Derive the labour demand function.

Assuming a unit price $p=1$ the profit function becomes $$G=4K^\alpha L^{1-\alpha}-cK-wL$$ where w is the wage. Maximize the profit with respect to $L$ $$\frac{\partial G}{\partial L}=4K^\alpha (1-\alpha)L^{-\alpha}-w=0$$ and solve for $L$ $$L=\big(4 (1-\alpha) K^\alpha /w \big)^{1/\alpha}$$

If $A=k[x_1,\dots,x_n]/I$ is a finitely generated $k$-algebra with $A\cong k^m$ as modules, what can we say about $I$?

Showing that the distribution of record times $(\tau_k)_{k\geq 1}$ doesn't depend on the distribution, $F$, of the records $X_i$

integration by substitution from two variables to one

Prove that there exists a canonical isomorphism of A-algebras [closed]

Subgradient of the $\ell_0$ "norm"

What are the conditions for $\arctan x+\arctan y+\arctan z=\arctan\frac{x+y+z-xyz}{1-xy-yz-zx}$ to be true?

Closed form solution of $\displaystyle\arg\min_{\alpha \in \Bbb R} \|X - \alpha Y\|_{\text F}^2$

Rotation matrix to construct canonical form of a conic

Why is a function at sharp point not differentiable?

Distinction between Lie Algebra of differentiable manifolds and Lie Algebra of Lie Group

Impulse function and exponential, integral

Question on intersecting lines. [closed]