Long Run Production Cost

Have you ever seen a building with solar power panels? Have you lived in a residence that had them? You might already know that, at least in the U.S., the purchase of solar panels requires a large financial investment or loan. So why buy them? It's an interesting choice that many businesses have to consider--make a large outlay of cash today in exchange for very low marginal electricity costs over the next few decades. If you own your own home, you probably know how expensive monthly electricity bills can be! Just like businesses, homeowners too can take advantage of opportunities to invest in home improvements, like solar power panels, that can lower their monthly costs in the future. How does the firm's cost function change when we look at the long run? That is the topic today - long-run production cost. What are you waiting for? Read on!

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Table of contents

    Long-run Production Costs Definition

    When we think of long-run production costs, we are no longer working with fixed costs. Why? Because all costs vary in the long run. Let's explain by starting with the short run. Businesses inherently have certain fixed costs that are usually monthly--rent, mortgage, utilities, payroll. Within a given timeframe--say, the length of a rental contract, or the length of mortgage repayment, there isn't anything they can do to change this monthly cost. These costs are independent of production and are often unavoidable costs.

    However, in the long run, firms can vary all costs, including fixed costs! Look at the example below.

    A coffee processing company rents five acres of land, and the current rent is due in one year. Let's assume that all the surrounding land is also occupied for that year. This means that the firm cannot buy extra land or get rid of the current land until the rent period is due. However, the company can choose to employ more workers to harvest the coffee it grows on the land. So far, this example describes the short-run where the company cannot control the cost of land. However, after that one year, the firm can choose to rent more or less than the original five acres of land.

    The above example shows that while the short run does not leave firms with much of an option regarding a fixed cost, given enough time, even the fixed cost can be changed by the firm!

    Many rental contracts can be negotiated on an annual basis. Many mortgage contracts can be renegotiated every few years as interest rates change. If a certain piece of property is too expensive, once the rental contract is over, the firm can look for another suitable option. This is how costs that are fixed in the short run become variable in the long run.

    So how do we define the short run and the long run? Precisely by whether there are costs that are fixed across the given the length of time. While you might generally think of the short run as being within one year and the long run as being longer than a year, the short run and the long run are not actually specific lengths of time, but rather depend on when the firm has the ability to make adjustments to its costs that were previously fixed.

    The short run is the period of time for which there is at least one fixed cost.

    The long run is the minimum period of time that it takes for all cost to become variable.

    Based on what we have learned now, let's define long-run production costs.

    Long-run production costs refer to the costs over the length of time in which all the costs of the firm are variable costs.

    Difference Between Short-run and Long-run Production Costs

    The main difference between short-run costs and long-run costs is the existence of fixed costs. In the short run, there is at least one fixed cost. However, in the long run, all costs are variable. Why? let's explain with an example.

    A bakery rents a facility on a busy street where all other facilities are occupied for a year. The facility rental of the bakery will also last a year, and until then, no changes can be made. The period where the facility rental cannot be changed is the short run, and the rental of the facility is a fixed cost. However, after the year ends, the bakery can choose to expand the facility by renting two facilities. This means that one year marks the long run, as the facility rental becomes a variable cost.

    The difference between short-run and long-run production costs is that long-run production costs are all variable costs whereas short-run production costs include at least one fixed variable.

    Economists may still talk about fixed costs in the long run. In this case, they are referring to costs that will be fixed in any given short-run period, even though they are variable in the long-run perspective.

    Long-run Production Cost Function

    To keep costs as low as possible while producing as much as possible, the firm needs to keep track of its costs. Here, we will assume that the firm only uses two factors of production: capital and labor. The long-run production cost function is concerned with finding the right mix of inputs as a function of rent and wage.

    Factors of production are inputs.

    Rent is the cost of capital and wage is the cost of labor.

    The long-run total cost function represents the lowest total cost of producing different levels of output when all inputs are variable. In the long run, total cost includes any outlay that may be required in order to produce at a certain level of output or in order to produce at a lower per-unit cost.

    Average total cost is an important metric to economists as it helps them figure out the per-unit cost of production based on the total cost and the quantity of output. It is calculated by dividing the total cost by the quantity of output.

    Average Cost (AC)=Total Cost (TC)Quantity (Q)

    Average total cost is the total cost of production divided by the quantity of output.

    Long-run Production Costs Curve

    The long-run production cost curve shows the relationship between cost and output in the long run. In other words, it shows the total cost of production for a given quantity of output. The term production cost refers to average total cost.

    Generally, when looking toward the long run, for each level of output, the firm can choose a different level of investment that would minimize the average total cost for that level of output. The firm invests in a level of capacity, say the size of the warehouse, or the acres of land, and that determines the firm's short-run cost curve. It may, for instance, increase the fixed costs, but decrease the variable costs, allowing the firm to produce larger and larger quantities for a lower per-unit cost. This means that if a firm has a certain level of output in mind, it must choose the investment that results in the lowest average total cost.

    Most firms have several possible choices to invest in greater capacity. At any given point in time, there is one minimum average total cost curve, but over time there are many. This means that most firms have several possible short-run average total cost curves as they look at the long-run possibilities.

    In the short run, a change in quantity is a movement along the short-run total cost curve. However, in the long run, a change in quantity can be accompanied by a change in capacity level that increases fixed costs but decreases variable costs, such that in the long run, the average total long-run cost for the new level of output is minimized. That is, in the long run, the firm can choose to put itself on a different short-run total cost curve!

    Essentially, we will have a long-run total average cost curve within which all the various short-run average total cost curves fall. Figure 1 demonstrates this visually.

    In Figure 1, suppose the firm examines this long-run average total cost curve (LRATC) and targets an output of eight units. However, the firm also considers two other options: two units of output and twelve units of output. The short-run average total cost curve for each of these options are shown in the graph and labeled ATC.

    long run production costs average total cost curve studysmarterFig 1. - Long-run average total cost curve

    Figure 1 shows the long-run production cost curve with the short-run production cost curves in it.

    By choosing an investment level that minimizes the short-run average total cost for a quantity of eight, the firm will be at point C in the graph. However, if the firm anticipates a production of two units in the long run, it will decrease its capacity investment and instead be at point A on in the graph.

    Note that the minimum point on ATC2 is not as low as the minimum point on ATC8. Therefore, the average total cost of production is higher at point A than at point C. However, point A represents the lowest possible average total cost for the production of two units.

    Finally, if the firm anticipates a production of twelve units it will invest in getting to point E, by putting itself on the short-run curve ATC12. Note that if the firm decides to pursue a quantity of eight, and then wants to change to a quantity of two or twelve, then in the short run, the firm will be at point B or D, respectively, until it can get out of its short-run cost constraints. This is why it's very important to choose optimally in the first place!

    What all this is saying is that if the firm makes a long-run decision and chooses a short-run cost curve that matches its planned level of output, then it will stay on the long-run average total cost curve (in addition to its existing short-run cost curve). However, if the market conditions change and the firm wants to produce a different quantity, then the new level of output is no longer on the long-run average cost curve.

    Look at it like this - if you go according to the long-run plan, you're on the long-run curve. However, if you alter your quantity along the way, then your existing short-run curve is no longer on the long-run curve for the new quantity, and there is another short-run curve that will provide a lower average total cost for that quantity.

    Long-run Production Costs and Scale

    The long-run total cost curve looks similar to the short-run total cost curve, just at a larger scale. Every decision is made in the short run, with an existing short-run cost curve, but a decision to make an investment in greater capacity, such as a larger manufacturing plant, is a long-run decision. It is a decision that allows the firm to be on a lower short-run average total cost curve (including both fixed and variable costs) in the future.

    The scale of production is the long-run efficiency of producing outputs from the inputs, characterized by choosing between the possible short-run average total cost curves. The process of expanding a business is called scaling up.

    Scaling up may or may not be beneficial for a given company. The long-run production process could have increasing, decreasing, or constant returns to scale. Like the short-run production function, the long-run production function has a U shape with a minimum value. In the long-run perspective, this minimum point is called the minimum efficient scale.

    Increasing returns to scale means that when the business scales up, the production becomes more efficient. That means the long-run average total costs are decreasing. Economists call this exhibiting economies of scale. In the U-shaped long-run production function, the downward sloping part exhibits economies of scale.

    On the other hand, decreasing returns to scale means that when the business scales up, the production becomes less efficient. That means the long-run average total costs are increasing. Economists call this exhibiting diseconomies of scale. In the U-shaped long-run production function, the upward sloping part exhibits diseconomies of scale.

    When the long-run average total cost decreases, this is referred to as economies of scale. When the long-run average total cost increases, this is referred to as diseconomies of scale.

    Being able to operate at minimum efficient scale can allow a firm to stay in business even if demand falls and the price is lower than expected. It means being the lowest-cost producer in the market. A market is productively efficient when the most efficient producers are the ones producing the good. In other words, operating at a minimum efficient scale helps improve market efficiency.

    Minimum efficient scale also helps keep the market competitive. In the long run, if there are sufficiently low barriers to entry, then only the firms that are able to operate at the most efficient scale will be able to survive. In that way, firms' decisions regarding long-term production costs help determine the market structure and the number of firms.

    Long-run Production Cost Examples

    Long-run production costs include those costs that are associated with long-run decisions. Examples include the decision to open a new firm branch, the decision to buy more farmland, or the decision to acquire a new business facility.

    We have finally reached the end of this article. Take your time to read it over once again if you have to! You should also read our article on the Production Function to perfect your understanding of everything production and cost!

    Long-run Production Costs - Key Takeaways

    • Long-run production costs refer to the costs over the length of time that it takes for all costs to be variable.
    • The difference between short-run and long-run production costs is that long-run production costs are all variable costs whereas short-run production costs include at least one fixed variable.
    • The long-run total cost function represents the lowest total cost of producing different levels of output when all inputs are variable.
    • The scale of production is the efficiency of producing outputs from the inputs. A long-run production process can have increasing, decreasing, or constant returns to scale.
    • Increasing returns to scale correspond to decreasing costs; decreasing returns to scale correspond to increasing costs
    • Average total cost is the total cost of production divided by the quantity of output. This is represented by the production cost curve.
    • At quantities where the average total cost is decreasing, there are economies of scale. At quantities where the average total cost is increasing, there are diseconomies of scale. Constant scale is when the average total cost is constant across different levels of output.
    Frequently Asked Questions about Long Run Production Cost

    What is long run production cost?

    Long-run production costs refer to the costs viewed over a length of time that is sufficiently long for all of the firm's costs to become variable. 

    How to derive long-run cost curves from production curves?

    The long-run cost curve shows the lowest total cost of producing different levels of output when all inputs are variable. Therefore, it is derived by considering not only the (short-term) production function and associated costs, but also any large investments that could be made in order to expand the capacity and produce on an even larger scale with a lower average total cost curve. The long-run cost curve is also derived by putting together all possible short-run production cost curves.

    How to graph the long-run production cost curve?

    The long-run production cost curve is graphed with the quantity of output on the horizontal axis and the cost of input on the vertical axis. It is the combination of the most efficient section of all possible short-run production cost curves, also called short-run average total cost curves.

    What is the formula for long-run production costs?

    Long run average total cost is calculated by dividing the long run total cost by the quantity of output. 

    What is an example of the long run in production costs?

    Long-run production costs include those costs that are associated with long-run decisions. Examples include the decision to open a new firm branch, the decision to buy more farmland, or the decision to acquire a new manufacturing plant. 

    Test your knowledge with multiple choice flashcards

    Long-run costs are all fixed.

    Fixed costs only count in the long run.

    The long-run average total cost curve is also the long-run production cost curve.

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