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How does one solve the following maximization problem?

$\underset{K_1, K_2, L_1, L_2}{\text{maximize }} min\{K_1 + L_1,K_2 + L_2\}$

subject to $c(K_1 + \mu K_2) + \beta c(L_1 + \mu L_2)$

where $c(.)$ is a cost function that is increasing and convex in its argument, and $\mu$ and $\beta$ are exogenous parameters.

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  • $\begingroup$ What does Maximize min mean? $\endgroup$ – BKay Oct 27 '16 at 0:05
  • $\begingroup$ @BKay, we're maximizing for a firm that has two outputs but can only sell the minimum of both outputs. Each output is produced with capital and labor that are perfectly substitutable. This is like maximizing a leontief utility (or min utility). $\endgroup$ – damamaharaj Oct 27 '16 at 0:15

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