Look again at the flexible budget shown in Exhibit 10-1 and consider the approaches that might have been used to develop the fixed amounts and the variable rates shown there. The fixed, variable, and semivariable categories used are in conformity with the definitions given above.In Exhibit 10-1, the activity base was units of output because Department 22 produces only one product.The next step was,by using analyses, estimates, and judgments, to determine the variability of each expense incurred in the responsibility center.Determination of yields the two components of each expense: (1) the fixed or constant amount per period and (2) the variable rate per unit of the activity base.A "pure" fixed expense has a constant component amount and a zero value for the variable component. A "true” variable expense has a zero value for the fixed component and a constant rate per unit of activity.A semivariable expense has both constant amount and a rate for the variable component. Determination of the variability of each expense item in a responsibility center is the most critical problem in the development of flexible expense budgets.Numerous methods have been developed for resolving this difficulty.The purpose of this section is to explain and illustrate the primary methods that are normally used. Most of these methods involve an analysis of historical expenses, which is only one input for extimating the variability of future costs.