# Difference between „equal variables“

Consider for example a production function with one variable.
Let’s say the function is f:R->R y=I, where y is the quantity produced and I is the quantity of some input used for production.
In this situation the quantity of some good produced and the quantity of some input used for production is always the same.
We still would say there are two quantities/variables but what’s the difference between them when they are always the same?

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• Why would quantities always be the same? 2 apples = 100ml of juice. 20 apples = 1L of juice?
– BrsG
2 days ago
• @BrsG That is an assumption. Suppose a relationship exists where two variables are the same. 2 days ago
• @Giskard: I see, quantities=variables. This threw me off.
– BrsG
yesterday

Suppose there is an economy with two industries, producing apples and oranges, the production functions of which are $$F_A(L) = L$$ and $$F_O(L) = L$$; i.e. in both industries the amount of output is equal to the amount of labor used. Yet clearly, labor and output are different, as it is possible that the 10 units of labor available are distributed so that the outputs in the industries are 8-2 respectively; thus neither output is equal to total labor. It is possible to transform an apple into an orange by reallocating labor, but apples are not oranges.