Newton's Method for optmization

[PBJinx]

This is less a homework problem and more conceptual help for a homework problem

I have been given the information for a revenue equation and a cost equation

I set up Newton's Method with



X_N+1=$$\frac{revenue-cost}{the derivative of the top}$$


where both revenue and cost are determined by price

what I would like to know is that my thinking is right with this set up. The root that I solve for is the price of maximization for the price.

 

[Stephen Tashi]

what I would like to know is that my thinking is right with this set up. The root that I solve for is the price of maximization for the price.

You didn't explain what your thinking was, you only gave a formula. The formula that you gave makes no sense to me.

 

[snipez90]

"the price of maximization for the price" doesn't seem to make much sense. Did you mean "the price of maximization for the profit"? The reason I ask is because profit is obviously defined as (revenue - cost) and it appears you have the ratio: profit/(derivative of profit).

First, note that you're missing an x_n term. Remember if you want to find a root for f, i.e., a p such such that f(p) = 0, Newton's method tells you to look at a sequence of the form x_(n+1) = x_n - f(x_n)/f'(x_n).

But if you are trying to maximize profit, I think you are making a mistake on a conceptual level. If f is the profit function defined by (revenue - cost), you're not trying to find a price at which profit is zero (though certainly there are many microeconomic situations where this would be of interest). Rather you need to find p such that f'(p) = 0.