<p>How does one solve the following maximization problem?</p>

<p>$\underset{K_1, K_2, L_1, L_2}{\text{maximize  }} min\{K_1 + L_1,K_2 + L_2\}$</p>

<p>subject to $c(K_1 + \mu K_2) + \beta c(L_1 + \mu L_2)$ </p>

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

CC BY-SA 3.0
2016-10-27T00:05:52.933Z
What does Maximize min mean?
BKay
CC BY-SA 3.0
2016-10-27T00:15:50.003Z
@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).
damamaharaj
<microeconomics><optimization><leontief>
Perfect complement outputs with each output being composed of substitutable inputs
damamaharaj
# Perfect complement outputs with each output being composed of substitutable inputs

(Asked by: username_0 on 2016-10-26)

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.

**Tags:** microeconomics, optimization, leontief

> **Comments:**
> **username_1**: What does Maximize min mean?  
> **username_0**: @username_1, 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).  

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## 0 answers

