Q22 — Relation between AC and MC & U-shape of LAC

Introduction

In the theory of the firm, the concepts of Average Cost (AC) and Marginal Cost (MC) occupy a central position in explaining a firm’s output and pricing decisions. The behaviour of AC and MC in the short run and the shape of the Long-run Average Cost (LAC) curve in the long run together form the backbone of the traditional cost theory as prescribed in Microeconomics by T.R. Jain & V.K. Ohri for B.Com Semester I (Panjab University).

A complete answer to this question requires: (i) precise definitions of AC and MC, (ii) a clear explanation of the mathematical and graphical relation between AC and MC, and (iii) an analytical discussion of why the LAC curve is usually U-shaped, supported by appropriate diagrams.

I. Meaning of Average Cost (AC) and Marginal Cost (MC)

1. Average Cost (AC) / Average Total Cost (ATC)

Average Cost (also called Average Total Cost) is the cost per unit of output. It is obtained by dividing total cost by the quantity of output produced:

AC = TC / Q

Since total cost (TC) is the sum of Total Fixed Cost (TFC) and Total Variable Cost (TVC), we have:

AC = (TFC + TVC) / Q = AFC + AVC

where AFC is average fixed cost and AVC is average variable cost. In the traditional theory, the AC curve is U-shaped due to the combined effect of falling AFC and the U-shaped AVC.

2. Marginal Cost (MC)

Marginal Cost is the addition to total cost when one extra unit of output is produced:

MC = ΔTC / ΔQ

Since TFC does not change with output, MC is also equal to the change in total variable cost:

MC = ΔTVC / ΔQ

In the traditional analysis, the MC curve is also U-shaped — it falls at first due to increasing marginal returns and then rises due to diminishing marginal returns (Law of Variable Proportions).

II. Relation between AC and MC

The relation between AC and MC is both mathematical and graphical. It can be explained with the help of a numerical schedule, a diagram, and intuitive reasoning.

1. Numerical Illustration

Consider the following hypothetical cost schedule for a firm in the short run:

Output (Q)	Total Cost (TC)	Average Cost (AC = TC/Q)	Marginal Cost (MC = ΔTC/ΔQ)	Behaviour of AC
1	60	60.0	–	–
2	110	55.0	50	AC falling (MC < AC)
3	150	50.0	40	AC falling (MC < AC)
4	190	47.5	40	AC still falling (MC < AC)
5	240	48.0	50	AC rising (MC > AC)
6	300	50.0	60	AC rising (MC > AC)

From the schedule we observe:

When MC is below AC (e.g. at Q = 2, 3, 4), AC falls.
When MC is above AC (e.g. at Q = 5, 6), AC rises.
When MC equals AC, AC is at its minimum (this would occur at some Q between 4 and 5 in the example).

Thus, the fundamental relation is:
(i) When MC < AC, AC falls.
(ii) When MC > AC, AC rises.
(iii) When MC = AC, AC is minimum.

2. Graphical Relation between AC and MC

This relation can be shown through the traditional U-shaped AC and MC curves:

Fig. 1 — Relation between AC and MC: MC cuts AC at the minimum point of AC. When MC lies below AC, AC falls; when MC lies above AC, AC rises.

3. Intuitive Explanation of the AC–MC Relation

The relation between AC and MC is analogous to the relation between an average and a marginal (or incremental) magnitude in arithmetic:

If the marks obtained in the last paper (marginal marks) are more than the average marks so far, the new average marks will rise.
If the marks obtained in the last paper are less than the average marks so far, the new average will fall.
If the marks obtained in the last paper are equal to the existing average, the average will remain unchanged and will be at its turning point.

Exactly in the same way, in cost analysis:

When the cost of producing an extra unit (MC) is less than the average cost, it pulls the average cost downwards.
When MC is greater than AC, it pushes the average cost upwards.
When MC equals AC, AC is at its minimum; before this point MC lies below AC, and beyond this point MC lies above AC.

Therefore, the MC curve necessarily cuts the AC curve at its minimum point. This is a standard, universal relationship and is frequently used in equilibrium analysis of the firm under different market forms.

III. Why is the Long-run Average Cost (LAC) Curve U-shaped?

In the long run, all factors of production are variable and the firm can adjust its plant size. The Long-run Average Cost (LAC) curve shows the minimum average cost of producing each level of output when the firm is free to choose the most suitable scale of plant.

