Production and Costs Long Run Production and Costs Understanding Short Run and Long Run Average Cost Curves Page 1 of 3

We’re back with cost curves and we’re going to take it slow here to try to clear up some confusion that I know I suffered in my economics class that maybe we can spare you from. And this is the confusing question of the relationship between the short run and the long run cost curves. All right. Now, let’s think for a moment, before we draw any curves, about what we’re talking about. The long run, is the period over which all inputs are variable. When I draw a long run cost curve, I’m assuming that the firm can change anything that it wants to, labor, capital, the combination of labor and capital, the scale of output, any of that stuff can be change when we draw the long run average cost curve. The short run cost curves, on the other hand, and you’ll recall them from our earlier lessons, these short run cost curves assume that some inputs are fixed. Now, how are these cost curves with fixed inputs related to this cost curve that has no fixed inputs, this cost curve where anything goes? The relationship works like this. Let’s suppose we have a firm that has a long run average cost curve. And let’s suppose the long run average cost curve for this firm has a U shape. What this U shape means is this. It means that a first the firm experiences decreasing returns to scale, or increasing returns to scale that cause the average costs to decrease. Over this region right here, the firm has increasing returns to scale and the average cost of production is falling. At the bottom of this curve, it’s temporarily flat, maybe just for an instance, and that’s the point of constant returns to scale. Finally, if you go beyond that point, you have increasing average costs, which is a signal of decreasing returns to scale. So here the firm has increasing, then constant, then decreasing returns to scale. So we have decreasing average cost, a moment of constant average cost and then increasing average cost. As we move along this curve, remember the firm can alter anything it wants to. It can change the way in which it combines the inputs. It can change the scale of operation. Anything goes, there are no fixed inputs. Suppose, however, we pick a point on this curve and the point on this curve that we pick will involve a certain combination of labor and capital to produce a given amount of output and that combination of labor and capital will have a particular cost and produce a certain amount of output. Suppose, now we freeze capital. We freeze capital at the amount that the firm is using at this point on its long run curve, a particular square footage of factory, a particular number of tools and conveyor belts. Now if we freeze capital now and allow this firm to alter its output by changing only labor, we’re back in the short run. We’re back in the short run, where the firm can only change its behavior by changing its variable input labor. All of its costs are going to be higher in that case. Do you know why? Why are all of the costs in the long run going to be lower than the costs in the short run? Why in the short run does it always cost a firm more to change its output than it costs the firm to change its output in the long run? The answer is, in the long run the firm has more options. The firm can combine labor and capital so as to minimize costs. In the short run, the firm can’t change its capital. It’s stuck with a given amount of capital. It has to use it, therefore its options are reduced and its costs are going to be higher necessarily. If there were better options with lower costs, the firm might not be able to get to it in the short run because of its fixed inputs. In the long run, of course, the firm can get there because none of the inputs are fixed. Everything is variable. So, if we want to look at the short run costs they’re going to lie above the long run costs. The short run costs of production are going to lie above the long run costs at every point except the one point that touches the curve. At this point, where the curve touches the amount of capital that’s being used is cost minimizing for that level of output. There’s one point, that the short run average cost curve has in common with the long run average cost curve. That’s the point at which the firm is operating with the cost minimizing combination of labor and capital for that particular amount of output. If you want to change output in the short run, you can hire more labor, but you can’t get down to the blue curve in the short run, because you have fixed inputs. Therefore, in the short run you’re stuck with higher costs. Well, that would be the situation if we froze capital at the amount associated with this point. Suppose we freeze capital at the amount associated with the point at the bottom of the curve. In this case, you’re going to get short run cost curves that look like this. If you’re at the bottom of the curve, using the cost minimizing combination of labor and capital, you will be at the point where the short run curves intersects the long run curve. However, if you freeze capital at that particular quantity, and want to change your output in the short run, all you can vary is your labor. And since you have less flexibility, your costs are necessarily going to be higher. That’s why the

Production and Costs Long Run Production and Costs Understanding Short Run and Long Run Average Cost Curves Page 2 of 3

