4.4.2. Long Run Supply Curve of a Firm

Let us turn to Figure 4.9 and derive the firm’s long run supply curve. As in the short run case, we split the derivation into two parts. We first determine the firm’s profit-maximising output level when the market price is greater than or equal to the minimum (long run) AC. This done, we determine the firm’s profit-maximising output level when the market price is less than the minimum (long run) AC.

In this chunk, we begin the process of deriving the long run supply curve for a firm. This involves dividing the process into two cases based on the market price relative to the firm's average cost. First, we look at situations where the price is at least equal to the minimum average cost (AC), which allows the firm to cover its production costs and earn normal profits. When the price is above this threshold, the firm is incentivized to maximize its output. In the second case, we consider what happens when the market price falls below the minimum average cost, indicating that the firm cannot cover its expenses and consequently would not choose to produce at all in the long run.

Think of a bakery that requires a minimum oven cost to bake bread. If the price of bread rises above the cost of baking (like a market price above its minimum average cost), the bakery will bake as much bread as possible to maximize profits. Conversely, if the price falls below their baking costs, they would shut down their operations to avoid losing money.

Case 1: Price greater than or equal to the minimum LRAC. Suppose the market price is p1, which exceeds the minimum LRAC. Upon equating p1 with LRMC on the rising part of the LRMC curve, we obtain output level q1. Note also that the LRAC at q1 does not exceed the market price, p1. Thus, all three conditions highlighted in section 3 are satisfied at q1. Hence, when the market price is p1, the firm’s supplies in the long run become an output equal to q1.

In this section of the analysis, when the market price is above the minimum long run average cost (LRAC), it assures the firm that they can not only cover their production costs but also earn profits. Thus, the firm identifies its profit-maximizing output level by finding the point where the long-run marginal cost (LRMC) equals the price. This enables them to set production at levels that maximize potential profits while still staying within the bounds of covering costs; therefore, they produce the quantity q1 as long as the market price remains at p1 or higher.

Imagine a farmer who grows tomatoes. When the market price of tomatoes rises above the cost of water, seeds, and labor, the farmer will plant as many tomatoes as possible to earn profits. If the price continues to rise, the farmer will keep increasing production until the cost of that last bushel of tomatoes equals the market price. This maximizes their profits without risking losses due to high operating costs.

Case 2: Price less than the minimum LRAC. Suppose the market price is p2, which is less than the minimum LRAC. We have argued that if a profit-maximising firm produces a positive output in the long run, the market price, p2, must be greater than or equal to the LRAC at that output level. But notice from Figure 4.9 that for all positive output levels, LRAC strictly exceeds p2. In other words, it cannot be the case that the firm supplies a positive output. So, when the market price is p2, the firm produces zero output.

In this scenario, when the market price drops below the minimum average cost, the firm realizes it cannot sustain operations and cover its costs. If producing something would incur greater costs than the revenue generated, the firm opts to cease production altogether in the long run to minimize losses. Hence, their output becomes zero at this price level, as producing no output is financially more feasible than producing at a loss.

Consider a small coffee shop. If the cost of coffee beans, milk, and other supplies exceeds what customers are willing to pay for coffee, the owner would rather close the shop than keep operating at a loss. They might wait for market prices to improve to ensure that when they open again, they can cover their costs and be profitable.

Combining cases 1 and 2, we reach an important conclusion. A firm’s long run supply curve is the rising part of the LRMC curve from and above the minimum LRAC together with zero output for all prices less than the minimum LRAC. In Figure 4.10, the bold line represents the long run supply curve of the firm.

The overall conclusion for the long run supply curve illustrates that it consists of two segments: one where the firm will actively supply goods when prices cover production costs and allow for profits, and another where the firm will not produce at all due to insufficient market prices. Therefore, the long run supply curve reflects the range of prices at which firms are willing to produce over the long term, effectively illustrating their responsiveness to market conditions.

Think of a new technology company that produces smartphones. If the price of smartphones exceeds the cost of production, the company will ramp up its manufacturing. Conversely, if a major competitor drops prices substantially, leading to prices below production costs, the tech company may halt all production until they can return to a profitable range. This behavior shapes the company's long run supply curve in the technology market.

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