0

Can anyone help me figure out how to maximise this problem knowing that the constraint is a leontief function?

$$ \max_{WS,W,S}\pi_{WS} = p_{WS}.WS - (p_W . W + p_S.S)\\ \text{subject to } WS = \min\left(\frac{S}{a_S}; \frac{W}{a_W} \right) $$

I dropped the subscripts to facilitate the example. "p" refers to prices, while "a" refers to the constants of the leontief function. In this example, I'm interested in obtaining a composite input WS using Water (W) and Land (S). The choice of the leontief function is simply because the two inputs are complementary, and not substitutes, they are also essential to the production process.

Rodrigo de Azevedo
  • 1
Meg
  • 15
  • Welcome to [math.se] SE. Take a [tour]. You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an [edit]): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance. – Another User Aug 03 '23 at 20:49
  • Thank you for the answer. I edited the question to explain the problem. I apologise for using an image as I'm new and don't know how to use the website's code to write the math. – Meg Aug 03 '23 at 20:56
  • For some basic information about writing mathematics at this site see, e.g., here, here, here and here. – Another User Aug 03 '23 at 21:38
  • I fixed it. Now I got equations showing. – Meg Aug 04 '23 at 00:04

0 Answers0