3 Production and Cost

Learn how production plans and input prices determine short-run costs, per-unit cost measures, marginal cost, and the shapes of cost curves.

Production and the

A firm's relates input quantities to output. Cost measures translate a production plan into dollars by combining the inputs required with their prices.

In the , at least one input is fixed, while variable inputs can be adjusted. This distinction determines which costs stay fixed as output changes and which vary with production.

Fixed, variable, and total cost

Fixed cost pays for fixed inputs and does not change with output in the . For example, a factory lease is a fixed cost, and it is incurred even when output is zero. Variable cost pays for adjustable inputs, such as hourly labor or materials, and changes with output.

Total cost is the sum of fixed and variable costs:

TC = FC + VC

Total costs are measured in dollars. The fixed and variable components depend on the firm's inputs and their prices.

Average and marginal costs

Average costs express cost per unit of output, while marginal cost measures the additional cost associated with additional output. Let $Q$ denote output.

Average fixed cost is fixed cost divided by output: $AFC = FC / Q$ .
Average variable cost is variable cost divided by output: $AVC = VC / Q$ .
Average total cost is total cost divided by output, and also equals the sum of average fixed and average variable cost: $ATC = TC / Q = AFC + AVC$ .
Marginal cost is the change in total cost divided by the change in output: $MC = \Delta TC / \Delta Q$ .

Average costs are measured in dollars per unit; total costs are measured in dollars. At zero output, the average-cost measures are undefined because they require division by zero. Since fixed cost does not change with output, the change in total cost equals the change in variable cost, so marginal cost can also be calculated as $MC = \Delta VC / \Delta Q$ .

Deriving costs from production

Consider a shop with a fixed weekly equipment cost of $\$60$ . Each worker costs $\$20$ for the period. The production schedule gives the following workers, output, marginal product, costs, and marginal cost:

With $0$ workers: output is $0$ ; fixed cost is $\$60$ , variable cost is $\$0$ , and total cost is $\$60$ . Marginal product and marginal cost are not listed for this starting point.
With $1$ worker: output is $10$ , marginal product is $10$ , fixed cost is $\$60$ , variable cost is $\$20$ , total cost is $\$80$ , and marginal cost is $\$2.00$ per unit.
With $2$ workers: output is $24$ , marginal product is $14$ , fixed cost is $\$60$ , variable cost is $\$40$ , total cost is $\$100$ , and marginal cost is about $\$1.43$ per unit.
With $3$ workers: output is $42$ , marginal product is $18$ , fixed cost is $\$60$ , variable cost is $\$60$ , total cost is $\$120$ , and marginal cost is about $\$1.11$ per unit.
With $4$ workers: output is $56$ , marginal product is $14$ , fixed cost is $\$60$ , variable cost is $\$80$ , total cost is $\$140$ , and marginal cost is about $\$1.43$ per unit.
With $5$ workers: output is $66$ , marginal product is $10$ , fixed cost is $\$60$ , variable cost is $\$100$ , total cost is $\$160$ , and marginal cost is $\$2.00$ per unit.
With $6$ workers: output is $72$ , marginal product is $6$ , fixed cost is $\$60$ , variable cost is $\$120$ , total cost is $\$180$ , and marginal cost is about $\$3.33$ per unit.

Marginal product is the extra output from one more unit of an input: $MP = \Delta Q / \Delta L$ , where $L$ is labor. The fourth worker raises output from $42$ to $56$ , so that worker's marginal product is $14$ units. The worker adds $\$20$ of cost for those $14$ units, giving marginal cost of $\$20 / 14 \approx \$1.43$ per unit.

More generally, when labor is the only variable input and its price $w$ is constant, marginal cost over each interval is $MC = w / MP$ . A higher marginal product therefore means lower marginal cost, while a falling marginal product means rising marginal cost.

Calculating average costs

At output of $42$ units in the shop example, variable cost is $\$60$ , total cost is $\$120$ , and fixed cost is $\$60$ . The resulting averages are $AVC = \$60 / 42 \approx \$1.43$ , $AFC = \$60 / 42 \approx \$1.43$ , and $ATC = \$120 / 42 \approx \$2.86$ per unit.

Total fixed cost stays at $\$60$ , but its per-unit amount falls as output rises. This is why average fixed cost declines with increasing output.

Reading cost curves

A total-cost curve plots total cost against output. Fixed cost determines the curve's vertical intercept, while variable cost makes total cost rise as production expands. The slope between two output levels is marginal cost. With output on the horizontal axis, diminishing marginal product of a variable input tends to make marginal cost rise, because each additional unit of output requires more of that input.

Average-cost curves show cost per unit. Since $ATC = AVC + AFC$ , average total cost lies above average variable cost when fixed cost is positive. Average fixed cost continually falls as output increases.

Average variable cost and average total cost may be U-shaped when marginal product first rises and later diminishes. This shape is not guaranteed for every production technology or output range. When marginal cost is below an average cost, it pulls that average down; when marginal cost is above it, it pulls the average up. Consequently, marginal cost crosses average variable cost and average total cost at their respective minimum points when those minima occur.

How input prices affect costs

Cost calculations depend on both the production plan and input prices. The calculations above assume input prices are constant. If the wage or the price of materials changes, the cost schedule can change even when the does not.

In general, deriving cost requires identifying the inputs needed for each output level and multiplying each input quantity by its price. Fixed cost pays for short-run fixed inputs, variable cost pays for adjustable inputs, and total cost combines the two. Dividing costs by output gives average costs, while comparing the change in total cost with the change in output gives marginal cost. With a constant price for the variable input, marginal cost is inversely related to that input's marginal product.

Production and the short run