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Non-economics student: marginal product revenue


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I'm not an economics student so while trying to understand the math part of this, the vocabulary got me confused. If the graph he drew (see video at given time) was marginal product revenue, why is the area under the curve also marginal product revenue?

 

My understanding is the graph he drew is say R(L) = y, so if say R(0.5) = 25 as he has on the graph, why is the integral of 0 to 0.5 also 25? Is something wrong here?

 

(1:00-1:30)

 

https://www.khanacademy.org/economics-finance-domain/microeconomics/firm-economic-profit/labor-marginal-product-rev/v/how-many-people-to-hire-given-the-mpr-curve

 

 

 

Also, the old IB econ book I looked at puts the MPR right at the x value of 1 instead of halfway between 0 and 1 (and every increment after that, etc)...which is the correct/easier way of writing it, and how to calculations have to be adjusted then?

 

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