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 Relationship between TP, AP, and MP, True or False Questions (Brain Twister)
Best ^^
Posted: Feb 5 2008, 03:14 PM


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I think the following question, though not so difficult, will definitely put you into some kind of brain-twisting. Hahaha!! laugh.gif Try to answer it. tongue.gif


For each of the following statements, state whether it is true or false and explain why it is true or false.

(a ) If average product is increasing, marginal product must be less than average product.

(b ) If average product is positive, total product must be rising.

(c ) If marginal product is negative, average product must be negative.

(d ) If total product is increasing, marginal product must also be increasing.
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dniven
Posted: Feb 5 2008, 10:14 PM


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I always find a bit of calculus helps with these sorts of questions!

Writing AP = Q/L (1)
and MP = dQ/dL (2)
and TP = AP x L = integral (MP) dL (3)

then d(AP)/dL = (MP - AP)/L

so statement (a) has to be false.

for (b ), from (3) we have a positive correlation between TP and AP, therefore an increasing and positive AP results in a positive and increasing TP. Hence (b ) is true.

for (c ) a negative MP only says AP is decreasing, but does not tell us the sign of AP. Therefore (c ) is not always true. i.e. it is false!

for (d)

d(TP)/dL=MP, i.e. for total product to increase we only need MP to be positive, not necessarily increasing. Therefore the statement is false.
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Best ^^
Posted: Feb 7 2008, 04:35 AM


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Hi dniven, good to see you here. happy.gif

The challenge in answering the above questions is not whether we can determine if it is true or false, but it is very challenging to be able to explain our reasoning using economic theories or graphical analysis. rolleyes.gif

Remember, the UOL examiners are not testing our mathematical skills in 02 Intro to Economics. They are interested in testing our understanding of economics. We can use calculus to determine quickly in our mind whether the statement(s) is true or false, but I doubt if we are allowed to use calculus (alone) as our basis of explanation. unsure.gif

This kind of question (the above questions) usually appear in question 1 (a) - (f) in the past years' exam questions, where we are required to answer any 3. From the examiners report, we are expected to write a short essay (aproximately 300 words) for each of the part (a) - (f). rolleyes.gif
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Best ^^
Posted: Feb 7 2008, 04:47 AM


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QUOTE
for (b ), from (3) we have a positive correlation between TP and AP, therefore an increasing and positive AP results in a positive and increasing TP. Hence (b ) is true.

I think it is worth reconsidering your approach in answering these question using calculus. For example, refering to your answer for (b ), we know that the AP graph is always positive throughout the domain of the TP graph. So, it is not a question of whether the AP is positive or not (it is always positive). The question is: is TP always rising? According to the law of diminishing marginal returns, this is not true; there will come a point when MP will be negative, hence TP decreasing. So (b ) should be false. biggrin.gif
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tonygreywolf
Posted: Feb 7 2008, 05:59 AM


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Hi guys,

Excellent answers Doug! The use of calculus adds a nice touch to the explanations.
I imagine the examiners will cast a benevolent eye on such an exposition.

And James, notwithstanding your concerns, this unit is, I believe, just as much about method as it is about economics.

Re: (b ) If average product is positive, total product must be rising.

Thatís a good point, James about the TP decreasing while AP is positive. I had answered all four parts basically along the lines that Doug did; but I see now where I went wrong in (b ).

Anthony
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dniven
Posted: Feb 7 2008, 11:28 PM


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Hi there,

Thanks for the feedback both of you. I take your point James about these answers not being in exam format. I was trying to think of the most efficient way of getting the answers out! They would certainly need more explanation and context if used in an exam.

You're right on question b - my answer was not so good there. Another way of seeing this is to plot the production function, and drawing some rays from the origin to points on the curve to indicate the average cost. If factor inputs increase then it is possible for total product to fall, whilst the ray having positive slope. (diminishing marginal returns whilst AP>0).

smile.gif
Doug
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