<p><span class="math-container">$\pi (tw, tr, tp)=t^2 p^2 / t (wr)^{1/2} = tp^2 / (wr)^{1/2} = t\pi (w, r, p) $</span></p>
<p>Hence, profit function is linearly homogeneous in both input and output prices.</p>

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2024-12-26T11:00:32.457Z
2024-12-26T11:00:32.457Z
Surabhi Gupta
<p>A farmer produces using two inputs; labour (l) and fertilizer (k). The profit function is given by π=p²/√wr
Where p is price of maize per bag and r,w are the unit prices for fertilizer and labour respectively. K is measured in 1kg bags and L is measured in man hours.
Question; a legitimate Profit function is convex and positively linearly homogeneous in both input and output prices. Is the above function legitimate?</p>

<microeconomics><profits>
How to prove a profit function is legitimate
Faith Njenga 
# How to prove a profit function is legitimate

(Asked by: username_0 on 2024-12-26)

A farmer produces using two inputs; labour (l) and fertilizer (k). The profit function is given by π=p²/√wr
Where p is price of maize per bag and r,w are the unit prices for fertilizer and labour respectively. K is measured in 1kg bags and L is measured in man hours.
Question; a legitimate Profit function is convex and positively linearly homogeneous in both input and output prices. Is the above function legitimate?

**Tags:** microeconomics, profits


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## 1 answers

### Answer by username_1 on 2024-12-26. Score: 0

$\pi (tw, tr, tp)=t^2 p^2 / t (wr)^{1/2} = tp^2 / (wr)^{1/2} = t\pi (w, r, p) $

Hence, profit function is linearly homogeneous in both input and output prices.


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