Extreme Analysis in the Concept of Economies of Scale: Searching for Minimum Production Inflation Points

Production Cost Sensitivity Analysis: Predicting Break Even Points and Losses in Business Economics Name: Alvinska Hebat Grade: 910-Math Application of Extreme Value in Economic Concepts • • • • The economic concept recognizes the various objectives of economic actors in carrying out their economic activities. These activities are divided into: consumption, production and distribution. Each economic actor has a goal to optimize their activities. The goal of optimizing these activities is divided into objectives: maximizing benefits or minimizing expenses (costs). The concept of extreme values of functions with one independent variable can be applied to the following economic concepts: 1. Economies of Scale Condition The condition of economies of scale of a company is a condition where the more production of goods produced, the lower the production cost until it reaches the lowest average cost. This lowest average cost (AC) causes the company to be said to experience the most economies of scale. If the company is a price taker then if: ✓ product price > minimum AC then in the optimal state the company will experience profits ✓ product price = minimum AC is the same then the company is at Break Even condition ✓ product price < its minimum AC then the company suffers a loss Example: Determine the minimum Average Cost (AC) of a producer of good X if the following cost structure is known: Fixed Cost (FC) IDR 800,- Variable Cost (VC) is expressed in the following function: VC = 0.2Q2 + 500Q; where Q = total output in liters, TC in Rupiah. In an optimal situation (minimum average cost) what is the price per unit of the good so that the producer makes a profit? Answer: Fixed Cost= FC = 800 and Variable Cost Function = VC = 0.2Q2 + 500Q Then the Total Cost Function (TC): TC = VC + FC = 0.2Q2 + 500Q + 800 Average Cost or total cost per unit (abbreviated as AC) is Minimizing AC: Minimizing AC is the same as finding AC in the extreme state, and then testing the extremity whether AC is minimum as follows: AC will have an extreme value if: Determining whether AC is minimum: it is sought whether at Q = 63,245 it turns out that (d2AC / DQ2) > 0 ? d 2AC/dQ2 = 1600Q-3 = 1600 (63.245)-3 = 0.006324 > 0 then at Q = 63.245 then AC is proven to be the minimum Maximum Profit of the Company • • • The company is said to have maximum profit when: TR - TC = maximum Conversely, the company will suffer a minimum loss if: TC - TR = minimum A company that experiences maximum profits or suffers minimum losses is referred to as a company that operates in an optimal state. Example: Find the optimum profit of a textile company if the total revenue function (TR) and total cost function (TC) are known as follows: TR = 1000Q - 2 Q2 and TC = Q3 - 59Q2 + 1315Q + 2000 where TR, TC are in million rupiah; Q = total output in thousand meters. Answer: Profit/Loss Function (π) = TR - TC = (1000Q - 2 Q2 ) - (Q3 - 59Q2 + 1315Q + 2000) = 1000Q - 2 Q2 - Q3 + 59Q2 - 1315Q - 2000 = - Q3 + 57Q2 - 315Q - 2000 Finding the extreme value/type of Π = - Q3 + 57Q2 - 315Q - 2000 will have an extreme value if: dΠ/dQ = 0 or -3Q2 + 114Q - 315 = 0 then the value of Q can be found through the quadratic formula, so we get Q1 = 3 and Q2 = 35 Determine the type of extreme: at Q = 3 d 2 Π/dQ2 = -6Q + 114 = -6(3) + 114 = 96 Since d2 Π/dQ2 > 0 at Q = 3 then profit will be minimum at Q = 3. at Q = 35 d 2 Π/dQ2 = 6Q + 114 = -6(35) + 114 = -96 Since d2 Π/dQ2 < 0 at Q = 35 then profit will be maximum at Q = 35. Maximum profit amount At Q = 35 the amount of Π = - (35)3 + 57(35)2 - 315(35) - 2000 = 13,925 So the textile company will earn a maximum profit of Rp 13,925,000,000 if it sells 35,000 meters of textiles.