Step 1: Understanding the Concept:
The question asks for the definition of a production function, a fundamental concept in the theory of production in microeconomics.
Step 2: Detailed Explanation:
A production function is a technological relationship that expresses the maximum quantity of a good that can be produced from a given set of inputs (factors of production), over a specific period of time, assuming a given state of technology.
In simple terms, it shows the relationship between physical inputs and physical output.
It can be expressed mathematically as:
\[ Q_x = f(L, K) \]
Where:
\begin{itemize}
\item \(Q_x\) is the maximum quantity of output of good X.
\item \(f\) denotes the functional relationship.
\item \(L\) is the quantity of labor used.
\item \(K\) is the quantity of capital used.
\end{itemize}
The production function is a purely technical concept and does not involve prices or costs. It simply describes what is technically feasible when the firm operates efficiently.
Step 3: Final Answer:
A production function is a technical relationship that shows the maximum amount of output that can be produced with a given combination of inputs, such as labor and capital, under a given state of technology.