3.7.2. Long Run Costs

In the long run, all inputs are variable. There are no fixed costs. The total cost and the total variable cost therefore, coincide in the long run. Long run average cost (LRAC) is defined as cost per unit of output, i.e.

$LRAC = \frac{TC}{q}$

Long run marginal cost (LRMC) is the change in total cost per unit of change in output. When output changes in discrete units, then, if we increase production from $q_{1}$ to $q_{2}$ units of output, the marginal cost of producing the $q_{2}^{th}$ unit will be measured as

$LRMC = TC_{at\,q_{2}} - TC_{at\,q_{1}}$

In the long run, a firm does not have any fixed costs, which means it can adjust all its inputs freely. As a result, the total cost (TC) and total variable cost (TVC) are the same in the long run. The Long Run Average Cost (LRAC) is calculated by dividing the total cost by the quantity of output produced. Similarly, the Long Run Marginal Cost (LRMC) measures how much the total cost changes when output increases by one unit, helping firms understand how much extra they will need to pay to produce more.

Imagine a restaurant that can change its menu completely based on customer feedback. In the long run, they can adjust everything from the ingredients they buy (all inputs) to how many chefs they hire (labor). Instead of worrying about fixed costs (like rent), they can focus on how much it costs to serve each additional plate of food, making their operations more efficient.

We have previously discussed the returns to scales. Now let us see their implications for the shape of LRAC.

IRS implies that if we increase all the inputs by a certain proportion, output increases by more than that proportion. In other words, to increase output by a certain proportion, inputs need to be increased by less than that proportion. With the input prices given, cost also increases by a lesser proportion. For example, suppose we want to double the output. To do that, inputs need to be increased, but less than double. The cost that the firm incurs to hire those inputs therefore also need to be increased by less than double. What is happening to the average cost here? It must be the case that as long as IRS operates, average cost falls as the firm increases output.

DRS implies that if we want to increase the output by a certain proportion, inputs need to be increased by more than that proportion. As a result, cost also increases by more than that proportion. So, as long as DRS operates, the average cost must be rising as the firm increases output.

CRS implies a proportional increase in inputs resulting in a proportional increase in output. So the average cost remains constant as long as CRS operates.

Long Run Average Cost (LRAC) curves demonstrate how a firm's average cost evolves as it changes output levels. Under Increasing Returns to Scale (IRS), a firm can produce more output without having to proportionally increase its input costs, which causes average costs to decrease. Conversely, under Decreasing Returns to Scale (DRS), a firm needs to increase its input use more than proportionately to achieve higher output levels, leading to increased average costs. Constant Returns to Scale (CRS) means that when inputs are increased, output rises in the same proportion, keeping average costs stable.

Consider a factory that manufactures bicycles. When they scale up production (IRS), they might find that by adding more assembly workers, they can produce a lot more bicycles without doubling their costs (like buying materials). However, once they hit a certain limit (DRS), adding more workers only adds a little to production and their costs skyrocket because they have to rent more space and buy more equipment. If everything goes perfectly balanced (CRS), then their costs remain stable as they add workers and equipment in equal measure.

It is argued that in a typical firm IRS is observed at the initial level of production. This is then followed by the CRS and then by the DRS. Accordingly, the LRAC curve is a ‘U’-shaped curve. Its downward sloping part corresponds to IRS and upward rising part corresponds to DRS. At the minimum point of the LRAC curve, CRS is observed.

Let us check how the LRMC curve looks like. For the first unit of output, both LRMC and LRAC are the same. Then, as output increases, LRAC initially falls, and then, after a certain point, it rises. As long as average cost is falling, marginal cost must be less than the average cost. When the LRAC is rising, marginal cost must be greater than the average cost. LRMC curve is therefore a ‘U’-shaped curve. It cuts the LRAC curve from below at the minimum point of the LRAC.

The Long Run Average Cost (LRAC) curve typically has a U-shape due to the stages of production scale a firm experiences. Initially, as production ramps up, firms enjoy decreasing costs (IRS). Once they reach an optimal level of production, costs stabilize (CRS), and if they continue to expand beyond capacity, costs begin to climb again (DRS). The Long Run Marginal Cost (LRMC) follows a similar U-shape pattern and intersects the LRAC at the lowest point, indicating the most efficient scale of production.

Think of a chef opening a restaurant. At first, the chef can prepare more dishes efficiently (IRS), and their costs per dish decrease. After reaching a certain number of dishes, adding more cooks leads to more kitchen congestion (DRS), causing disorganization. The optimal number of dishes to serve signifies the LRAC's lowest point, where efficiency peaks—much like a well-timed dinner service!

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