Question

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The demand equation for video games is given by x = 320 − 10p where x...

The demand equation for video games is given by x = 320 − 10p where x is the number of video games and p is in dollars. Find the value of p that maximizes the total revenue.

Expert Solution

Step 1)

we know that revenue is given by revenue = number of units x price per unit

As given we the The demand equation for video games is given by x = 320 − 10p where x is the number of video games and p is price

Hence we have number of units = 320 - 10p and price per unit = p

we can write,

Hence,

equate it to 0 we can say that,

It means p = 16 is a critical point for a revenue function

Step 2)

we have,

Hence,

As R''(16) = -20 < 0 according to second derivative test we can say that p = 16 is a maximum point

Hence we can say that revenue is maximum at p = 16 dollars

milcah answered 3 years ago

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