Costs in the Long Run

Long-run costs are completely variable. The firm will opt for the production technology that minimizes its costs.

In the long run, a firm can alter all of its inputs; none are fixed. This means that the firm can choose the levels of its inputs and the production technology it uses to minimize its costs of production. A firm's long-run total cost is the minimum per-unit cost of producing any level of output when all inputs are variable

As an example, consider the firm Enviro Pools, which installs swimming pools in a small Midwestern town. Enviro can dig the holes in which to install the pools in many ways: it can hire many laborers with shovels, it can use a backhoe and one driver, or something in between. Suppose Enviro can dig a small pool in one day. It has three options for digging the hole: 10 workers with 10 shovels, 2 workers with 2 mini-excavators, or 1 worker with a large backhoe.

Production Options for Enviro Pools
Production Technology Capital Input Labor Input
Option 1 10 shovels 10 workers
Option 2 2 mini-excavators 2 workers
Option 3 1 large backhoe 1 worker

The production options for Enviro pools depend on variations in capital input (different types of machinery) and labor input (workers).

Each of the three production technology options has different costs, which depend on the costs of the inputs used. In this case workers cost $150 per day no matter which tool they use, while the rent for the tools varies: shovels are$10 per day, each mini-excavator is $250 per day, and the backhoe is$600 per day.
Production Costs for Enviro Pools
Production Technology Capital Input Cost of Capital Labor Input Cost of Labor Total Cost
Option $1$ $10$ shovels
$= 10 \times \10 = \100$
$10$ workers
$= 10 \times \150 = \1\text{,}500$
$\1\text{,}600$
Option $2$ $2$ mini-excavators
$= 2 \times \250 = \500$
$2$ workers
$= 2 \times \150 = \300$
$\800$
Option $3$ $1$ large backhoe
$= 1 \times \600 = \600$
$1$ worker
$= 1 \times \150 = \150$
$\750$

The total cost of each production option is the cost of capital plus the cost of labor.

Which of the three options should the firm choose? It should opt to hire one worker and rent one backhoe to dig the pool because this minimizes the firm's cost.

However, the price of capital is not fixed. Suppose that the rents on capital all double. Now a shovel costs $20 per day, each mini-excavator is$500, and the backhoe is $1,200. This may change the firm's decision. Here, the firm's cost-minimizing option would be to rent two mini-excavators and hire two workers. Production Costs for Enviro Pools after Price of Capital Increases Production Technology Capital Input Cost of Capital Labor Input Cost of Labor Total Cost Option $1$ $10$ shovels $= 10 \times \20 = \200$ $10$ workers $= 10 \times \150 = \1\text{,}500$ $\1\text{,}700$ Option $2$ $2$ mini-excavators $= 2 \times \500 = \1\text{,}000$ $2$ workers $= 2 \times \150 = \300$ $\1\text{,}300$ Option $3$ $1$ large backhoe $= 1 \times \1\text{,}200 = \1\text{,}200$ $1$ worker $= 1 \times \150 = \150$ $\1\text{,}350$ The increase in capital input for each production option increases the total cost of each option. Prior to the increase, however, the total cost of Option 3 was slightly higher than the total cost of Option 2. Now the total cost of Option 2 is higher than that of Option 3. Option 1 has the highest total cost both before and after the increase in capital input. In the long run, the firm can adjust both its capital and its labor to minimize costs. However, if the firm signs a lease to rent the capital over a period of time (e.g., six months), it would not be able to change to a different production option until the lease expires. Now suppose that the price of labor rises to$250 per day. Option 2 is no longer the cost-minimizing option, but the firm will not be able to adjust its capital until it is no longer under the existing lease. The lesson is that once a firm chooses its level of capital, it is in the short run once again until that capital can be adjusted.

In the short run, the firm is limited to operating on a short-run average total cost curve associated with its level of fixed inputs. In the long run, the firm can choose any average total cost curve to minimize its costs for a certain output level. Thus, the firm's long-run average total cost (LATC), the minimum per-unit cost of producing any level of output when all inputs are variable, is made up of the cheapest per-unit costs associated with any short-run average cost curve's level of output.

Suppose that Toasty Knits, a sweater manufacturer operating in Tennessee, is considering constructing a new factory. For simplicity, assume that the factory only has a choice of five different-size factory buildings: extra-small, small, medium, large, and extra-large. Once Toasty Knits decides on a factory size and builds it, it has chosen a level of capital and will be in the short run until it can alter that decision. Each factory size has a set of short-run cost curves associated with it.
Toasty Knits has to decide which size factory is the best to build. The answer to this question lies in knowing how many sweaters it plans to produce. For example, if it produces a very low quantity of sweaters, the best choice would be the extra-small factory. The extra-small factory yields the minimum cost at a low quantity because at that level of output, the ATC curve for the extra-small shop is at its minimum point, and while other ATC curves may have lower costs per unit of output, they require increased output to achieve those costs. If the firm wants to produce more sweaters, it would minimize its costs by choosing perhaps the small, or medium factory. The large and extra-large factories would only be built if the firm expected to produce a very large quantity of sweaters. The firm's long-run average total cost is the minimum cost of producing any level of output when all inputs are variable. Although this example limited the choice of factory size to five, in the real world the options for factory size are infinite. (For example, the size could probably be adjusted to the square inch.) Imagine that there are an infinite number of short-run ATC curves lined up as output quantity increases. Connecting all the points at which possible short-run ATC curves intersect the long-run ATC curve results in a smoothly shaped long-run ATC curve. This is known as the “envelope relationship,” and it demonstrates that the short-run ATC is always greater than or equal to the long-run ATC.
The long-run average total cost curve shows the firm's minimum average total cost of producing any level of output. But what happens as the firm's scale of operations increases? In other words, what happens as the firm's level of output increasingly rises?

Consider the long-run average total cost curve. As the firm goes from being a very small firm to being a medium firm, the firm's long-run average total cost falls. This is known as economies of scale, the situation that occurs when a firm's long-run average total costs decrease as production levels increase, which lowers the break-even price that the firm needs to charge; proportionate savings in cost are gained by increasing production size. As the firm initially increases its output level, it often has the opportunity to pay a lower per-unit price for the inputs it uses. Workers are more likely to be able to specialize, and capital investments are amortized over increased output resulting in lower per-unit costs as well.

However, the gains from increasing the firm's scale of production begin to be offset by the difficulty of managing larger-scale enterprises. After initially declining, , the firm's long-run average total cost remains constant as output quantity increases because the benefits of getting larger are completely counterweighed by the difficulties of managing an increasingly larger number of workers. This is known as constant returns to scale, which occurs when long-run average total cost remains the same as output increases.
Eventually, the firm gets so large that the problems associated with supervising and coordinating the actions of such a large number of employees become overwhelming. This leads to a rising long-run average total cost curve and is called diseconomies of scale, which occurs when long-run average total cost rises as output rises. But this situation is unlikely to last for long; an overly large firm cannot compete with smaller firms because its per-unit costs are higher. To remain competitive, this firm will likely adjust its size in order to reduce its long-run average total cost.