A function showing the maximuin output possible with any given set of inputs. The expression of production possibilities by a production function assumes that inputs are used efficiently, so the production function is the upper boundary of the production set. A production function satisfies the ‘Inada conditions’ if the marginal product of each input tends to infinity as the quantity of input tends to zero, and tends to zero as the quantity of input tends to infinity. These conditions are firequently imposed in models since they imply a positive quantity of every input is used whenever input prices are finite.
Reference: Oxford Press Dictonary of Economics, 5th edt.