1. production function

2. You lost patience? Sorry. I did think about it. What have you been doing?

If we fix the production, Q, or the ratio Q/A, we see that K can be expressed as a function of L.

Rewrite the expression as $\left(\frac{Q}{A}\right)^{\alpha} = b*K^{\alpha} + (1-b)*L^{\alpha}$

Find the implicit derivative with K = f(L)

$0 = \alpha b*K^{\alpha - 1}\left(\frac{dK}{dL}\right) + \alpha (1-b)*L^{\alpha - 1}$

Solve for $\frac{dK}{dL}$, which is the marginal change in K associated with a unit change in L.