7.3 Costs in the Short Run

Production and Costs in the Short Run

In the short run, firms can't change everything about how they produce. At least one input is fixed (usually capital like machinery or a building), so firms adjust output by changing variable inputs like labor. This constraint shapes the entire cost structure of a firm and drives key decisions about how much to produce, when to keep operating, and when to shut down.

The Short-Run Production Framework

The short run is defined as any period where at least one factor of production is fixed. That fixed factor creates fixed costs that must be paid regardless of how much (or how little) the firm produces. Think rent on a factory lease or insurance premiums.

Variable factors, like labor and raw materials, can be adjusted. These create variable costs that rise and fall with output. The core relationship is straightforward:

$TC = FC + VC$

As a firm ramps up production, it adds more of the variable input (say, workers) to the fixed input (the factory). At first, this works well. But eventually, the Law of Diminishing Marginal Returns kicks in: each additional worker contributes less and less to output because the fixed capital is being shared among more people. This is why costs eventually rise faster as output increases.

Factor Prices of Production

Every input has a price, and these prices determine a firm's costs:

• Labor: Wages paid to workers
• Capital: Interest on borrowed funds, or the opportunity cost of using capital the firm already owns
• Land: Rent for land or natural resources (farmland, mining sites)
• Entrepreneurship: Profit earned by the owner for organizing and managing production, which also reflects the opportunity cost of their time and resources

Types of Short-Run Costs

Here are the cost measures you need to know, along with their formulas:

• Total Cost (TC): The sum of all production costs at a given output level.
  • $TC = FC + VC$
• Fixed Costs (FC): Costs that stay the same no matter how much you produce. Examples: rent, insurance, depreciation on machinery.
• Variable Costs (VC): Costs that change with output. Examples: wages, raw materials (lumber, steel), electricity.
• Marginal Cost (MC): The additional cost of producing one more unit.
  • $MC = \frac{\Delta TC}{\Delta Q}$
  • This is the most important cost for decision-making because it tells you what the next unit actually costs.
• Average Total Cost (ATC): Cost per unit of output.
  • $ATC = \frac{TC}{Q}$
• Average Fixed Cost (AFC): Fixed cost per unit.
  • $AFC = \frac{FC}{Q}$
  • AFC always falls as output rises because you're spreading the same fixed costs over more units. This is sometimes called "spreading the overhead."
• Average Variable Cost (AVC): Variable cost per unit.
  • $AVC = \frac{VC}{Q}$
  • AVC initially falls (workers become more efficient as you add a few) but eventually rises due to diminishing marginal returns.

Profit and Average Profit

Profit is the difference between what a firm earns and what it spends:

$Profit = TR - TC$

where $TR$ is total revenue. You can also express profit on a per-unit basis:

$\text{Average Profit} = \frac{TR - TC}{Q} = \frac{TR}{Q} - \frac{TC}{Q} = P - ATC$

So average profit is simply price minus average total cost. If $P > ATC$, the firm earns a positive profit per unit. If $P < ATC$, the firm is taking a loss on each unit.

Cost Patterns and Profitability Rules

Firms use the relationship between marginal revenue (MR) and marginal cost (MC) to decide how much to produce:

1. If $MR > MC$, producing one more unit adds more to revenue than to cost, so the firm should increase output.
2. If $MR < MC$, the next unit costs more than it brings in, so the firm should reduce output.
3. If $MR = MC$, the firm is at its profit-maximizing (or loss-minimizing) quantity.

Three critical output points to know:

• Profit-Maximizing Point: Where $MR = MC$. This is the output level that generates the most profit (or smallest loss) given the firm's cost structure.
• Break-Even Point: Where $P = ATC$. The firm covers all its costs exactly, earning zero economic profit. If price is above ATC at the profit-maximizing quantity, the firm earns positive profit.
• Shutdown Point: Where $P = AVC$ (at the minimum of AVC). If price falls below AVC, the firm can't even cover its variable costs and should stop producing in the short run. It still pays fixed costs, but it loses less by shutting down than by continuing to operate.

Graphical Analysis of Costs and Profitability

Short-Run Cost Curves

Each cost measure has a characteristic shape on a graph:

• FC curve: A horizontal line, since fixed costs don't change with output.
• VC curve: Starts at the origin and increases. It rises slowly at first (when workers are becoming more productive), then rises more steeply (as diminishing returns set in).
• TC curve: The same shape as VC, but shifted up by the amount of FC.
• MC curve: U-shaped. It falls initially, reaches a minimum, then rises. The rising portion reflects diminishing marginal returns.
• ATC curve: U-shaped. It falls as both AFC and AVC decline, reaches a minimum, then rises as increasing AVC outweighs the declining AFC.
• AVC curve: Also U-shaped, but reaches its minimum at a lower output level than ATC.
• AFC curve: Slopes downward continuously, getting closer and closer to the horizontal axis but never touching it.

A key relationship: MC passes through the minimum of both AVC and ATC. When MC is below ATC, it pulls the average down. When MC is above ATC, it pulls the average up. The crossing point is therefore the minimum of ATC (same logic applies to AVC).

Graphical Profitability Analysis

In a perfectly competitive market, the MR curve is a horizontal line at the market price, since each unit sells for the same price.

• Profit-maximizing quantity: Found where the MR curve intersects the MC curve (with MC rising through MR, not falling through it).
• Profit or loss per unit: The vertical distance between the price (MR) and the ATC curve at the profit-maximizing quantity.
  • If $P > ATC$: the firm earns profit. Total profit is $(P - ATC) \times Q$.
  • If $AVC < P < ATC$: the firm operates at a loss but still covers variable costs, so it should keep producing in the short run.
  • If $P < AVC$: the firm should shut down.

Time Horizons and Scale Economies

• Short run: At least one input is fixed. This is the focus of this section.
• Long run: All inputs are variable. The firm can change its plant size, equipment, and everything else.
• Economies of scale: Long-run average total cost decreases as the firm produces more. Larger scale brings cost advantages (bulk purchasing, specialization).
• Diseconomies of scale: Long-run average total cost increases as the firm grows. This often results from coordination problems and bureaucratic inefficiency at very large scales.
• Opportunity cost: The value of the best alternative you give up when making a choice. This concept underlies all cost calculations in economics, including the cost of capital the firm already owns.