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A Firm has the production function

Q= 0.95 x + ln(z) + 100

where x and z are a variable inputs. Derive the "marginal product" of x and z by taking the partial derivatives of the production function.

i'd really love to know the theory of how you do this, as i'm struggling with the process.

This would really help my revision process for my finals.

Usif Beldog
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1 Answers1

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What do you mean, "the theory of how you do this"? It's all just differentiation. Since Q is a function of two variables--x & z--you'll need to calculate two partial derivatives:

  • the partial derivative of Q with respect to x (which gives you the marginal product of x)
  • the partial derivative of Q with respect to z (which gives you the marginal product of z)

Or are you, in effect, asking: "How do I take the derivative?" If that's the case then your best bet is probably Khan Academy--you can find a video on partial differentiation here.

Steve S
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