Homothetic production function and Profit Function I know that homothetic production function implies that cost function is multiplicatively separable in input prices and output, and it can be written as 
C(w,y)=h(y)C(w,1). Can some one help me derive the functional form of profit function in case of homothetic production functions?
I have figured this as the answer to this question;
As we know profit maximization problem is given as,
$$
\pi(p,w) = \mathop{max}_{\textbf{y}}\quad p.y - C(\overrightarrow{w},y)
$$
When $f(\overrightarrow{x})$ is homothetic, 

$$
C(\overrightarrow{w},y)=h(y).C(\overrightarrow{w},{1})
$$

Substituting in the profit function gives; 

$$
\pi(p,w) = \mathop{max}_{\textbf{y}}\quad p.y - h(y). C(\overrightarrow{w},1)
$$

First order condition gives us; 
$$
p=h'(y)C(\overrightarrow{w},1) 
$$

Which can be written as; 
$$
h'(y)=\frac{p}{C(\overrightarrow{w},1)} 
$$

or

$$
y=(h')^{-1}\frac{p}{C(\overrightarrow{w},1)} 
$$
$$
\Rightarrow y= \gamma(p).\beta(w)
$$

Therefore $y(p,w)$ is separable.
Since 
$$
\pi(p,w)=\int{y(p,w)}dp
$$

$$
\pi(p,w)=\int{\gamma(p).\beta(w)}dp
$$

$$
\pi(p,w)=\beta(w)\int{\gamma(p)}dp
$$

$$
\pi(p,w)=\beta(w)\alpha(p)
$$

Thus $\pi(p,w)$ is also separable in factor prices and output prices.