1. LAC as an Envelope of Short-run AC Curves

The traditional theory (followed in T.R. Jain & V.K. Ohri) assumes that the firm has a set of alternative plant sizes, each with its own Short-run Average Cost (SAC) curve, all U-shaped. For every level of output, the firm chooses the plant that gives the lowest possible AC. The locus of these minimum points forms the LAC curve.

Thus:

LAC is the “envelope” curve tangential to each SAC curve.
For a low output, a small plant (SAC₁) is optimal; for a medium output, a medium plant (SAC₂) is best; for a large output, a large plant (SAC₃) is optimal.

Fig. 2 — LAC as Envelope of SAC Curves: For each output level, LAC shows the minimum possible average cost when the firm can choose the most suitable plant size.

2. U-shape of LAC: Role of Economies and Diseconomies of Scale

The U-shape of the LAC curve is explained by the interaction of economies of scale and diseconomies of scale as the firm expands its scale of operations.

A. Falling Portion of LAC: Economies of Scale

In the initial range of output, as the firm increases its scale, it enjoys various internal and external economies of scale:

Technical economies: use of larger and more efficient machinery, better utilisation of fixed plant.
Managerial economies: specialisation of managerial functions, improved supervision.
Marketing economies: bulk buying and selling, spreading advertising cost over more units.
Financial economies: easier and cheaper access to finance.
Risk-bearing economies: diversification of products and markets.

Due to these economies, long-run average cost falls as output increases. This gives the downward sloping part of the LAC curve.

B. Flat Portion of LAC: Constant Returns to Scale

Over some intermediate range of output, economies of scale may be exhausted, but diseconomies have not yet started. In this range:

Increasing scale neither reduces nor increases average cost significantly.
The firm experiences constant returns to scale.
LAC is approximately flat or gently sloping.

This region is often called the range of constant cost in the long run.

C. Rising Portion of LAC: Diseconomies of Scale

Beyond a certain size, further expansion of the firm gives rise to diseconomies of scale:

Managerial difficulties: problems of coordination and control in a very large firm.
Communication delays: complex hierarchical structure slows down decisions.
Labour problems: reduced personal contact, low morale, possible industrial disputes.
Over-burdened infrastructure: congestion, higher transport and storage costs.

When diseconomies of scale outweigh remaining economies, LAC begins to rise. This gives the upward sloping part of the U-shaped LAC curve.

Fig. 3 — U-shaped LAC Curve: Falling part due to economies of scale; minimum point at optimum scale Q*; rising part due to diseconomies of scale.

Conclusion on LAC:
LAC is U-shaped because at low levels of output, economies of scale dominate; at intermediate levels, economies and diseconomies balance; and at high levels of output, diseconomies dominate. The lowest point of LAC corresponds to the optimum size of the firm in the long run.

IV. Combined Summary: AC–MC Relation and U-shape of LAC

In the short run, AC is the cost per unit and MC is the cost of an additional unit. Both curves are U-shaped due to the law of variable proportions.
The relation between AC and MC is governed by a general average–marginal principle: when MC < AC, AC falls; when MC > AC, AC rises; and when MC = AC, AC is minimum. Hence, the MC curve must cut the AC curve at its minimum point.
In the long run, the LAC curve is the envelope of a family of short-run AC curves, and its U-shape reflects economies and diseconomies of scale. The falling part shows increasing returns to scale; the flat portion shows constant returns to scale; the rising part shows decreasing returns to scale.

Exam Tip (for 15 Marks): To secure full marks in Panjab University B.Com (Sem I), structure your answer as follows: (i) define AC and MC with formulae; (ii) give a small numerical table showing the AC–MC relation; (iii) draw a neat diagram showing AC and MC with MC cutting AC at its minimum point; (iv) define LAC and explain it as an envelope of SAC curves with a second diagram; (v) analytically explain the U-shape of LAC using economies and diseconomies of scale; and (vi) conclude with a short summary. This systematic pattern closely matches the expectations of university examiners.

Conclusion

To conclude, the relation between AC and MC is a fundamental tool of microeconomic analysis. Marginal cost governs the movement of average cost and determines the firm’s equilibrium output under different market structures. The U-shaped LAC curve summarises the long-run cost behaviour of the firm when scale of operations can be varied freely. Together, these concepts provide a complete and coherent picture of cost in the short and long run as presented in the traditional cost theory of your prescribed text by T.R. Jain & V.K. Ohri.

These notes form part of a carefully curated set of important questions which have frequently appeared in past university examinations and therefore carry a high probability of being reflected, in whole or in part, in future question papers. However, they are intended as high-quality academic support material only and should not be treated as a guarantee or assurance of any specific questions being asked in forthcoming exams.