Currently, the demand equation for baseball bats is Q = 100 - 2P

We want to begin by finding the total revenue (TR) function for a firm producing baseball bats. Recall that :

TR=P∗QTR=P∗Q

We can substitute the demand equation in for Q to find:

TR=P∗(100−2P)=100P−2P2TR=P∗(100−2P)=100P−2P2

From calculus, we know that a function is maximized (or minimized) when its derivative is set equal to zero. We take the derivative of TR with respect to price, set this equal to zero, and solve for P:

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ddPTR=100−4P=0ddPTR=100−4P=0

4P=1004P=100

P=25P=25

Thus, the price that maximizes revenue is $25, not $15.