.write( "Specifically, each time the price goes up by $1, the demand goes down by 2000 pounds.<BR>\n" );
document.write( "Unlike the negative y intercept not making much sense, the slope can be negative. It's always negative for demand equations. The price and amount demanded move in opposite directions for demand equations.\r<BR>\n" );
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document.write( "Like before, I'll use the slope and first point to find the y intercept<BR>\n" );
document.write( "y = mx+b<BR>\n" );
document.write( "580 = -2000*(1.40)+b<BR>\n" );
document.write( "580 = -2800+b<BR>\n" );
document.write( "580+2800 = b<BR>\n" );
document.write( "b = 3380\r<BR>\n" );
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document.write( "The equation<BR>\n" );
document.write( "y = mx+b<BR>\n" );
document.write( "becomes<BR>\n" );
document.write( "y = -2000x+3380\r<BR>\n" );
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document.write( "To check this, we plug in x = 1.40 and should get y = 580. Also, plugging in x = 1.20 should lead to y = 980. I'll let you do those checks.\r<BR>\n" );
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document.write( "Answer:<BR>\n" );
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document.write( "The demand equation is <BR>\n" );
document.write( "y = -2000x+3380<BR>\n" );
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document.write( "Part C\r<BR>\n" );
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document.write( "We found from the previous parts that:<BR>\n" );
document.write( "Supply equation is y = 2500x-2425<BR>\n" );
document.write( "Demand equation is y = -2000x+3380\r<BR>\n" );
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document.write( "Equilibrium is reached when the quantity supplied equals quantity demanded. Visually, it's where the supply and demand lines intersect. \r<BR>\n" );
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document.write( "Let's use substitution to find that solution<BR>\n" );
document.write( "y = -2000x+3380<BR>\n" );
document.write( "2500x-2425 = -2000x+3380<BR>\n" );
document.write( "2500x+2000x = 3380+2425<BR>\n" );
document.write( "4500x = 5805<BR>\n" );
document.write( "x = 5805/4500<BR>\n" );
document.write( "x = 1.29\r<BR>\n" );
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document.write( "The equilibrium price is $1.29 per pound.\r<BR>\n" );
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document.write( "Plug that x value into either y equation<BR>\n" );
document.write( "Supply: <BR>\n" );
document.write( "y = 2500x-2425<BR>\n" );
document.write( "y = 2500*1.29-2425<BR>\n" );
document.write( "y = 800<BR>\n" );
document.write( "Or,<BR>\n" );
document.write( "Demand:<BR>\n" );
document.write( "y = -2000x+3380<BR>\n" );
document.write( "y = -2000*1.29+3380<BR>\n" );
document.write( "y = 800<BR>\n" );
document.write( "The equilibrium quantity is 800 pounds. \r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "<font color=red>Equilibrium price = $1.29 per pound.<BR>\n" );
document.write( "Equilibrium quantity = 800 pounds</font><BR>\n" );
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