![]() The value worked out using calculus differs from the value calculated conventionally because the first derivative provides the instantaneous rate of change of the cost function instead of average change in cost from 14th to 15th unit. If we want to find the marginal cost of 15th unit, all we need to do is to plug 15 in place of Q is the formula above: Since marginal cost equals the slope of the total cost curve (or the total variable cost curve), it equals the first derivative of the total cost (or variable cost) function. Instead of creating the table we did in the example above, we can calculate marginal cost of a unit directly using calculus. It means that MC curve crosses AVC curve at its minimum point. Marginal cost is equal to the average variable cost when the average variable cost is at its minimum.As long as the marginal cost curve lies below the average cost curve, the average cost decreases and the average cost curve declines, but as soon as the marginal cost curve crosses the AVC curve, average cost starts to rise.The following general relationship exists between marginal cost curve and other cost curves: If we plot the average variable cost (AVC) and the marginal cost (MC) value, we get the following graph: Relationship between MC and AVC Using the function above and the information about fixed costs, we can create the following cost table: Q When Q = 0, total cost TC equals $200 and this is the total fixed cost. As the slope of any function can be determined by finding its first derivative, MC can also be defined as follows: MC =Īssume you work as analyst at a firm whose total cost curve is given by the following equation: It equals the slope of the total cost curve/function or the total variable cost curve. Marginal cost is the change in total cost (or total variable cost) in response to a one unit change in output. Since equal amount of fixed costs is included in TCQ and TCQ – 1, if we subtract FC from both sides, we can define marginal cost as the difference between total variable cost at Q units minus total variable cost at Q – 1 units ![]() This can be written mathematically as follows: Marginal cost can be calculated directly by subtracting total cost of Q – 1 units from total cost of Q units. Firms compare marginal revenue of a unit sold with its marginal cost and produce it only if the marginal revenue is higher or equal to the marginal cost. It is because it directly affects a firm’s production decision. Therefore, the formula for Average Fixed Cost (AFC) can be written as: AFC ATC - AVC Now, we can calculate the output rate that minimizes Average Variable Cost: AVC VC/QVC TC - FCVC 1000 + 10Q - 0.9Q2 + 0.04Q3 - (1000 + 500)VC 10Q - 0.9Q2 + 0. Of all the different categories of costs discussed by economists, including total cost, total variable cost, total fixed cost, etc., marginal cost is arguably the most important. The marginal cost curve is generally U-shaped. It equals the slope of the total cost function. In economics, marginal cost is the incremental cost of additional unit of a good.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |