Simple function substitution question

[Gameowner]

Homework Statement

if I had a function such that

B(p, y) = py - c(y)

and then knowing that y=y(p), does that mean

B(p) = p^2 - c(p)?

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

Hi Gameowner!

(I would prefer to write it C(p) = B(p,y(p)), but …)

yes

 

[tiny-tim]

Hey, thanks for your response to my topic, but I want to ask you further since it was great help!

Originally, the question imposes that

B(p,x) = px - c(x), given a constraint that x=f(y).

If we assume a given optimal value of y (y*), then find a function V(p)...

Answer:

I asked my lecturer and he said to replace the x's with the function x = f(y*)...

so I get

B(p,y*) = py - c(y)

Then he goes on saying that V(p) is gotten realizing that y is a function of p such that y*(p).

So can I then go on and say

V(p) = p^2 - c(p) ?

I don't understand what V is supposed to be

 

[Gameowner]

I don't understand what V is supposed to be

Opps, V(p) is suppose to be an indirect function which should be the same as B(p,x), but given the x=f(y), we can substitute in and out to get an 'indirect version of the same function' but in terms of p alone.