Algebra.Com's Answer #836263 by ikleyn(52788)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
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document.write( "A local coffee shop charges €2.50 for an espresso.
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document.write( "The owner of the coffee shop wants to increase his total revenue.
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document.write( "A recent market research shows that the price elasticity of demand for espresso is about 1.80.
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document.write( "Should the coffee shop lower or raise the price of espresso? Explain your answer.
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document.write( "DEFINITION\r\n" );
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document.write( " Price elasticity of demand is a measurement of the change \r\n" );
document.write( " in the consumption of a product in relation to a change in its price.\r\n" );
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document.write( "Thus in this problem  = 1.8. (1)\r\n" );
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document.write( "It means, if to follow to the problem LITERALLY, that the dependence Q(consumption) \r\n" );
document.write( "of P(price) has the form Q = 1.8*(P-2.50).\r\n" );
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document.write( "But it is clear that it is ILLOGICAL: according to (1), if the price rises over €2.50,\r\n" );
document.write( "the consumption should increase.\r\n" );
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document.write( "So, actually it should be Q = -1.8*(P-2.50),\r\n" );
document.write( "and my first inference that the \"problem's composer\" is not able to formulate his \"economics problem\" correctly.\r\n" );
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document.write( " | But, thanks to god, I have my common sense |\r\n" );
document.write( " | in my mind, so I am able to interpret it correctly. |\r\n" );
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document.write( "Next, I will not consider a profit (since I have no data for calculating it), \r\n" );
document.write( "and will consider the REVENUE, only. The revenue is\r\n" );
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document.write( " R = P*Q = -1.8*P*(P-2.50), (2)\r\n" );
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document.write( "and our goal (the goal of the coffee shop, from the context) is to increase the revenue (2).\r\n" );
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document.write( "We write the revenue (2) in equivalent form\r\n" );
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document.write( " R = -1.8*P^2 + 1.8*2.50*P.\r\n" );
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document.write( "The derivative  is -2*1.8P + 1.8*2.50, and at the price P= 2.50€ it is\r\n" );
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document.write( " = -2*1.8*2.50 + 1.8*2.50 = -4.5.\r\n" );
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document.write( "Since this derivative is negative, then, if the coffee shop wants to increase the revenue, it should decrease the price from €2.50.\r\n" );
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document.write( "Solved, with complete explanations.\r
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document.write( "I answered question \"a\" ONLY,\r
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document.write( "and my advise to the visitor is NEVER pack more than one problem/question per post,\r
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document.write( "in accordance with the rules of this forum (and in accordance with the rules of common sense, too).\r
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