Marginal cost is the additional cost of producing one more unit of output. The formula is. It is not the cost per unit of all units produced, but only the next one or next few. We calculate marginal cost by taking the change in total cost and dividing it by the change in quantity. For example, as quantity produced increases from 40 to 60 haircuts, total costs rise by — , or The marginal cost curve is generally upward-sloping, because diminishing marginal returns implies that additional units are more costly to produce.
We can see small range of increasing marginal returns in the figure as a dip in the marginal cost curve before it starts rising. Table 6. When discussing cost minimization, it is important to understand what we actually want to minimize.
We cannot minimize total cost. Actually, we can, but this would occur when production is 0 and only the fixed costs are present…but this is not going to be our goal. Instead, what we want to minimize is average total cost.
This means that we want to minimize how much it costs to produce each product. To identify the method to accomplish this task, we have to think about the relationship between average total cost and marginal cost.
Instead of thinking about costs, let us go in a slightly different direction. Let us think about grades. This is your average grade just like an average total cost. Your average grade will go up. This is the same thing that happens with costs. Think about your next exam grade as the marginal grade. Note that when the marginal grade is greater than the average grade, your average increases.
This is exactly the same as cost. When the marginal cost is greater than the average total cost, the average total cost is increasing. The same applies to costs. If the marginal cost is less than the average total cost, then the average total cost will be decreasing. Your grade would stay the same. The same applies for cost. If the marginal cost is equal to the average total cost, the average total cost will not change. Let us apply this to the average total cost curve.
Remember, it is U-shaped. Therefore we want to determine the quantity at the bottom of the U. This will occur when the marginal cost is equal to the average total cost. If we are producing less than this quantity, average total cost will exceed marginal cost, so the average total cost curve will be falling. On the other hand, if we are producing at a quantity that exceeds the minimization point, the marginal cost will exceed the average total cost curve and average total cost will be increasing.
This is shown in the figure below. From: Openstax: Principles of Microeconomics Chapter 7. Consider a pizza restaurant that has one pizza oven. They can produce more or less pizza based on the number of employees. If they expect to be busy, they can have more people work that day. This is illustrated in the table below:.
What if a festival is in town and they believe that they can sell pizzas. Is this possible? Regardless of how many people they hire, they do not have enough capital. In the short-run, we assumed that firms were unable to change the amount of capital. This means that they must choose their level of production from the menu above. But, in the long-run, they can change their level of capital. This means that they can add pizza ovens.
A long-run production schedule is given below:. In the long-run, we first decide on our level of capital, then pick the level of labor to produce at the desired level.
Re-consider the long-run production function in the previous section. Suppose that we want to produce pizzas. We can accomplish this in more than one way.
This is shown in the table below. There is also a larger point here: there are no fixed costs in the long-run. This is because we have control over both labor and capital, so all costs are variable. A firm can perform many tasks with a range of combinations of labor and physical capital. For example, a firm can have human beings answering phones and taking messages, or it can invest in an automated voicemail system. A firm can hire file clerks and secretaries to manage a system of paper folders and file cabinets, or it can invest in a computerized record-keeping system that will require fewer employees.
A firm can hire workers to push supplies around a factory on rolling carts, it can invest in motorized vehicles, or it can invest in robots that carry materials without a driver. Firms often face a choice between buying a many small machines, which need a worker to run each one, or buying one larger and more expensive machine, which requires only one or two workers to operate it.
In short, physical capital and labor can often substitute for each other. Once a firm has determined the least costly production technology, it can consider the optimal scale of production, or quantity of output to produce. Many industries experience economies of scale. Economies of scale refers to the situation where, as the quantity of output goes up, the cost per unit goes down. In everyday language: a larger factory can produce at a lower average cost than a smaller factory.
This means that an increase in output can lead to a decrease in the average total cost. One prominent example of economies of scale occurs in the chemical industry. Chemical plants have many pipes. The cost of the materials for producing a pipe is related to the circumference of the pipe and its length. However, the cross-section area of the pipe determines the volume of chemicals that can flow through it.
A doubling of the cost of producing the pipe allows the chemical firm to process four times as much material. This pattern is a major reason for economies of scale in chemical production, which uses a large quantity of pipes. Of course, economies of scale in a chemical plant are more complex than this simple calculation suggests. While in the short run firms are limited to operating on a single average cost curve corresponding to the level of fixed costs they have chosen , in the long run when all costs are variable, they can choose to operate on any average cost curve.
More precisely, the long-run average cost curve will be the least expensive average cost curve for any level of output. The figure below shows how we build the long-run average cost curve from a group of short-run average cost curves. Five short-run-average cost curves appear on the diagram.
Think of this family of short-run average cost curves as representing different choices for a firm that is planning its level of investment in fixed cost physical capital—knowing that different choices about capital investment in the present will cause it to end up with different short-run average cost curves in the future.
The long-run average cost curve shows the cost of producing each quantity in the long run, when the firm can choose its level of fixed costs and thus choose which short-run average costs it desires. If the firm plans to produce in the long run at an output of Q 3 , it should make the set of investments that will lead it to locate on SRATC 3 , which allows producing q 3 at the lowest cost. At SRATC 2 the level of fixed costs is too low for producing Q 3 at lowest possible cost, and producing q 3 would require adding a very high level of variable costs and make the average cost very high.
At SRATC 4 , the level of fixed costs is too high for producing q 3 at lowest possible cost, and again average costs would be very high as a result. The shape of the long-run cost curve in the figure above is fairly common for many industries. The left-hand portion of the long-run average cost curve, where it is downward- sloping from output levels Q 1 to Q 2 to Q 3 , illustrates the case of economies of scale.
In this portion of the long-run average cost curve, larger scale leads to lower average costs. In the middle portion of the long-run average cost curve, the flat portion of the curve around Q 3 , economies of scale have been exhausted. In this situation, allowing all inputs to expand does not much change the average cost of production. We call this constant returns to scale.
In this LRATC curve range, the average cost of production does not change much as scale rises or falls. Finally, the right-hand portion of the long-run average cost curve, running from output level Q 4 to Q 5 , shows a situation where, as the level of output and the scale rises, average costs rise as well. We call this situation diseconomies of scale. A firm or a factory can grow so large that it becomes very difficult to manage, resulting in unnecessarily high costs as many layers of management try to communicate with workers and with each other, and as failures to communicate lead to disruptions in the flow of work and materials.
Not many overly large factories exist in the real world, because with their very high production costs, they are unable to compete for long against plants with lower average costs of production. However, in some planned economies, like the economy of the old Soviet Union, plants that were so large as to be grossly inefficient were able to continue operating for a long time because government economic planners protected them from competition and ensured that they would not make losses.
Diseconomies of scale can also be present across an entire firm, not just a large factory. The leviathan effect can hit firms that become too large to run efficiently, across the entirety of the enterprise. Firms that shrink their operations are often responding to finding itself in the diseconomies region, thus moving back to a lower average cost at a lower output level. Diminishing marginal productivity MPk f 2 f kk f11 0 k k 2 MPl f 2 f ll f 22 0 l l 2.
Average Physical Product Labor productivity Often means average productivity. Average product of labor output q f k , l APl labor input l l APl also depends on the amount of capital employed. Isoquant Maps Isoquant map To illustrate the possible substitution of one input for another.
An isoquant Shows those combinations of k and l that can produce a given level of output q0. Isoquants record the alternative combinations of inputs that can be used to produce a given level of output. The slope of these curves shows the rate at which l can be substituted for k while keeping output constant.
The negative of this slope is called the marginal rate of technical substitution RTS. In the figure, the RTS is positive and diminishing for increasing inputs of labor. Marginal rate of technical substitution RTS Shows the rate at which labor can be substituted for capital Holding output constant along an isoquant dk RTS l for k dl.
Not possible to derive a diminishing RTS From the assumption of diminishing marginal productivity alone. The ratio will be negative if fkl is positive Because fll and fkk are both assumed to be negative.
Returns to Scale How does output respond to increases in all inputs together? Suppose that all inputs are doubled, would output double? As inputs are doubled Greater division of labor and specialization of function Loss in efficiency - management may become more difficult Cengage Learning.
Returns to Scale Production function Constant returns to scale for some levels of input usage Increasing or decreasing returns for other levels The degree of returns to scale is generally defined within a fairly narrow range of variation in input usage.
The above production function exhibits DRTS! Larger output associated with lower cost. Arise because the larger scale of operation allows managers and workers to specialize their tasks and use of more sophisticated equipments and factories. One firm is more efficient than many. The isoquants get closer together.
The marginal productivity functions Are homogeneous of degree zero If a function is homogeneous of degree k, its derivatives are homogeneous of degree k-1 Cengage Learning. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a 29 license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
Constant Returns to Scale Marginal productivity of any input Depends on the ratio of capital and labor Not on the absolute levels of these inputs.
The RTS between k and l Depends only on the ratio of k to l Not the scale of operation Homothetic production function All of the isoquants are radial expansions of. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a 30 license distributed with a certain product or service or otherwise on a password-protected website for classroom use. An additional feature is that the isoquant labels increase proportionately with the inputs. The elasticity of substitution is defined to be the ratio of these proportional changes; it is a measure of how curved the isoquant is.
Elasticity of Substitution Elasticity of substitution between two inputs The proportionate change in the ratio of the two inputs To the proportionate change in RTS With output and the levels of other inputs constant.
Three possible values for the elasticity of substitution are illustrated in these figures. In a , capital and labor are perfect substitutes. In this case, the RTS will not change as the capitallabor ratio changes. In b , the fixedproportions case, no substitution is possible. A case of limited substitutability is illustrated in c. Technical Progress Methods of production change over time Following the development of superior production techniques The same level of output can be produced.
Technical progress shifts the q0 isoquant toward the origin. The new q0 isoquant, q0, shows that a given level of output can now be produced with less input.
For example, with k1 units of capital it now only takes l1 units of labor to produce q0, whereas before the technical advance it took l2 units of labor. Measuring Technical Progress Differentiating the production function with respect to time we get dq dA df k , l.
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Carousel Previous Carousel Next. Jump to Page. Search inside document. Diminishing Marginal Productivity Marginal physical product Depends on how much of that input is used Diminishing marginal productivity MPk f 2 f kk f11 0 k k 2 MPl f 2 f ll f 22 0 l l 2 Cengage Learning.
Average Physical Product Labor productivity Often means average productivity Average product of labor output q f k , l APl labor input l l APl also depends on the amount of capital employed Cengage Learning. Size of firms operation does not affect productivity. May have a large number of producers. Isoquants are equally spaced. Constant Returns to Scale Marginal productivity of any input Depends on the ratio of capital and labor Not on the absolute levels of these inputs The RTS between k and l Depends only on the ratio of k to l Not the scale of operation Homothetic production function All of the isoquants are radial expansions of one another Cengage Learning.
Decreasing efficiency with large size. Reduction of entrepreneurial abilities. Communication between workers and managers can become difficult to monitor. Isoquants become farther apart. Katherine Sauer. Eva Das. Amit Naik. Ravi Shankar. Harvin Waraich. Akshay Dembra. Tika Gusmawarni. Anonymous BBs1xxk96V. Monika Jha. Joydeep Adak. Ganesh Ojha.
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