7.4 Production in the Long Run

In long-run production, firms can adjust all factors of production, including capital and labor, to find the most efficient way to produce. This flexibility is what separates long-run analysis from the short run, where at least one input is fixed. Understanding long-run production helps explain how businesses grow, why some firms are larger than others, and how cost structures change with scale.

Long-Run Production

Long run vs short run production

The core distinction is simple: in the short run, at least one factor of production is fixed (like factory size or major equipment), while in the long run, every input is variable. "Long run" doesn't refer to a specific amount of time. It just means enough time has passed for a firm to change anything it wants, from hiring decisions to building a new plant.

• In the short run, a firm might want to produce more but is stuck with its current factory. It can only add workers or raw materials.
• In the long run, that same firm can build a bigger factory, buy better machines, or relocate entirely.

This matters because short-run constraints often force firms to operate inefficiently. A restaurant with a tiny kitchen can keep hiring cooks, but at some point they're just getting in each other's way. In the long run, the restaurant can renovate or move to a larger space, removing that bottleneck.

Long-run flexibility also lets firms pursue economies of scale, where expanding production lowers average cost per unit. But if a firm expands too much, it can run into diseconomies of scale, where average costs start rising due to coordination problems and bureaucratic overhead.

Firm adjustments for long-term efficiency

Firms use the long-run average cost (LRAC) curve to figure out the best production scale. The LRAC curve plots the lowest possible average cost at each level of output, assuming the firm can adjust all inputs freely. The optimal scale of production sits at the minimum point of the LRAC curve.

To reach that minimum, firms can make several types of adjustments:

• Change input proportions. If capital becomes cheaper relative to labor (say, automation technology drops in price), a firm can substitute machines for workers. The goal is always the cost-minimizing combination of inputs.
• Expand output to capture economies of scale. As production grows, fixed costs like R&D or marketing get spread across more units. Firms also benefit from greater specialization, where workers focus on narrower tasks and get better at them.
• Avoid overexpansion. Growing too large brings diseconomies of scale. Communication breaks down across departments, decision-making slows, and management layers multiply. These coordination costs push average costs back up.
• Choose the right plant size. Each possible plant size has its own short-run average cost curve. The LRAC curve is the "envelope" of all these short-run curves, touching each one at the output level where that plant size is most efficient. The firm picks the plant size that minimizes average cost for its target output.

Input factors and marginal productivity

The law of diminishing marginal returns states that as you add more of one input while holding others constant, each additional unit of that input eventually produces less additional output. This is primarily a short-run concept because it requires at least one fixed input.

• A classic example: a factory with 10 machines hires more workers. The first few extra workers boost output significantly. But eventually, workers are sharing machines and waiting for turns, so each new hire adds less and less to total output.
• This diminishing productivity is why the short-run marginal cost (MC) curve slopes upward. Producing each additional unit requires more and more of the variable input.

In the long run, the relevant concept is returns to scale, not diminishing marginal returns (since no input is fixed). Returns to scale describe what happens when all inputs increase proportionally:

• Increasing returns to scale: Doubling all inputs more than doubles output. This corresponds to the downward-sloping portion of the LRAC curve (economies of scale).
• Constant returns to scale: Doubling all inputs exactly doubles output. Average costs stay flat.
• Decreasing returns to scale: Doubling all inputs less than doubles output. This corresponds to the upward-sloping portion of the LRAC curve (diseconomies of scale).

The long-run marginal cost (LMC) curve reflects this pattern. It slopes downward at first when the firm experiences increasing returns to scale, then slopes upward once decreasing returns to scale set in.

Production and Scale

The production function describes the maximum output a firm can produce from any given combination of inputs. It's the technical relationship between what goes in and what comes out.

Returns to scale, as described above, are read directly from the production function. If a firm's production function is $Q = f(L, K)$, then you check returns to scale by scaling both labor ($L$) and capital ($K$) by the same factor and seeing whether output scales by more, less, or exactly the same amount.

The expansion path traces the cost-minimizing combination of inputs as a firm scales up production. Think of it as connecting the dots on a graph where each dot represents the cheapest way to produce a given output level. Along the expansion path, the firm is always choosing the input mix where the ratio of marginal products equals the ratio of input prices: $\frac{MP_L}{MP_K} = \frac{w}{r}$, where $w$ is the wage rate and $r$ is the rental rate of capital.