Economics: Determining a Firm's Return to Scale

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In the last lecture, we discussed the first problem that the firm faces in the long run. That's the problem of choosing the cost minimizing technique, the way of combining capital and labor so as to minimize the cost of producing a given quantity of output. In this lecture, we're going to consider the second problem that the firm faces in the long run. And that is the choice of the optimal scale, the right size of operation for maximizing your profits.
In the short run, the firm can't help but change its scale and change its technique at the same time. If the firm wants to produce more output in the short run, they've got a fixed amount of capital and they can only increase output by adding more labor. That means, that in order to increase the size of their operation, or their output of television sets, they've got to add more workers, which increases the intensity of labor. That is, they're using more labor per unit of capital. So, they're also choosing scale, the size of their operation at the same time as they're choosing the technique of production. Three workers and one tool may be the only option that's available to the firm for increasing their output in the short run. The firm is simultaneously choosing the technique of production and the size of their operation.
In the long run, the firm gets to choose these two things separately, which is one of the reasons why long run costs of production are always lower than the short run costs. The firm has more flexibility. If the firm wants to increase the size of its operation, it doesn't necessarily have to use more labor per unit of capital. It can also increase the amount of capital that each worker has, thereby keeping the labor capital ratio constant even as its firm grows bigger. That is, it keeps the cost minimizing technique that it prefers while allowing the scale of operation to grow larger.
The definition of the scale of operation is as follows. Scale is said to increase if the firm has a proportional increase in all of its inputs. So, if we start with one worker and one unit of capital, the scale of the firm is said to increase if we add a second worker with a tool of his own, and a third worker with a tool of her own. To have an increase in the scale, it is required that all inputs increase by a particular proportion. That they all increase by the same proportion. If we just increase labor and hold capital constant, that is not a change in scale. If we just increase capital and hold labor constant, that is not a change in scale. To change the scale of operation, we must have a proportional increase in all of the factors of production.
Now, here's the question that we want to answer. How does the firm's productivity change as we change the scale of operation? In order to answer that question, we're going to need to define a concept very specifically and that's the concept of economies of scale. What happens to the firm's productivity when the scale of its operation changes? Suppose we go from one worker with one unit of capital to two workers and two units of capital. What happens to output? Well, you can imagine that one of three things would happen. The first is probably the most reasonable assumption. And that is that if both of our inputs double, our output would double as well.
This is the case when the firm is said to have constant returns to scale. Constant returns to scale is defined as a technology where increasing all inputs by a given proportion increases output by the same proportion. The reason this seems like a reasonable assumption is the possibility of replication. If we've got a guy over here making television sets by using a particular tool and he can make ten television sets a day, if we have another worker who has the same toolkit, we would imagine that that worker could also make ten television sets a day. Replicating this operation, would allow us to double the amount of output we get in a single day from our factory
If we add a third worker, also with a tool, we should be able to replicate the operation again. Tripling inputs, we would expect to be able to triple output. That is the idea of constant returns to scale. And it seems like a reasonable assumption because of the possibility of replication, having someone else do what another worker with his tools is already doing successfully. Now, there are two other possibilities. The first is the possibility that things are actually better than constant returns to scale. That adding a worker with a tool, adding a second worker with a second tool allows us to more than double our output.
That is, if we have one worker with one tool, producing ten television sets, two workers with two tools might actually be able to produce 30 television sets in a day. That would be the case if somehow there's some kind of teamwork and specialization between these workers, if working together, they can operate in a way that's more productive then if both of them worked separately. Having the workers work together and cooperate, using their labor and tools together, may actually allow them to be more productive than two workers simply replicating what each other are doing. This is the case with increasing returns to scale.
The final possibility is the possibility of decreasing returns to scale. It may be that by doubling all of our inputs, we actually increase output by a smaller proportion, maybe only ten percent or 20 percent. Now, you might ask yourself, "Why would we ever have decreasing returns to scale?" What could ever lead to a situation where two workers with two tools would do less productive work than they could do if they were working separately? And it has to do with the problem of a growing organization. As an organization gets larger and larger, you have more and more activity under a single manager and that manager is responsible for making decisions about how this process in organized, how the workers are paid, how they are scheduled, how their activities are coordinated.
When you've got a manager who's over this whole operation, it may be that the individual workers say to themselves, "Hey, rather than trying to make my money by working harder, producing television sets, I'll go and lobby the manager for a raise. I'll go and ask for favors. I'll ask for a better schedule. I'll try to use my influence to improve my position in this organization. This is a form of rent seeking and it goes under the name of influence activities. Influence activities are efforts on the part of the workers to influence the organization to their advantage and the cost of these influence activities is this. When workers believe that they can get more benefits by lobbying the boss, they'll spend less time actually producing televisions for the firm.
Because of that, as the organization grows larger and the manager has more and more power, it is a greater and greater temptation for the individual workers to engage in influence activities, rather than to produce television sets. And the cost of production then goes up as the firm has to employee monitors to make sure that people stay on the job an don't spend their time taking too many breaks, going and lobbying the boss and such things like that. This is the idea behind decreasing returns to scale. As the firm gets very large, the problem becomes managing workers and preventing them from engaging in influence activities.
So, this is the idea of scale economies. The firm wants to consider, what is the potential for teamwork and specialization? What is our scope for enjoying increasing returns to scale? Because as long as we're enjoying increasing returns to scale, it will probably pay for us to expand our operation. Also, we want to know when are we likely to have constant returns to scale. Because any time a firm has constant returns to scale, replication is a possibility. And finally, there's the problem of decreasing returns to scale. If the firm grows too large, its workers are tempted to engage in influence activities, thus raising the cost of production. In the next lecture, we'll see how economies of scale translate into the costs of the firm in the long run.
Production and Costs
Long Run Production and Costs
Determining a Firm's Return to Scale Page [2 of 2]