7.2 Production in the Short Run

Production in the Short Run

In the short run, firms have at least one input they can't change (like a factory or a piece of machinery), so the only way to adjust output is by changing their variable inputs (like labor). Understanding how output responds as you add more of a variable input is central to figuring out costs, which drives most of the decisions firms make in this unit.

Components of Production Functions

A production function describes the relationship between inputs and the quantity of output a firm produces. In the short run, it's typically written as:

$Q = f(K, L)$

• $Q$ = quantity of output
• $K$ = capital (fixed in the short run)
• $L$ = labor (variable in the short run)

Since capital is fixed, the only way to change $Q$ in the short run is by adjusting $L$. The production function tells you exactly how output responds as you hire more (or fewer) workers.

Fixed vs. Variable Inputs

Fixed inputs are production factors that can't be changed in the short run. Think buildings, land, and heavy machinery. No matter how much or how little a firm produces, these stay the same.

Variable inputs are factors the firm can adjust. Labor is the classic example, but raw materials and energy count too. A firm ramps output up or down by changing the quantity of these inputs.

The defining feature of the short run is this split: at least one input is fixed. That constraint is what creates diminishing returns, which you'll see next.

Changes in Product Measures

Three measures track how output changes as you add more of a variable input:

• Total Product (TP): The total quantity of output produced. As you add workers, TP first rises quickly, then rises more slowly, and can eventually fall.
• Marginal Product (MP): The additional output from one more unit of the variable input. Calculated as $MP = \frac{\Delta TP}{\Delta L}$. MP first increases, hits a peak, then declines.
• Average Product (AP): Output per unit of the variable input. Calculated as $AP = \frac{TP}{L}$.

The relationship between TP and MP breaks into three stages:

1. Stage 1: MP is increasing, so TP rises at an increasing rate.
2. Stage 2: MP is decreasing but still positive, so TP rises at a decreasing rate.
3. Stage 3: MP turns negative, and TP actually falls.

A useful connection: MP intersects AP at AP's maximum. When MP is above AP, average product is rising. When MP falls below AP, average product is falling. This works the same way as grade averages: if your next exam score (marginal) is higher than your current average, your average goes up.

Law of Diminishing Marginal Returns

This law states that as you keep adding units of a variable input to a fixed input, the marginal product of that variable input will eventually decrease.

Notice the word "eventually." The first few workers you add might actually increase MP because they can specialize and divide tasks more effectively. But at some point, the fixed input (say, a single factory floor) becomes a bottleneck. Workers start getting in each other's way, sharing equipment, or waiting for machines. Each additional worker adds less and less to total output.

Diminishing marginal returns only applies in the short run, precisely because at least one input is fixed. It's what produces the three stages described above.

Firms aim to operate in Stage 2, where MP is declining but still positive. In Stage 1, the firm could still gain efficiency by hiring more. In Stage 3, hiring more workers actually reduces total output, so no rational firm would operate there.

Short-Run vs. Long-Run Production Decisions

In the short run, firms can only adjust variable inputs. Fixed inputs create a ceiling on how much output can grow efficiently, and diminishing returns kick in as the firm pushes against that ceiling.

In the long run, all inputs become variable. The firm can build a bigger factory, buy more machines, or redesign its entire operation. This means:

• Diminishing marginal returns (a short-run problem tied to fixed inputs) can be avoided by scaling up all inputs together.
• Firms can pursue economies of scale, where increasing the scale of production lowers average cost per unit.
• The firm chooses the combination of inputs that minimizes cost for a given level of output.

The short run is about optimizing within your current setup. The long run is about choosing the right setup in the first place.