Profit Function

def. Profit Function. Given input and output prices, returns the maximum achievable profit.

$$\pi (w,r,p)$$

(HowTo) Derive Profit Function §

1. Get Input Demand and Output Supply.
2. Substitute into the profit equation
   1. $\pi =p\cdot x(w,r,p)-w\cdot l(w,r,p)-r\cdot k(w,r,p)$

Properties §

• HD1 in $w,r,p$
• Increasing in $p$
• Decreasing in $w,r$
• Hotelling’s Lemma applies