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 Economics Economics Forum - Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance

 September 9th, 2017, 07:22 AM #1 Newbie   Joined: Sep 2017 From: Latvia/Denmark Posts: 21 Thanks: 0 TR and MR Hello! I am not quite sure what do I need to do here. Help would be appreciated!  Last edited by skipjack; September 9th, 2017 at 08:13 AM. September 9th, 2017, 08:16 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,978 Thanks: 2229 TR = PQ = 100Q - 4Q² What definition have you been given for MR? September 10th, 2017, 03:18 AM #3 Newbie   Joined: Sep 2017 From: Latvia/Denmark Posts: 21 Thanks: 0 Yet, I do not see and understand why and what does the 0.3 and 12 mean in this context. I don't get how you get the answer too. Last edited by skipjack; September 10th, 2017 at 03:55 AM. September 10th, 2017, 04:48 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,978 Thanks: 2229 P is the price of a unit of production and Q is the number of units produced. Hence TR (Total Revenue) = P × Q. If P were a constant, d(TR)/dQ would be P, which would be exactly the extra revenue caused by producing 1 more unit. If P isn't constant, but is given as a function of Q, it's reasonable to use d(TR/dQ) to estimate the change in TR due to a change in Q. If TR = Q(100 - 4Q) = 100Q - 4Q², MR = d(TR)/dQ = 100 - 8Q. You are probably expected to substitute Q = 12, to get MR = 4. As that would be an estimate of the change in TR due to a 1 unit increase in output, you need to multiply it by 0.3, giving 1.2 as your estimate of the change in TR due to a 0.3 unit increase in output. As the question is about an increase in Q from 12 to 12.3, you might wonder why I substituted Q = 12 rather than Q = 12.3. Indeed, why not choose to "split the difference" by substituting Q = 12.15? That would give MR = 2.8, so that your answer would be 0.3 × 2.8 = 0.84, which is a better estimate (spot on, in fact). Since when have economists been concerned about accuracy, though? I suggest you do what you were taught if you can. Thanks from vizzy22 September 10th, 2017, 06:09 AM   #5
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 Originally Posted by skipjack P is the price of a unit of production and Q is the number of units produced. Hence TR (Total Revenue) = P × Q. If P were a constant, d(TR)/dQ would be P, which would be exactly the extra revenue caused by producing 1 more unit. If P isn't constant, but is given as a function of Q, it's reasonable to use d(TR/dQ) to estimate the change in TR due to a change in Q. If TR = Q(100 - 4Q) = 100Q - 4Q², MR = d(TR)/dQ = 100 - 8Q. You are probably expected to substitute Q = 12, to get MR = 4. As that would be an estimate of the change in TR due to a 1 unit increase in output, you need to multiply it by 0.3, giving 1.2 as your estimate of the change in TR due to a 0.3 unit increase in output. As the question is about an increase in Q from 12 to 12.3, you might wonder why I substituted Q = 12 rather than Q = 12.3. Indeed, why not choose to "split the difference" by substituting Q = 12.15? That would give MR = 2.8, so that your answer would be 0.3 × 2.8 = 0.84, which is a better estimate (spot on, in fact). Since when have economists been concerned about accuracy, though? I suggest you do what you were taught if you can.
Your explanation is helping me tons. Thank you. As of this point, I understand simple differentiation, and have done my homework without mistakes. You are a lifesaver! Thank you again. I'll try to help people as much as you helped me!  Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode

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