7.2 Production in the Short Run

Production in the Short Run

Production in the short run focuses on how firms adjust output using variable inputs while fixed inputs remain constant. This concept is crucial for understanding how businesses make decisions when faced with constraints and limited flexibility in their production processes.

The law of diminishing marginal returns plays a key role here, explaining why productivity eventually declines as more variable inputs are added. This principle helps firms determine optimal input levels and make efficient production choices.

Components of Production Functions

A production function describes the relationship between the quantities of inputs a firm uses and the quantity of output it produces.

• Inputs are the resources used to produce goods or services: labor, capital, raw materials, energy.
• Outputs are the final goods or services that result from combining those inputs.

In the short run, at least one input is fixed (typically capital) while others can vary (typically labor). The short-run production function is written as:

$Q = f(L, \bar{K})$

where $Q$ is the quantity of output, $L$ is the variable input (labor), and $\bar{K}$ is the fixed input (capital, with the bar indicating it's held constant).

Fixed vs. Variable Inputs

The distinction between fixed and variable inputs is what defines the short run in economics.

• Fixed inputs cannot be changed in the short run. Think of a bakery's ovens, a factory's floor space, or a restaurant's kitchen equipment. No matter how much or how little the firm produces, the quantity of these inputs stays the same.
• Variable inputs can be adjusted in the short run. A bakery can hire more bakers, buy more flour, or use more electricity. These inputs rise and fall with the level of output the firm wants to produce.

Because fixed inputs are locked in, the only way a firm can change its output in the short run is by adjusting the quantity of its variable inputs.

Changes in Total, Marginal, and Average Product

Three measures describe how output responds as a firm adds more of a variable input:

Total Product (TP) is the total output produced from a given amount of variable input, holding fixed inputs constant. As you add more labor, TP follows a characteristic pattern: it first increases at an increasing rate, then increases at a decreasing rate, and eventually decreases.

Marginal Product (MP) is the change in total product from adding one more unit of the variable input. For example, if hiring a 5th worker raises output from 40 to 52 units, the MP of the 5th worker is 12 units. MP initially rises, hits a maximum, and then declines.

Average Product (AP) is total product divided by the number of units of variable input used: $AP = \frac{TP}{L}$. It tells you the output per worker (or per unit of whatever your variable input is).

The Three Stages of Production

The relationship between TP and MP creates three distinct stages:

1. Stage 1: MP is increasing. TP rises at an increasing rate. Each additional worker adds more output than the previous one.
2. Stage 2: MP is decreasing but still positive. TP continues to rise, but at a decreasing rate. Each additional worker still adds output, just less than the worker before.
3. Stage 3: MP turns negative. TP actually falls. Adding more workers now reduces total output.

Law of Diminishing Marginal Returns

This law states that as more units of a variable input are added to a fixed input, the marginal product of the variable input will eventually decrease.

The word "eventually" matters. MP can rise at first. Picture an empty factory with one worker trying to do everything alone. A second and third worker allow specialization and teamwork, so MP increases. But at some point, the factory gets crowded. Workers start waiting for equipment, getting in each other's way, or standing idle. The fixed input (the factory) becomes increasingly scarce relative to the growing variable input (labor), and MP falls.

Two things to keep straight about this law:

• It only applies in the short run, when at least one input is fixed.
• It doesn't say MP decreases immediately. It says MP decreases eventually, after some point.

Short-Run vs. Long-Run Production Decisions

In the long run, firms can build bigger factories, install new equipment, or downsize entirely. This flexibility allows firms to achieve economies of scale, where long-run average costs decrease as output increases. The short run is about making the best of what you've got; the long run is about choosing what to have in the first place.

Production Analysis Tools

• Isoquants are curves showing different combinations of inputs that produce the same level of output. They work like indifference curves but for production instead of consumer preferences.
• Returns to scale describe how output changes when all inputs are increased proportionally in the long run. If doubling all inputs more than doubles output, you have increasing returns to scale.
• Factor proportions refer to the ratio of inputs used in production (e.g., the ratio of capital to labor). In the long run, firms can adjust these ratios to find the most efficient combination.