Optimization theory

Total, average and marginal concepts in optimization theory

 

In order to calibrate and predict a firm’s optimal level of profit, the total, average and marginal concepts are used. Salvatore says this relationship reflects the firm’s dealing with revenue, product, cost, or profit which is key components analyzing its benefits and expected values (2006, p. 43). A conceptual question then arises—how do firms maximize profits? In order to understand firms’ optimization strategy, we should first look at the relationship between total, average, and marginal costs driven geometrically in average-cost and marginal-cost curves.

Total cost (TC) describes economic cost of production incurred by total fixed costs plus total variable costs (Salvatore, 2006, p. 669). Total revenue (TR) can be calculated as the price per unit of the commodity times the quantity sold. Average cost (AC) equals total cost divided by output (Q) (Salvatore, 2006, p. 43). Average costs affect the supply curve and therefore are a fundamental component of supply and demand. Marginal cost (MC) equals the change in total cost per unit change in output. Marginal revenue and marginal profit are similarly defined.

The point in the total profit curve that is neither rising nor falling is where the marginal profit is zero. So from the graphic representation, it can be concluded that an output decision is not ideal or optimal unless the corresponding marginal profit is zero. This zero value functions as a profit gauge indicating all is set for producing profit. Profit should be calculated in terms of marginal analysis. This means marginal cost and marginal benefit are relevant factors in making optimal decisions. Marginal cost (MC) is equal to the slope of the total cost curve, whereas marginal revenue (MR) is the slope of the total revenue curve (Baumol and Blinder, 2009, pp. 166-168). Profit is incurred when MR=MC. Thus, when MR is not equal to MC, the firm needs to increase profits by either increasing or reducing its output (Baumol and Blinder, 2009, p. 167); therefore, MR should be equal to MC for profits to be maximized.

The logic of marginal analysis of profit can be generalized for optimization analysis. Generally, decision makers are often faced with making decisions to select the magnitude of some variables. For example, they would always struggle to know exactly how much to spend on advertising and supplies or how many employees to hire. Every act they make somehow brings benefits, theoretically meaning the larger the number, the larger the total benefits derived. But as the numbers increase, more costs are incurred. The main problem here is to take the trade-off approach into account so as to find the point where net gain is the greatest. So if a decision is to be made about the quantity of some variable, net benefit (total benefit - total cost) can be maximized at a point at which marginal benefit equals to marginal cost (Baumol and Blinder, 2009, pp. 166-169). This logic applies any cases when considering the net gains, for example, to a firm, to an organization, to a consumer, or to society as a whole.

Business managers should make optimal decisions based on some quantifiable data and geometric analysis using total, average, and marginal concepts. Guldmann (1986), for example, uses average-cost-based and marginal-cost-based models to find optimal conditions for gas distribution utilities. Using raw data from the East Ohio Gas company, his research proves the superiority of marginal-cost analysis over average-cost analysis in terms of less capital requirements, better productivity and higher efficiency. However, the reality is that those who open up a business cannot always seek help from executives from Wall Street who can calculate marginal cost and marginal revenue for them to decide how much to produce—just like consumers rarely use marginal analysis while grocery shopping. Most of time, the business decisions are made based on intuition and business hunches, which cannot easily be described by any set of rules. In this light, total, average, and marginal concepts construct a systemic model to help us analyzes and predict economic behavior of a firm and constitute the core of microeconomics. 

 

References:

 

Atkinson, J. B. (1996) ‘A Note on a Queueing Optimization Problem’, The Journal of the Operational Research Society, 47(3), pp. 463-467 [Online]. Available from: http://www.jstor.org/stable/3010588 (Accessed 16 January, 2010).

 

Baumol, W.J. and Blinder, A.S. (2009) Microeconomics: Principles & Policy. 11th ed. Ohio: South-Western Cengage Learning.

 

Guldmann, Jean-Michel (1986) ‘A Marginal-Cost Pricing Model for Gas Distribution Utilities’, Operations Research, 34 (6), pp. 851-863 [Online]. Available from:

http://www.jstor.org.ezproxy.liv.ac.uk/stable/pdfplus/170766.pdf (Accessed 17 January, 2010)

 

Salvatore, D. (2006) Managerial Economics in a Global Economy. 6th ed. New York: Oxford University Press.