Cost Function PDF

Cost function Cost is typically the expense incurred for making a product or service that is sold by a company. Price is the amount a customer is willing to pay for a product or service. The cost of producing a product has a direct impact on both the price of the product and the profit earned from i...

Cost function Cost is typically the expense incurred for making a product or service that is sold by a company. Price is the amount a customer is willing to pay for a product or service. The cost of producing a product has a direct impact on both the price of the product and the profit earned from its sale. The term cost function refers to the relationship between firms output of goods and services and the cost of production. Since the cost of production is the sum of the input multiplied by their prices, one can easily move from the production function to the cost function The term cost function therefore refers to the total payment that the firm makes for its factors of production, inputs or resources. In economics, the term cost is not merely the firm’s historical cost, but more so its opportunity cost. This is because the owner of the resources must be paid the minimum of what their resources could have earned in their next best alternative uses. Types of cost based on who owns the factors of production Based on the classification, cost can be divided into categories: 1. Explicit cost 2. Implicit cost Explicit cost – the total explicit cost refers to the payment that the firm makes to non-owners for the resources that it employs. They include the salaries paid to employees, the payment for raw materials, the payment for insurance services etc. Implicit cost – the implicit cost on the other hand refers to the opportunity cost of the resources that the firm employs but owns. If a firm uses the resources that it owns, it must be paid at least what those resources could have earned in their next best alternative uses. For example, the entrepreneur could manage another firm and earn a salary of $200,000 monthly. The building that the firm operates could have been rented for $50,000 monthly and the money that was used to start the business could have been placed in the bank earning a monthly interest of $50,000. The total implicit cost is $300,000. If the firm is to operate its own business, it must make a minimum profit of $300,000. Types of cost based on how they vary with production They include: 1. Total fixed cost 2. Total variable cost Total fixed cost – refers to the payment that the firm makes for fixed resources such as buildings, machinery, insurance etc. The total fixed cost remains the same regardless of the level of output. If the firm produces zero units or thousands of units of output, the total fixed cost remains the same. Therefore, when the level of output is zero, the total cost is the fixed cost. The total variable cost – on the other hand varies directly with the level of output. When the output is zero, the total variable cost is zero and as output increases, variable cost also increases and vice versa. Examples of variable costs are labour, utility and raw materials. TC TVC Cost TFC 0 1 2 3 4 5 Units of output The graph shows the total cost can be attained by adding the total fixed cost and the total variable cost. Units of TFC TVC TC output 0 100 0 100 1 100 30 130 2 100 90 190 3 100 100 200 4 100 110 210 5 100 130 230 6 100 160 260 7 100 200 300 8 100 300 400 9 100 350 450 10 100 410 510 Unit cost The total cost can be further subdivided into unit cost. These costs are really cost in the short run since they are based on the premise that there is a total fixed cost. The total variable cost can be divided into the average fixed cost. TC = TFC + TVC. By dividing both sides by Q, one obtains TC/Q = ATC; TFC/Q = AFC and TVC/Q = AVC. This shows the average total cost is obtained by dividing the total cost by the number of units (Q). The average fixed cost can be obtained by dividing the total fixed cost by the number of units of output (Q). the same thing is done for TVC. TC/Q = TFC/Q + TVC/Q. TC/Q = ATC, TFC/Q = AFC TVC/Q = AVC The average total cost can be obtained in two ways: 1. By dividing the total cost by the quantity of output = TC/Q 2. By adding the AFC and the AVC The unit costs are the average total cost and the marginal cost. The marginal cost is the cost of providing one more or one less unit while the average cost is the cost of producing one unit Units TC ATC MC of output 0 100 − 1 190 190 90 2 270 135 80 3 330 110 60 4 380 95 50 5 450 90 70 6 540 90 90 7 630 90 90 8 800 100 170 Unit TFC AFC TVC AVC of output 0 100 - 0 ∞ 1 100 100 90 90 2 100 50 170 85 3 100 33.33 230 77 4 100 25 286 72 5 100 20 350 70 6 100 17 440 73 7 100 14 530 76 8 100 13 700 88 ` All the unit costs with the exception of the average fixed cost are u-shaped. This means they fall, reaches a minimum and the begin to rise. This shape arises in the short run due to the law of diminishing marginal product. If additional units of variable inputs lead to a decrease in output, the average cost and the marginal cost must be increasing.  MC ATC AC MP AP The graph shows that there is a close relationship between the average product and marginal product, and the average cost and marginal cost. When the average product and marginal product are rising and the firm adding more output per unit of input, the average and the marginal cost must be falling. Note the average fixed cost is not fixed but variable. It actually decreases as output increases. This is because a fixed number is being divided by a larger quantity of output. The fixed cost is spread over a wide range of output, each unit bearing a smaller percentage of the cost. On a graph, it is a downward sloping curve that approaches the x-axis but never touches it. Unit cost 0 1 2 3 4 5 6 Units of output When both the average and the marginal cost are decreasing, economists refer to this as increase in returns to the variable inputs. Where the firm is experiencing decreasing returns to the variable inputs, the average and marginal costs are increasing. b Unit cost ($) c a » AFC d b » AVC c » ATC d » MC a Units of out put Relationship between average cost and marginal cost When marginal cost is below average cost, it pulls the average cost downwards and so, the average cost must be decreasing. When the marginal cost rises above the average cost, it pulls the average upwards and so, average cost must be increasing. When average cost and marginal cost are equal, average cost is at its minimum. Marginal cost is defined as the change in the total cost arising from the change in the number of units of output by one when the total cost is increasing, the marginal cost can be defined as the addition to the total cost arising from increasing output by one unit.