# Need help! Marginal renevue problem

• May 3rd 2008, 04:46 PM
graceglover1
Need help! Marginal renevue problem
I need help solving this problem......anyone help!(Rofl)

Marginal revenue. A defense attorney charges her client $4000 plus$120 per hour. The formula R= 120n + 4000 gives her revenue in dollars for n hours of work.
What is her revenue for 100 hours of work? $16,000 What is her revenue for 101 hours of work?$16,120
By how much did the one extra hour of work increase the revenue? The increase in revenue is called the marginal revenue for
• May 3rd 2008, 08:47 PM
Aryth
The formula for Marginal Revenue is:

$\displaystyle MR = P + Q*\frac{dP}{dQ}$

Where:

$\displaystyle MR = \text{Marginal Revenue}$

$\displaystyle P = \text{Initial Cost}$

$\displaystyle Q = \text{Quantity}$

$\displaystyle \frac{dP}{dQ} = \text{Change in price with respect to the quantity}$

As you can see, you are only dealing with 1 hour of work, so we can plug in what we know:

$\displaystyle MR = 120 + \frac{dP}{dQ}$

Now we must ponder what happens to her pay as the amount of hours she works changes. Does it go up? Does it go down? or does it stay the same?

It's obvious to see that no matter how many hours she works, her pay will still be 120 dollars per hour. So, therefore:

$\displaystyle \frac{dP}{dQ} = 0$

And therefore:

$\displaystyle MR = 120$

There you go.