The Methodology of Profit Maximization - Case Study Example

Profit Maximisation Profit Maximisation is whereby a firm can determine and allocate the price and output level that generates the highest profit yield for the firm (Samuelson & Marks,). Before tackling the methods that deal with profit maximisation several concepts must be taken into account which is Revenue, Costs and Marginal Revenue and Cost. Costs are the expenditures the firm incurs during operation and also when idle, costs are divided into two distinctions which are Fixed and Variable Costs. Fixed costs are costs that are incurred regardless of production status for example rent and salaries, while Variable Costs that are dependent upon amount of quantity produced by the firm for example the cost for raw materials used in which if there is a low amount of production then there is a lesser amount of raw material used as compared to a production facility operation at a high capacity whereby higher costs will accumulate due to a greater use of raw materials (Varian, Hal R. Intermediate Microeconomics: A Modern Approach 1999). Revenue is the amount of money that a firm receives from its economic activities such as money from the sale of services and goods. Marginal Cost and Revenue in simple is defined as the difference in cost or revenue for every additional unit added to production (Wiley 2003) There are two methods that tackle the concept of profit maximisation which are the Total Revenue (TR) – Total Cost (TC) method and the Marginal Revenue (MR) =Marginal Cost (MC) method. The TR-TC method is based upon the simple calculation of profit that is that Profit equals total revenue minus the total cost. While the MR-MC method uses the concept that in a perfectly competitive market total profit reaches its maximum when Marginal Cost equals Marginal Revenue. For the profit maximizing output quantity using the TR-TC method, we start by taking into consideration that profit is equal to total revenue (TR) minus total cost (TC). This method is illustrated by the following diagram: The output quantity is whereby TR-TC gives the highest amount as can be seen in the diagram where at CQ intersects the TC curve at point B. As for the MR=MC method, for each added unit sold off, marginal profit (MP) equals marginal revenue minus marginal cost. Then if MR is larger than MR, marginal profit is rendered positive, and if the vice-versa situation marginal profit would be negative. When marginal revenue equals marginal cost, marginal profit becomes zero. Whereas total profit improves while marginal profit remains positive though total profit falls while marginal profit is negative, it must reach a peak amount (maximum) when the marginal profit becomes zero or when marginal cost equates marginal revenue. The following diagram illustrates this: Profit maximisation is where MC = MR that is at point “A”. Firms maximize profit through operating at where the marginal revenue equals the marginal cost. Changes to fixed costs cause no effect on the profit maximizing quantity/output or the price. The firm will treat fixed costs in the short run as sunk costs and proceed to operate normally.  This can be established graphically, using the diagram showing the total cost - total revenue method, the firm maximizes its profits at the point where the gradient of the TC line and TR line are equal. A change in TC will cause the TC curve to shift upwards by the magnitude of change.  There will be no effect on the total TR curve or the shape/size of the TC curve. Subsequently also the profit maximising value would remain as it was. This process can also be explained by using the diagram for the marginal revenue- marginal cost method. A difference in fixed cost would have no consequence on the position or shape of the curves. (Landsburg, S Price Theory & Applications) If a firm exists in a non-competitive market structure, subtle changes will have to be applied to the diagrams, for example the MR curve will have a downward sloping gradient due to overall market demand. As for firms within non-competitive structures, a major concept that is used for profit maximisation strategy is the game theory which attempts to mathematically predict behaviour in certain predicaments whereas an individual's success in making the right choice depends on the possibility of certain choices made by others.  "game theory is a sort of umbrella or 'unified field' theory for the rational side of social science, where 'social' is interpreted broadly, to include human as well as non-human players (computers, animals, plants)" (Aumann 1987). Economists have used game theory to try and interpret and analyze a multitude of economic matters such as bargaining, duopolies etc. This research usually focuses certain particular strategies known as equilibria. These "solution concepts" are based on what could/is needed in order to be able to be rational. An example of the usage of game theory can be seen in the much noted “Prisoners Dilemma”. It is assumed that firms are implementing rational decision-making methods and either produce or aim for the highest profit-maximizing output/point. Using this assumption there are four categories into which a firm's profit may be divided and considered: A firm makes an economic profit where its average total cost is greater than the price of the product at the profit-maximizing quantity/output. Economic profit is equal to the output multiplied by the difference between the average total cost (ATC) and price. A firm makes a normal profit when its economic profit equates to zero. This occurs when average total cost (ATC) equals price at the profit-maximizing output. If the price is between ATC and average variable cost (AVC) at the profit-maximizing output, then the firm is placed in a loss-minimizing condition/situation. It is considered that the firm should continue to operate normally. However since it would face a loss which would be greater if it was to stop operating. Through continuing operation the firm can offset at the very least its fixed cost and part of their variable costs but by completely halting operations they would lose the equivalent of their fixed cost. Now should the firm shuts down its TR would be zero and the TC would equal fixed costs. So the firm should continue producing, as long as the variable costs are being covered. Hence TR is greater than the TVC because losses are then less than the total fixed coat. Fixed costs are considered sunk costs and hence cannot be recovered through shutting down in the short run time period. The option of continuing to produce depends on revenue and the variable costs of the firm. If average revenue is greater than average variable costs then the firm should stick and continue to operate. It is a more rational decision to continue producing, as long as the AVC is less than the Price which in turn is less than ATC. If the price is below the AVC at the profit-maximizing output, then the firm is at the shutdown point. Losses are minimized by completely not operating, because any production will not generate any significant returns that would be enough to offset the fixed cost and part of the variable cost. A firm should exit the industry when revenues are less than the costs incurred by the firm while operating in the long run. A firm exits if TR is less than TC (Price is less than ATC). Within competitive market structures a firm will make normal profits in the long run. If firms are making more than a normal profit (economic profit) it will encourage other firms to enter the industry in order to reap such profits. Firms enter if TR is greater than total cost (Price is greater than AC). If firms are making normal profits, there is a relatively lesser amount of entry and exit within the industry, which is a long run situation. To put it simply a firm shuts down when Price (AR equals MR) is less than AVC, to minimize their losses and the firm's short-run supply curve equals the marginal cost curve above AVC. The firm therefore operates where profit equals marginal cost. The diagrams below illustrate the concepts of shutdown point and loss minimising condition/situation: Loss Minimisation Shutdown Point The general rule is that a firm maximises its profit through producing at an output where MR equals MC. The issue of profit maximization can also be observed from the opposite (input) side. To maximize profits a firm should increase production till the point where MR equals to MC therefore mathematically   the profit maximizing rule is MRP = MC. The marginal revenue product is the difference in total revenue per unit change in the variable input. That is MRP equals Change in TR/Change in VC. In conclusion Profit Maximisation is a business plan that aims to maximize the difference between revenues and costs. It is assumed that the objective of a firm is to maximize profits to the fullest extent. Profits are maximized where the MC of production is equal to the MR from sales. If the marginal costs are below the marginal revenue then output should be expanded in an effort to make an extra profit through the marginal unit of output. If marginal costs are above marginal revenue then the firm is incurring a loss on the marginal unit of output produced. It would then reduce its losses or increase its profits through the reduction of its output. 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