Posted by **Lee** on Tuesday, July 19, 2011 at 11:02pm.

The number of people taking the bus at price p dollars per ticket is given by x=5000(5-p)^1/2.

For what value of P is the demand unitary?

- Calculus -
**drwls**, Wednesday, July 20, 2011 at 12:02am
"Unitary demand" occurs where p*x = constant, which also implies that

dp/p = -dx/x,

which is another way of saying

dx/dp = -x/p

In your case

dx/dp = -5000*(1/2)/(5-p)^1/2

= -2500/(5-p)^1/2

= -x/p = -5000*(5-p)^1/2*(1/p)

1 = 2*(5-p)/p

p = 10 - 2p

p = $3.33

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