Indicate the correct code from the following types of the long run average cost curves on which the minimum average cost of production in long run can be determined: (i) Long run average cost curve under normal production function (ii) Long run average cost curve under linearly homogeneous production function (iii) Planning curve (iv) Envelope curve Choose the correct answer from the code given below :
Understanding Long Run Average Cost Curves and Minimum Cost
The long run is a period where a firm can change all its inputs, including the size of its plant. The long run average cost (LRAC) curve shows the minimum average cost of production for different levels of output when the firm has had sufficient time to adjust all factors of production.
The minimum point on the LRAC curve represents the optimal scale of production, where the firm can produce output at the lowest possible average cost in the long run. The question asks which types of LRAC curves allow us to determine this minimum average cost.
Analyzing Each Type of Curve
- Long run average cost curve under normal production function: A "normal" production function typically leads to a U-shaped LRAC curve. This U-shape reflects economies of scale (falling average costs as output increases) followed by diseconomies of scale (rising average costs). The bottom of this U-shaped curve is the point where the average cost is at its minimum in the long run. Therefore, this type of curve clearly allows the determination of the minimum average cost.
- Long run average cost curve under linearly homogeneous production function: A linearly homogeneous production function exhibits constant returns to scale. This means that if all inputs are increased by a certain percentage, output increases by the same percentage. Under constant returns to scale, the long-run average cost is constant regardless of the output level. The LRAC curve is a horizontal line. While the average cost is at its lowest possible level (because it's constant), there isn't a unique "minimum point" in the sense of the bottom of a curve like the U-shape. The average cost is the same at all output levels. However, the question asks where the minimum average cost *can be determined*. In this case, the average cost is always at its minimum possible long-run level, but it's constant, not a specific lowest point reached at a particular output before costs rise again. The standard interpretation of finding the minimum average cost usually refers to the lowest point on a curve that changes slope. Thus, this type is less likely to be considered as clearly showing a distinct minimum point compared to a U-shaped curve.
- Planning curve: The LRAC curve is often called the planning curve. This is because it helps firms plan their optimal plant size for producing various output levels. For any given output level, the planning curve shows the minimum average cost achievable by operating the most efficient plant size for that output. The lowest point on the entire planning curve (LRAC) represents the overall minimum long-run average cost attainable at the optimal plant size. So, the planning curve definitely allows the determination of the minimum average cost.
- Envelope curve: The LRAC curve is the envelope of the short-run average cost (SRAC) curves for different plant sizes. It touches each SRAC curve at one point (or is tangent to it). For any given output, the LRAC shows the lowest average cost by selecting the appropriate short-run plant scale. The minimum point of the LRAC curve is where it is tangent to the SRAC curve that corresponds to the optimal plant size, and also where the SRAC curve itself is at its minimum. This envelope property inherently defines the lowest possible average cost in the long run across all possible plant sizes. Thus, the envelope curve allows the determination of the minimum average cost.
Based on the analysis, the long run average cost curve under a normal production function (U-shaped), the planning curve (synonym for LRAC), and the envelope curve (how LRAC is derived from SRACs) all allow for the determination of the minimum average cost of production in the long run. The long run average cost curve under a linearly homogeneous production function shows a constant average cost, which is technically the minimum, but lacks the typical 'minimum point' feature of the other curves.
Conclusion
The types of long run average cost curves on which the minimum average cost of production in long run can be determined are typically those that are U-shaped or are synonymous with the LRAC curve itself, which has a defined minimum point under normal assumptions. These are the long run average cost curve under normal production function, the planning curve, and the envelope curve.
Therefore, items (i), (iii), and (iv) are the correct ones.
| Curve Type | Description | Allows Determination of Minimum LRAC? |
|---|---|---|
| (i) Normal Production Function LRAC | Typically U-shaped due to economies/diseconomies of scale. | Yes (bottom of the U-shape). |
| (ii) Linearly Homogeneous Production Function LRAC | Horizontal (constant returns to scale). | Less likely (constant cost, no unique lowest point). |
| (iii) Planning Curve | Synonym for LRAC; used for optimal plant size planning. | Yes (lowest point on the curve). |
| (iv) Envelope Curve | Derived from SRAC curves; shows lowest cost for each output. | Yes (lowest point on the curve). |
Revision Table: Long Run Costs
| Concept | Definition | Significance |
|---|---|---|
| Long Run | Period where all inputs, including plant size, are variable. | Allows firms to adjust scale of operations. |
| Long Run Total Cost (LRTC) | Minimum total cost of producing a given output when all inputs are variable. | Foundation for LRAC. |
| Long Run Average Cost (LRAC) | LRTC divided by output; Minimum cost per unit in the long run. | Indicates optimal scale of production. |
| Economies of Scale | LRAC falls as output increases. | Firm becomes more efficient with larger scale. |
| Diseconomies of Scale | LRAC rises as output increases. | Firm becomes less efficient with larger scale. |
| Optimal Scale | Output level where LRAC is at its minimum. | Most efficient long-run production level. |
Additional Information on Production Functions and Costs
A production function describes the technical relationship between inputs (like labor and capital) and the maximum output a firm can produce. Different types of production functions can lead to different shapes of cost curves.
Returns to Scale: This concept relates to how output changes when all inputs are increased proportionally in the long run.
- Increasing Returns to Scale: Output increases more than proportionally to the increase in inputs. This leads to falling long-run average costs (economies of scale).
- Constant Returns to Scale: Output increases proportionally to the increase in inputs. This leads to constant long-run average costs. A linearly homogeneous production function typically exhibits constant returns to scale.
- Decreasing Returns to Scale: Output increases less than proportionally to the increase in inputs. This leads to rising long-run average costs (diseconomies of scale).
The U-shape of the LRAC curve under a normal production function arises from a phase of increasing returns to scale (leading to economies of scale) followed by a phase of decreasing returns to scale (leading to diseconomies of scale).
Important Questions from Production Function
What is constant along an isoquant?
During the first stage of a total product curve, the total product is ______
Match List I with List II
LIST I
(Production Cost)
LIST II
(Underlying Meaning)
A.
Implicit Costs
I.
Change in the total cost per unit change in output.
B.
Marginal cost
II
Total increase in costs resulting from the implementation of a particular managerial decision.
C.
Incremental Cost
III.
Inputed value of inputs owned and used by the firm.
D.
Sunk Cost
IV.
The costs that are not affected by managerial decision.
Choose the correct answer from the options given below:
For the following two statements of Assertion (A) and Reasoning (R) suggest the correct code:
Assertion (A): Low initial price regarded as the principal means for entering into mass market for some new products.
Reasoning (R): Firms generally enter into production of new products with excess capacity of the plant initially.
Code:
In which one of the following concepts, a buyer is passively involved in an exchange transaction, and he accepts whatever is offered to him by a marketer?
