Marginal Revenue

The Marginal Revenue indicates the increase in revenue when the quantity increases a little bit.

Example

Zoe's lemonade stand satisfies a demand characterized by:

P=10−2Q

Her revenue is

R(Q)=PQ=(10−2Q)Q=10Q−2Q2

The marginal revenue is the derivative of the revenue R(Q):

MR(Q)=dR(Q)dQ=10−2×2Q=10−4Q

Question

The inverse demand for lemonade is P=70−3Q.

What is Zoe's marginal revenue?

First, her revenue is

R(Q)=PQ=(70−3Q)Q=70Q−3Q2

So her marginal revenue is

MR(Q)=dR(Q)dQ=70−3×2Q=70−6Q
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