What does this notation mean as a production function: f = min [t, 1.05k]

Question

I'm attempting to work on an econ problem, but I'm having trouble understanding the notation that the production functions are given in to even begin to attempt to solve the problem.

This is what is given (I've changed the numbers/variables a bit, I'm just looking to understand the process, not for someone to do my homework)

f = min[t, 1.05k] k = min[m, 2f]

t = m = 10

You are then prompted to graph the functions and find the non-zero equilibrium.

Does this just mean take the minimum of the two values?

Thanks for any help you can provide!

Answer 1

You simply take the minimum of the two values.

Answer 2

The "min" function gives you the minimum of two values. For example, min(3,4) = 3, and min(6,-9) = -9.

Answer 3

The other comments are exactly right. $min(x,y) = x$ if and only if $x \leq y$ and $=y$ otherwise.

To obtain a decent answer to your problem, you should provide some context to the question.

When the production function is expressed with the $min$-operator, it usually reflects perfectly complementaty production inputs.

As an example: To produce 1 car, you need 1 car body (denoted by $b$) and 4 wheels (denoted by $w$). Hence the production function is $output = \min (b,\frac{w}{4})$. That way 2 car bodys and 8 or 9 wheels produce 2 cars - and also 2 car bodys and 100 wheels only produce 2 cars, because you need both.