Perfect complement graph and isoquant

Question

$f(x_1,x_2) = min {x_1,x_2} + x_2$ if that was the production, what would the isoquant be? 
Would it simply follow $x_1 = x_2$? I'm not entirely sure what it the graph would look like.

An economist · Answer

An isoquant is a contour line drawn through the set of points at which the same quantity of output is produced while changing the quantities of two or more inputs.

Having production function: $f(x_1, x_2) = min {x_1, x_2 } + x_2$ for $x_i in [1, 10]$

We can produce isoquants for varying number of inputs. Below you will find 10 isoquants for quantities ranging from 1 to 10 (keep in mind that $Q = 1$ and $Q = 2$ are overlapping). I hope it helps to visualize the problem.

Amit · Answer

$f(x_1,x_2) = min(x_1,x_2) + x_2 = begin{cases} x_1 + x_2 & text{if } x_1 leq x_2  2x_2 & text{if } x_1 > x_2 end{cases}$

Here is the isoquant map for the production function :

Perfect complement graph and isoquant

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