The Concept of Profit Maximization and How it Relates to Economics - Example

Running header: profit maximization Student’s name: Instructor’s name: Subject code: Date of submission: The concept of profit maximization and how it relates to economics According to Douglas & Berniheim (2007), Economics may be defined as the study of how different people make choices on how to use the inadequate productive resources. The decisions may involve what goods and services to produce, how to produce them and how they will be distributed to different members of the society. Since the resources are limited and there are competing needs, individuals are compelled to make decisions to satisfy some wants at the expense of others. What this implies is that the choices made must have the maximum benefit to the individual or firm. Therefore, we can conclude that economics aims at analyzing how individuals can efficiently use the limited resources to satisfy competing needs while ensuring maximum benefit is derived. In other words, economics is all about profit maximization. All the costs that a firm incurs are either fixed costs or variable costs. The Fixed cost includes costs that firms incur at any given level of production, even at zero level of output. Such costs may include rent, maintenance, fixed wages and costs incurred for general upkeep. On the other hand, variable costs change with output level increasing as output increases. The main component of variable costs is raw materials used up in production. Therefore, the total costs of a firm are composed of both fixed costs and variable costs. The total sum of cash received by a firm from its normal operations i.e sale of goods and services constitute its revenue. Michael (2007) asserts that profit maximization in economics is the process through which firms determine the price and production (output) level which yields the greatest profit to the firm. In determining the production level that maximizes profits, firms use a number of approaches which include the total cost- total revenue method and the marginal revenue-marginal cost approach. The total revenue –total cost method makes use of the fact that total profits are given by subtracting total costs from total revenues. On the other hand , marginal revenue-marginal revenue makes use of the fact that profits in a perfectly competitive market is at its maximum when marginal revenue is equal to marginal cost. However, this paper will only illustrate how the concept of marginal cost allows firms to practice profit maximization. Marginal cost and profit maximization According to Steve (2001), marginal cost is defined as the change in total cost resulting from a change in production by one unit. In other words, it can be said to be the cost of producing an extra unit of a good. Mathematically it is the primary derivative of the total cost function in relation to quantity. It is worthwhile noting that changes with output and hence at a given level of production, marginal cost equals the cost of the next unit produced. For example, if production of one more tractor would require employing two more employees, the marginal cost of the extra tractor would include the cost of employing the new employees. Therefore, marginal costs at a given level of production or production period is composed of all costs that vary as the quantity produced changes (i.e. valuable costs) while the other costs are known as fixed costs. Just like marginal cost, marginal revenue is the change in total revenue as a result of changes in the quantity sold. It is also expressed as the first derivative of total revenue function in relation to the quantity sold. Marginal revenue may also vary with volume and hence at each level of output, marginal revenue is the revenue realized when the next unit is sold. Marginal profit for any unit sold is the difference between the marginal revenue and marginal cost. When the marginal revenue is more than marginal cost, the profit is said to be positive while if it is less than marginal cost, the marginal profit is termed as negative. On the other hand, marginal profit is zero if marginal cost is equal to marginal revenue. Alain (2005), states that total profit increases when the marginal profit is positive and decreases when it is negative. Graphically, this can be illustrated as follows. Therefore, firms maximize profits at a point where marginal profit is equal to zero or when both marginal costs and marginal revenue are equal. As can be seen from the graph, the firm at this point will have collected positive profit up to where marginal cost (MC) intersects with (MR). At this point, zero marginal profit is collected and more output results to negative marginal profit since MC becomes greater than MR. in the graph, this is illustrated at point A. If the firm operates in a