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September 9th, 2017, 07:22 AM   #1
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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.
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September 9th, 2017, 08:16 AM   #2
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TR = PQ = 100Q - 4Q²

What definition have you been given for MR?
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September 10th, 2017, 03:18 AM   #3
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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.
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September 10th, 2017, 04:48 AM   #4
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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.
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September 10th, 2017, 06:09 AM   #5
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Quote:
Originally Posted by skipjack View Post
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!
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