short run and average cost curve lies everywhere above the long run average cost curve. I’ve labeled this the average variable cost. It’s not average variable costs. In fact, it’s average total cost. It’s the cost of all labor and capital combined. So make sure you labeled your curves correctly. I made a mistake and called it average variable, which would only refer to the labor costs. In fact here, we’re referring to the combined costs of labor and capital. That’s why I need to call that the average total cost. I hope I’m making my point clear. The point is, that in the short run, your average costs will always be higher than it will be in the long run, to produce any given quantity of output. That’s because in the long run you have more flexibility. You can change the combination of labor and capital to get to the cost minimizing technique. Now, one diagram that you’ll see in your Economics textbook, is one that has the long run average cost curve with a lot of short run cost curves all along it. So, what you get is, this, and that, and finally, if we go over here into a region of decreasing returns to scale, and increasing average cost, you get that. This is a picture that shows the relationship between the long run average cost curve, the blue curve, and all of the short run cost curves that are associated with it. The blue curve becomes the envelope. It becomes the envelope that contains all of the green curves. All of the green curves fit on top of it, because the average costs, and here again I’ve got to make sure I’m saying average total cost. The average total cost will always be greater in the short run than it is in the long run and that’s quite simply because in the long run, you have more flexibility. By changing labor and capital together, by finding the cost minimizing techniques, you can always lower your costs in the long run. Unless you happen to be right at this point of tangency, right at the point where the firm has just the right amount of capital to be cost minimizing even in the short run. If you start at a point on this curve and then change only labor, costs will be higher. But if you happen to be at the point that’s tangent to the blue curve that means that you’ve got just the right combination of labor and capital in the short run to be cost minimizing. In the long run, you wouldn’t want to change anything to produce that particular quantity of output. One more thing to notice that’s kind of a technical thing that students sometimes have trouble with, this material. And that is, when you’re drawing the short run cost curves, in relation to the long run cost curve, notice that it’s only at the very bottom that the minimum average total cost in the short run is the same as the point of tangency. It’s only at the very bottom that that happens. Otherwise, if you looked up here, at a point where the long run average cost curve is downward sloping, the bottom of the green curve is not going to be where it touches the blue curve. That’s because the tangency is at a point where the blue curve is downward sloping. The point where the two curves coincide is going to be at a point where the green curve and the blue curve are touching and they share a downward slope. Over here, they touch and they’re sharing an upward slope. So, when you draw these curves, you want to be careful. So, what’s the intuition of that? What’s the intuition? Why is the point where they touch not always the minimum point? And I guess the answer has something to do with the way fixed costs work. You can always decrease your costs a little further by increasing labor productivity in the short run, or over here, if you’re at a point where labor productivity is now, you’ve got diminishing returns to scale. You’ve want to back off a little bit to get to the point of minimum. But, I’m not sure that that’s—it’s a bit of a subtle point and it’s not something that you probably need to fret too much over right now. The point that I’m trying to make is, the key to understanding this diagram is the relationship between costs in the long run and costs in the short run. Costs in the short run are always higher, because in the short run, you have fixed inputs and you can’t necessarily get to the cost minimizing technique. Costs in the long run are always lower, because you have more options and can therefore more likely get to the cost minimizing technique. We’ve looked at three extreme cases of the long run average cost curve. In one case, we had increasing returns to scale for every level of output. In another case, we had constant returns to scale for every level of output. And finally, in the third case, we had decreasing returns to scale. Now, it will seem apparent that not every technology is going to have constant, increasing or decreasing returns throughout. In fact, it’s probably unreasonable to expect that each technology would not have some range of each of these. That is, for most technologies, whenever a firm is small and growing, it will be experiencing some increasing returns to scale, as workers and tools are used with teamwork and specialization.

Production and Costs Long Run Production and Costs Understanding Short Run and Long Run Average Cost Curves Page 3 of 3

At some point, constant returns to scale will occur and as the operation grows still larger and problems with coordinating and management begin to arise, then decreasing returns to scale will then kick in. If this is the case, and this is what economists usually believe is true with firms, that there is increasing returns to scale at the beginning then constant returns to scale at some point and finally decreasing returns to scale as the firm grows larger. Then the long run average cost curve will have the U shape that I’m showing right here. The U shaped long run average cost curve represents a technology that has increasing returns to scale then constant returns to scale and then decreasing returns to scale. As a quick review, let’s see how the scale economies relate to the shape of the average cost curve. Whenever there are increasing returns to scale, due to teamwork and specialization, the average cost of production is diminishing. If the firm is producing only a few units, there’s not a lot of scope for teamwork and specialization. But as output expands, workers and tools can be used in conjunction with each other in a kind of complimentary way, with teamwork and specialization, and as productivity increases, the cost of production is falling. Finally, at some point, constant returns to scale will kick in. That is the scope for teamwork and specialization has played out, it’s been exhausted. And now, here, at the bottom of the average cost curve, where it’s flat for just an instant, the firm has constant returns to scale. That is, expansion leaves the average cost constant. However, if the firm continues to grow, that is, if output continues to expand, the capital and labor needed to expand output is now making the organization so large that the firm begins to have some of those management problems we talked about earlier, influence activities and rent seeking within the firm that take away from productivity. Beyond this point, we find then that the average cost to production begins to rise again because proportional expansion in all inputs results in a less than proportional expansion in output. Which means the average cost to production is rising. So, the region of increasing returns to scale, where the average cost is falling, constant returns to scale at the bottom, where the curve is flat, if only for an instant, and then decreasing returns to scale as the average cost begins to rise again. Let me introduce one more concept that will become important, later when we talk about the long run and how firms enter and leave the market. And that is this point right here, at the bottom of the long run average cost curve, this point where constant returns to scale exists for jus a moment, where the curve is flat. If we put a straight line at the bottom of this curve it will be tangent at the very bottom, that is, at the point at the bottom of the long run average cost curve. We call this point, where long run average cost is at its minimum, we call this the point of efficient scale. This is the size of the firm’s operation. This is the quantity of output or the number of television sets that the firm produces when it is in some sense the right size. The right size means, the point at which the cost of producing a television set is at its minimum, the average cost is at its minimum. And in the long run, as we’ll see a little later, the firm is going to wind up at this point. So, the point where the long run average cost is at its minimum, this point where the long run average cost curve is flat, right at the bottom, that moment of constant returns to scale, that has a special name in Economics. We call it the point of efficient scale and we’ll be returning to that point in just a little bit. Next, we’re going to look at how the long run and the short run cost curves are related.