Let us note that the firm may expand in two ways. But in state 2, we now have a pressure low and volume is high. Principle of Least Cost combination: A given level of output can be produced using many different combinations of two variable inputs. Let me write this down. In other words, the expansion path shows how factor proportions change when output changes, relative factor prices remaining constant.
State number 1 was right there. The only relevant portion of the isoquant is the one that is convex to the origin, part of the curve which is not convex to the origin implies negative marginal product for factors of production. The Laws Of Returns to Scale Introduction Long run is a period during which all factors of production can vary. The term returns to scale arises in the context of a firm's Production Function. In this case the distance between every successive isoquants becomes smaller and smaller i. But this is a neat result.
Isoquants nearer to origin represent less quantity of output and vis-a-visa. Business may become unwieldy and produce problems of supervision and coordination. This is found whore Iso-quant and Iso-cost lines tangent to each other. In this case, production function is homogenous of degree less than one. And we're doing it at very small increments.
Transport bottlenecks and Marketing difficulties. This is after removing each of the pebbles, so that our pressure and volume macro states are always well defined. It describes the firm's alternative methods for producing a given level of output. So before I did anything, when my canister was just here, I had all the pebbles on it. Work can be divided into small tasks and workers can be concentrated to narrower range of processes. As the industry continues to expand the demand for skilled labour, land, capital, etc. Now we said that the work done at any given point by the system is the pressure times the change in volume.
I'm going to do two graphs here. We wouldn't be doing a quasi-static process, or a reversible process, which isn't always the same thing. Decreasing Returns to Scale: Figure 9 shows the case of decreasing returns where to get equal increases in output, larger proportionate increases in both labour and capital are required. As in all the previous examples, the output expansion path is thus a ray from the origin. Well now our pressure is a little bit lower.
Use of better and sophisticated technology f. So let's say I was at this state. The firm expands its output along this line keeping factor prices as constant. Constant Returns to Scale: Figure 10 shows the case of constant returns to scale. In this case the distance between every successive isoquant remains equal i. And then, let's say I just start removing pebbles.
And what's important is the direction that it's going. External economies of scale 2. So if I said, I did all of this stuff and came back here, what is my change in internal energy? Large management creates difficulties of control and rigidities. So the area under this curve is the integral of the pressure as a function of volume, that's the height at any point, times our very small change in volume. It must be stressed that the optimal expansion path is defined for a given input price ratio. Now, let me ask you one more thing.
Easy enough, it's the area under this curve. So pressure was high and volume low. Remember, our state variable pressure volume, we did stuff to it then we went back to that state. Cost levels are made higher and higher and then efforts are made to maximise the level of output subject to the cost constraint. Improvement in large scale operation d. An isoquant map can also indicate decreasing or increasing based on increasing or decreasing distances between the isoquant pairs of fixed output increment, as output increases.
And later we can use this notion to come up with some other ideas behind our state variables I'll make one little aside here. And maybe I'll do that in a different color, so green for work done to the system. It shows that if inputs are doubled then the output also gets doubled. Not only this, a firm also enjoys increasing returns to scale due to external economies. If the distance between those isoquants increases as output increases, the firm's production function is exhibiting decreasing returns to scale; doubling both inputs will result in placement on an isoquant with less than double the output of the previous isoquant. A Isoquant Iso product curve: Iso means equal and quant means quantity. We started off at this volume, and let's say when we removed one pebble we got to this volume.