For planning purposes, company headquarters seeks to obtain accurate information about the productive capacity of one of its plants. The plant manager knows that the facility’s capacity is Q = 10,000 units, but knows that headquarters is in the dark. Using a bonus system, headquarters also wants to encourage the manager to strive for maximum plant output.
a. Headquarters decides to use the bonus system:
B = .5(Q - QT),
Where the plant manager forecasts the likely output QT. If actual output Q exceeds QT at the end of the year, the bonus increases. If Q falls short of QT, the bonus is reduced. Under this system, will the manager report the plant’s true capacity, 10,000 units? Explain.
b. Suppose instead that headquarters uses the following bonus system:
B = .4QT + .3(Q - QT), if Q > QT.
B = .4QT + .5(Q - QT), if Q ≤ QT.
Will the manager report the plant’s true capacity? Will the manager strive for maximum output? Explain.