Question

What do you understand by Average Cost (AC) and Marginal Cost (MC)? Explain the mutual relation between these curves.

Hint:

The AC curve is U-shaped because of economies of scale and diminishing returns, while the MC curve typically intersects the AC curve at its minimum point, reflecting the most efficient level of production.

Answer 1

Average Cost (AC) refers to the total cost of production per unit of output. It is calculated by dividing the total cost (TC) by the number of units produced (Q). Mathematically, it is expressed as: \[ AC = \frac{TC}{Q} \] where \(TC\) represents total cost and \(Q\) represents the quantity of output. Average Cost includes both fixed and variable costs, averaged over all units produced. The AC curve typically decreases initially, reflecting increasing returns to scale, but after a certain point, it starts to increase due to diminishing returns to variable inputs. Marginal Cost (MC) refers to the additional cost incurred from producing one more unit of output. It is the change in total cost resulting from a change in the level of output, and is mathematically expressed as: \[ MC = \frac{\Delta TC}{\Delta Q} \] where \(\Delta TC\) is the change in total cost and \(\Delta Q\) is the change in the quantity of output. MC reflects how cost changes as production increases or decreases. It typically follows the law of diminishing marginal returns, meaning it initially decreases as production increases but eventually starts to increase due to inefficiencies when production exceeds optimal levels. Mutual Relation between AC and MC: The relationship between Average Cost (AC) and Marginal Cost (MC) is a key aspect of production theory. The MC curve has a crucial role in determining the behavior of the AC curve:
1. When MC is less than AC: When the marginal cost is lower than the average cost, each additional unit of output reduces the average cost. This is because the additional unit of output is produced at a lower cost than the average of previous units, thereby pulling the AC curve downwards. The AC curve is therefore falling. 

2. When MC is greater than AC: When the marginal cost exceeds the average cost, producing an additional unit increases the average cost. In this case, the MC curve lies above the AC curve, and the AC curve starts rising. This situation typically occurs when production exceeds the optimal capacity, leading to inefficiencies. 

3. When MC equals AC: The MC curve intersects the AC curve at its minimum point. This is the point of optimal production, where average cost is at its lowest. At this point, the firm is operating at maximum efficiency in terms of cost per unit of output. The AC curve is typically U-shaped due to economies of scale (when increasing output leads to lower average costs) followed by diseconomies of scale (when increasing output leads to higher average costs). The MC curve, on the other hand, usually starts below the AC curve, rises sharply as output increases, and intersects the AC curve at its lowest point. Importance of AC and MC Curves: - Profit Maximization: Firms use these curves to decide the level of output at which they should operate to minimize costs and maximize profits. The point where MC equals AC represents the most efficient production level in the short run. - Decision Making: Understanding the relationship between AC and MC helps firms decide how much to produce. If MC is rising rapidly and exceeds AC, it signals the need to reduce output to avoid inefficiencies. 

Example: Consider a factory producing widgets. If the factory produces 100 widgets, the total cost (TC) is \$ 1,000, so the average cost (AC) per widget is \$ 10. If the factory decides to produce one more widget, and the additional cost (marginal cost, MC) for that widget is \$ 9, the AC of all the widgets decreases slightly because the additional cost is lower than the average cost. However, if producing the 101st widget raises the marginal cost to \$ 12, the AC of each widget will increase, signaling that the factory may be approaching its optimal production level.