Production and Costs

The Short-Run Production Function

A bakery has 3 ovens. Each oven can bake 50 loaves per hour at full capacity. With 1 baker running all 3 ovens, output is 40 loaves (the baker can't keep up). Add a 2nd baker and output jumps to 100. A 3rd baker pushes it to 140. A 4th only gets it to 155. That pattern -- fast gains early, diminishing gains later -- is the short-run production function in action.

The short run means at least one input is fixed. The bakery cannot install a 4th oven by tomorrow. Ovens, lease agreements, equipment -- all locked in. The only lever is labor.

Total product (TP) tracks output as workers are added. Marginal product (MP) measures extra output per additional worker. Baker 2 added 60 loaves (MP = 60). Baker 3 added 40 (MP = 40). Baker 4 added 15 (MP = 15). MP rose initially through specialization, then fell as the fixed ovens became a bottleneck. That rise-then-fall pattern drives every cost curve in this module.

The Law of Diminishing Marginal Returns

The law of diminishing marginal returns is not a theory. It is a physical constraint. Pack enough workers into a fixed space with fixed equipment and each additional hire contributes less than the one before.

The word "eventually" matters. Early on, specialization boosts MP. Two workers on an assembly line outperform two solo operators because one wires and the other solders. A third running quality control adds even more. MP rises during this phase.

Crowd twenty workers onto that same three-station line and they wait for equipment, bump into each other, and slow production down.

The link to costs is direct. If worker 8 adds 15 units and worker 9 adds only 10, those last 10 units each cost more to produce than the previous 15. Diminishing marginal returns cause marginal cost (MC) to rise. That is why the MC curve eventually slopes upward.

From Production to Cost Curves

Production curves and cost curves are mirror images. Rising MP means falling MC. Falling MP means rising MC.

Total cost (TC) has two components. Total fixed cost (TFC) covers rent, insurance, equipment leases -- bills that arrive whether the firm produces zero units or ten thousand. Total variable cost (TVC) covers wages, raw materials, electricity on the production line. These scale with output.

TC = TFC + TVC.

Four per-unit curves appear on the standard cost graph. Marginal Cost (MC) = change in TC / change in Q. Average Total Cost (ATC) = TC / Q. Average Variable Cost (AVC) = TVC / Q. Average Fixed Cost (AFC) = TFC / Q.

AFC falls continuously. A $5,000 monthly lease divided by 100 units is $50 each. Divided by 1,000 units, $5 each. It never stops declining. ATC and AVC converge at high output levels because the shrinking AFC wedge between them approaches zero.

MC Crosses ATC and AVC at Their Minimums

Consider your GPA. If this semester's grades come in below your cumulative average, the cumulative drops. Above it, the cumulative rises. The marginal pulls the average in its direction.

Cost curves follow identical math. While MC sits below ATC, every additional unit is cheaper than the current average, so ATC falls. Once MC climbs above ATC, each new unit costs more than the average, and ATC rises. MC must cross ATC at its minimum point. Same logic applies to AVC.

AVC bottoms out at a lower quantity than ATC. The reason is arithmetic: ATC = AVC + AFC, and AFC is still declining at the point where AVC starts climbing. That declining AFC component keeps pulling ATC downward for a stretch even after AVC has turned upward. ATC's minimum therefore comes later.

Economies and Diseconomies of Scale

In the long run, nothing is fixed. A firm can triple its factory floor, replace every machine, or relocate to another state. The question shifts from "how many workers?" to "what size should this entire operation be?"

The long-run average total cost (LRATC) curve answers that question across three zones.

Economies of scale occupy the downward-sloping left portion. Toyota producing 500,000 Camrys a year can afford robotic welding systems, negotiate steel at bulk rates, and spread a $1.8 billion R&D budget across more units. Per-unit cost falls as scale grows.

Diseconomies of scale occupy the upward-sloping right portion. A company with 200,000 employees drowns in management layers, duplicated departments, and slow internal communication. Per-unit cost creeps back up.

Constant returns to scale fill the flat middle. Doubling all inputs doubles output. Average cost holds steady. The output level where LRATC first reaches this floor is called minimum efficient scale. Industries where that number is enormous (semiconductor fabrication, commercial aircraft manufacturing) naturally end up dominated by a handful of firms.

Connecting Costs to Market Structure

Every output decision traces back to these cost curves. A competitive firm produces where P = MC. A monopolist produces where MR = MC. The MC curve is the backbone of the production decision regardless of market structure.

Deciding how much to produce is only half the question. The other half: should the firm produce at all?

Price above ATC means economic profit. AVC below price but price below ATC means the firm loses money, but operating still beats shutting down. Revenue covers variable costs and chips away at fixed costs. Shutting down means eating the entire fixed cost bill with zero revenue coming in. Price below AVC means each unit produced makes losses worse. Shut down. That threshold is the shutdown point.

Stitch those rules together and a competitive firm supplies output along its MC curve, but only at prices above minimum AVC. Below that, quantity supplied is zero. The short-run supply curve is the segment of MC above AVC.

Worked Example

A screen-printing shop pays $120/day in rent and equipment leases. Today it printed 8 shirts at a total cost of $280.

TVC = TC - TFC = $280 - $120 = $160. That covers ink, blank shirts, and labor.

Per-unit averages:
- AFC = $120 / 8 = $15 per shirt
- AVC = $160 / 8 = $20 per shirt
- ATC = $280 / 8 = $35 per shirt

Check: AVC + AFC = $20 + $15 = $35 = ATC. Always holds.

The shop prints a 9th shirt. That shirt costs $42 to produce. MC = $42. What happens to ATC?

New TC = $280 + $42 = $322. New ATC = $322 / 9 = $35.78. ATC rose from $35 to $35.78 because MC ($42) exceeded the old ATC ($35), pulling the average up.

Flip the scenario. If the 9th shirt cost $28 (MC = $28, below ATC = $35), new ATC = $308 / 9 = $34.22. The average falls. MC below ATC pulls it down. MC above ATC pushes it up. That tug-of-war is why MC intersects ATC at ATC's lowest point.