APPENDIX C6A. SIMULATION MODELING OF COSTS

In Appendix B3A to Chapter B3 we introduced the SIMMOD Java applet computer program as a model simulation system. We have discussed its applicabilities to revenue and demand in Appendix C2A, and its usefulness to the analysis of production in Appendix C4A. Our purpose is this appendix is to further elaborate its potential usefulness in the analysis of cost relationships.

Suppose that empirical research and regression analysis has yielded parameters for a third-order total cost function (TC) with equation

TC = 120 + 30 * Q + -1.7 * Q² + .04 * Q³.

In this representation, the asterisk (*) serves as a multiplication symbol. It is the power 3 in the fourth term on the right side of this function which makes it a third-order equation. The constant in this equation, 120, is a scale value which may be interpreted as the firm's total fixed cost and serves as the vertical axis intercept for the total cost function. The equation of the total variable cost function (TVC) may be given as

TVC = 30 * Q + -1.7 * Q² + .04 * Q³.

A graphic display of these functions is illustrated in Figure C6A-1. Since the constant term in the TVC equation is missing (implicitly zero), the TVC curve passes through the origin. The bottom panel of Figure C6A-1 illustrates the average and marginal cost functions derived from the total cost functions.

Figure C6A-1.

As illustrated in Figure C6A-2, the constant value has been changed from its initial value of 120 to the larger value, 180. The revised TC equation is

TC = 180 + 30 * Q + -1.7 * Q² + .04 * Q³.

The TVC equation remains unchanged. The loci of the new total and average total cost functions illustrated in Figure C6A-2 lie higher in coordinate space than those illustrated in Figure C6A-1. Since the TVC equation did not change, the TVC, the AVC, and the MC curves remain unchanged.

Figure C6A-2.

As we have noted in Chapters C5 and C6, the loci of the firm's cost functions may change either because in the short run the costs of the inputs into the production processes change, or because in the long run the management of the firm implements changes in the technologies employed in the firm's production processes. A short-run increase in input costs may be expected to shift the cost functions upward; if input costs fall, the cost functions will shift downward. If the long-run technology changes are output-increasing, they will shift the cost curves to the right; if they are input-saving they will shift the cost curves downward.

The management of an organization may gather cost data via its cost accounting system; its research staff may perform regression analysis upon the data to estimate the parameters of its cost functions. With this information in hand, the management of the firm could employ SIMMOD to model the equations of its total, average, and marginal cost functions. When any of these functions shift either by deliberate actions of the management or due to matters beyond the control of the management, it may analyze the effects of such shifts in SIMMOD by making appropriate changes to the respective functions as illustrated above.

The reader may access SIMMOD to experiment with parameter changes by clicking-on SIMMOD.