CES Cheatsheet¶
The formulas below collect the capital--labor CES results. Assume \(0<\alpha<1\), \(\sigma>0\), positive inputs and productivities, and competitive factor rewards. The output price is \(p\); \(\alpha\) is a technology parameter, whereas \(\alpha_K\) and \(\alpha_L\) are income shares. Read the expressions at \(\sigma=1\) by taking their Cobb--Douglas limits.
Main results: input choices, shares, and factor rewards¶
Each derivative is a local elasticity evaluated at the initial allocation. Technology includes \(z,A_K,A_L\) and the weight \(\alpha\); variables not named in an experiment are held fixed. For a decrease in the variable in the denominator, reverse the sign of the response.