competitive industry, it faces the demand curve D that is identical to its MR curve (a horizontal line at price P, which depends on, industry demand and supply). ATC represents the average total costs while total economic profit is the area shown by PABC. Q is the optimum quantity that maximizes the total profits. Example Mr. Josepha Mogen a promoter has a hall that has a capacity of 20000 which he hired at a cost of 10000 dollars for a show. The agreement between him and the owner stipulates that the owner should get concessions, the parking and is to meet all other expenses related to the show. Mr. Mogen estimates that the demand for the show seats is Q =40000 -2000P. Q represents the number of seats while P represents the price charged for every seat. Determine the profit maximizing price of tickets to be sold. Solution In this case Mr. Mogen’s marginal costs are zero since the owner meets them. Therefore, he maximizes his profit by selling the tickets at a price that maximizes the revenue. The total revenue is achieved by multiplying price, P by the quantity sold. Since total revenue is a function of quantity, we work out inverse demand curve as follows. P (Q) =20-Q/2000 this is the total revenue expressed as a function of quantity i.e. TR (Q) =P (Q) × Q, TR (Q) = 20Q – Q2 /2000. As earlier stated, a rational firm maximizes profits at a point where MR – MC is zero. But for this case, the marginal cost is zero. Therefore, Mogen will achieve maximum profit at a point when marginal revenue will be zero. Note that marginal revenue is given by obtaining the fist derivative of TR. MR (Q) =TR’ (Q). Therefore, MR (Q) =20-Q/1000. For Mogen to obtain maximum profit, the function must be equal to zero. Therefore, 0=20-Q/1000, Q=20000. But the price IS a function of the quantity of tickets sold, therefore, for Mogen to sell a quantity of 20000, P (20000) = 20-20000/2000 =10 dollars per ticket. Cost is a function of the quantity of tickets sold but not the price of the tickets. However, Mr. Mogen’s marginal costs are zero and as such, he will obtain maximum profit if he charges a price which yields maximum revenue. Therefore, we express total revenue in terms of price. TR2 (P) = (40000-2000P) P = 40000P -2000P2, but total revenue is at its maximum if marginal revenue is zero. Therefore, 0 = 40000-2000P2, P= 10. To obtain the total profit, we subtract total cost from total revenue i.e. Profit = TR2 (P) - TC, in this case, π = (40000P – 20000P2) -10000, TR= 40000(10) – 2000(10)2 Therefore, π =400000 -200000 – 10000 = 190000. If Mogen had charged a price of 11 dollars per ticket, Q = 40000 – 2000P = 40000-2000 (11) Q = 40000 – 22000 = 18000 tickets. The profit at a price of 11 dollars would be 18000(11) – 10000 = 188000. This implies that Mogen can only maximize his profit by selling each ticket at 10 dollars and not at any other price. At 10 dollars, the marginal revenue is zero. As earlier stated, a rational firm maximizes its profit by operating at a point where marginal revenue is equal to marginal costs. Further, the marginal costs are the variable costs involved in the production. According to Heyne (2007), Changes in fixed costs do not affect the price or the quantity that maximizes profits. The short term fixed costs are treated as sunk costs and the firm continues operating as before. This can be illustrated from the graph above. Any change in fixed costs does not affect the marginal cost curve and the marginal revenue curve in any way. Therefore, the point of profit maximization does not change in any way. For example if the owner decided to double the price of the hall in the next show but all other factors are not changed, Mr. Mogen should continue charging the price of 10 dollars. The 10000 dollars increase in hiring costs should be treated as sunk costs and ignored in arriving at profit maximization price. The overall effect of the increase in fixed costs would be a reduction in profits by 10000 dollars. From the discussion above, a rational producer ought to produce and put on the market the last unit if marginal costs are less than market price. Since the market price is determined by forces of demand and supply, the producer maximizes profits at a point where marginal revenue is equal to marginal revenue. However, the ability of a firm to maximize profits by selling at this point depends on competition, time frame being considered among other factors. References: Alain, A 2005, Adexcel economics, Pearson education, New York. Douglas, B & Berniheim, M 2007, microeconomics, McGraw-Hill education Pvt limited, New Delhi. Heyne, T 2007, The economic way of thinking, Prentice hall, London. Michael, P 2007, Studying microeconomics, Addison Wesley higher education, Wesley. Steve, K 2001, Debunking economics: The naked emperor of the social sciences, Zed books, London. Read More