Describe with the help of a diagram interaction between the Short-run Average Total
Cost curves and the Long-run Average Total Cost curve given that the firm has five
plant sizes to consider viz. I, II, III, IV and V (in ascending order of their size),
wherein plant size III turn out to be optimal plant size in the long run.
Answers
Answer:
Long Run Average Cost Curve
In the short run, some inputs are fixed while the others are variable. On the other hand, in the long run, the firm can vary all of its inputs. Long run cost is the minimal cost of producing any given level of output when all individual factors are variable. The long run cost curve helps us understand the functional relationship between out and the long run cost of production. In this article, we will look at understanding the long run average cost curve.
Deriving a Long Run Average Cost Curve
To understand the derivation of a long run average cost curve, let’s consider three short run average cost curves (SACs) as shown in Fig. 1 below.
long run average cost curve
These SACs are also called plant curves. In the short run, a firm can operate on any SAC, given the size of the plant. For the sake of our understanding, let’s assume that there are only three plants that are technically possible. Therefore, the firm increases or decreases its outputs by changing the amount of the variable inputs.
However, in the long run, the firm examines each SAC to find the curve that allows it to produce a given level of output at the minimum cost. Hence, it chooses between SAC1, SAC2, and SAC3. From Fig. 1 above, you can see that to generate OB amount of output, the firm can choose between SAC1 and SAC2. Note that the firm will choose SAC1 due to the lower costs as compared to SAC2.
Further, you can also see that if the firm tries to produce an output OA, then it costs
AL per unit with SAC1
AH per unit with SAC2
Clearly, AH > AL. Therefore, the firm chooses SAC1. Similarly, if the firm tries to produce an output which is greater than OB but less than OD, then it chooses SAC2 since SAC1 involves higher costs. Also, for outputs larger than OD, the firm uses SAC3. Summing up, we can say that in the long run, the firm employs the plant yielding maximum output at minimum cost per unit.
Long Run Average Cost Curve
Imagine if a firm has a choice of varying a plant by infinitely small gradations leading to infinite average cost curves. In such a case, the smooth curve enveloping all these short-run average cost curves is a long run average cost curve.
long run average cost curve
As you can see in the figure above, the long run average cost curve is drawn tangential to all SACs. In other words, every point on the long run average cost curve is a tangent point on some SAC. Hence, whenever a firm desires to produce a certain output, it operates on the corresponding SAC.
From the Fig. 2 above, you can observe that to produce an output OM, the corresponding point on the long run average cost curve is ‘G’. Also, the corresponding SAC is SAC2.
Therefore, the firm operates on SAC2 at point G. Similarly, the firm chooses different SACs based on its output requirement. It is also possible for the firm to produce the output OM with SAC3.
However, this will lead to a higher cost of production as compared to SAC2. On the other hand, to produce a higher output OV, the firm requires SAC3. If the firm uses SAC2 for the same, then it results in higher unit similarity.
Note:
The long run average cost curve is not tangent to the minimum points of the SACs. For that matter, the long run average cost curve is tangential to
the falling portions of the SACs while it is declining and
the rising portions of the SACs while it is rising
Therefore, to produce an output less than OQ at the least cost, the firm operates the plant at less than its full capacity or less than its minimum cost of average production. To produce an output larger than OQ at the least cost, the firm operates the plant beyond its optimum capacity.
OQ is the optimum point because the output OQ is produced at the minimum point of the long run average cost curve and the corresponding SAC (SAC4). While other plants are used at less than or more than their full capacity, only SAC4 is operated at the minimum point.
I Hope This Will Help uh !
Answer:
Long Run Average Cost Curve
In the short run, some inputs are fixed while the others are variable. On the other hand, in the long run, the firm can vary all of its inputs. Long run cost is the minimal cost of producing any given level of output when all individual factors are variable. The long run cost curve helps us understand the functional relationship between out and the long run cost of production. In this article, we will look at understanding the long run average cost curve.
Deriving a Long Run Average Cost Curve
To understand the derivation of a long run average cost curve, let’s consider three short run average cost curves (SACs) as shown in Fig. 1 below.
long run average cost curve
These SACs are also called plant curves. In the short run, a firm can operate on any SAC, given the size of the plant. For the sake of our understanding, let’s assume that there are only three plants that are technically possible. Therefore, the firm increases or decreases its outputs by changing the amount of the variable inputs.
However, in the long run, the firm examines each SAC to find the curve that allows it to produce a given level of output at the minimum cost. Hence, it chooses between SAC1, SAC2, and SAC3. From Fig. 1 above, you can see that to generate OB amount of output, the firm can choose between SAC1 and SAC2. Note that the firm will choose SAC1 due to the lower costs as compared to SAC2.
Further, you can also see that if the firm tries to produce an output OA, then it costs
AL per unit with SAC1
AH per unit with SAC2
Clearly, AH > AL. Therefore, the firm chooses SAC1. Similarly, if the firm tries to produce an output which is greater than OB but less than OD, then it chooses SAC2 since SAC1 involves higher costs. Also, for outputs larger than OD, the firm uses SAC3. Summing up, we can say that in the long run, the firm employs the plant yielding maximum output at minimum cost per unit.
Long Run Average Cost Curve
Imagine if a firm has a choice of varying a plant by infinitely small gradations leading to infinite average cost curves. In such a case, the smooth curve enveloping all these short-run average cost curves is a long run average cost curve.
long run average cost curve
As you can see in the figure above, the long run average cost curve is drawn tangential to all SACs. In other words, every point on the long run average cost curve is a tangent point on some SAC. Hence, whenever a firm desires to produce a certain output, it operates on the corresponding SAC.
From the Fig. 2 above, you can observe that to produce an output OM, the corresponding point on the long run average cost curve is ‘G’. Also, the corresponding SAC is SAC2.
Therefore, the firm operates on SAC2 at point G. Similarly, the firm chooses different SACs based on its output requirement. It is also possible for the firm to produce the output OM with SAC3.
However, this will lead to a higher cost of production as compared to SAC2. On the other hand, to produce a higher output OV, the firm requires SAC3. If the firm uses SAC2 for the same, then it results in higher unit similarity.
Note:
The long run average cost curve is not tangent to the minimum points of the SACs. For that matter, the long run average cost curve is tangential to
the falling portions of the SACs while it is declining and
the rising portions of the SACs while it is rising
Therefore, to produce an output less than OQ at the least cost, the firm operates the plant at less than its full capacity or less than its minimum cost of average production. To produce an output larger than OQ at the least cost, the firm operates the plant beyond its optimum capacity.
OQ is the optimum point because the output OQ is produced at the minimum point of the long run average cost curve and the corresponding SAC (SAC4). While other plants are used at less than or more than their full capacity, only SAC4 is operated at the minimum point.