Production & Costs

You’ll be able to

Explain the production function and the law of diminishing marginal returns
Distinguish fixed, variable, and total costs and their per-unit measures
Relate marginal product to marginal cost

The production function and diminishing returns

A firm’s production function relates inputs to output. In the short run, at least one input (usually capital) is fixed, and the firm varies a variable input (usually labor). Total product is total output; marginal product (MP) is the extra output from one more worker; average product is output per worker. The law of diminishing marginal returns states that as more of a variable input is added to a fixed input, marginal product eventually falls — the fifth worker in a small kitchen adds less than the second. This law drives the shape of the cost curves.

The cost categories

Costs split by whether they vary with output. Fixed costs (FC) do not change with output (rent, insurance) and exist even at zero output. Variable costs (VC) rise with output (labor, materials). Total cost (TC) = FC + VC. Per-unit measures divide by quantity: average fixed cost (AFC) = FC/Q (always falling as output spreads the fixed cost), average variable cost (AVC) = VC/Q, and average total cost (ATC) = TC/Q = AFC + AVC. Marginal cost (MC) is the change in total cost from producing one more unit — the single most important cost for decisions.

From marginal product to marginal cost

Marginal product and marginal cost are mirror images. When marginal product is rising, each additional unit of output takes fewer added inputs, so marginal cost falls. When diminishing returns set in and marginal product falls, each additional unit requires more inputs, so marginal cost rises. That is why the MC curve is U-shaped: it declines while MP rises, then climbs once diminishing returns dominate. The MC curve intersects both the AVC and ATC curves at their minimum points.

Key cost relationships

TC = FC + VC · ATC = TC/Q = AFC + AVC · MC = ΔTC / ΔQ

Marginal cost pulls the averages: when MC is below ATC, ATC falls; when MC is above ATC, ATC rises; MC crosses ATC (and AVC) at their minimums.

Worked example

A firm has fixed costs of $100. Producing 10 units costs $300 total; producing 11 units costs $325 total. Find the ATC at 10 units, the marginal cost of the 11th unit, and the AVC at 10 units.

1.ATC at 10 units = TC/Q = 300/10 = $30 per unit.
2.Marginal cost of the 11th unit = ΔTC/ΔQ = (325 − 300)/(11 − 10) = 25/1 = $25.
3.Variable cost at 10 units = TC − FC = 300 − 100 = $200.
4.AVC at 10 units = VC/Q = 200/10 = $20 per unit.

Answer: ATC at 10 units is $30, the marginal cost of the 11th unit is $25, and AVC at 10 units is $20. Because MC ($25) is below ATC ($30), producing the 11th unit will pull average total cost down.

Checkpoint

As a firm hires additional workers in the short run with capital fixed, the marginal product of labor eventually begins to fall. This is the result of:

Watch out

Diminishing marginal returns is a short-run idea (at least one input fixed) and describes marginal product. Do not confuse it with economies of scale, a long-run concept about average cost when all inputs can vary. They are different phenomena.

Checkpoint

At the current output level, a firm’s marginal cost is below its average total cost. What is happening to average total cost as output increases by one unit?

On the exam

Remember the marginal-average rule: when MC < ATC, ATC falls; when MC > ATC, ATC rises; and MC crosses ATC and AVC at their minimum points. This lets you locate the minimum of the average curves directly on a graph.

Answer the 2 checkpoints as you read.