A firm's total cost of producing a given level of output is the expenditure required to produce that output in the most economical way.
Costs can be either variable or fixed. Variable cost is the cost of inputs that vary as the firm's output changes. Fixed cost is the cost of inputs that do not vary as the firm's output changes.
Fixed costs can be either avoidable or sunk. A firm will not incur an avoidable fixed cost if it decides to produce no output, but it cannot avoid a cost that is sunk.
What do economic costs include?
A firm's true economic costs of production include not only its out-of-pocket expenditures, but also the opportunity costs it incurs when it forgoes opportunities to use resources in their best alternative use.
When a firm owns some of the long-lived capital used in production, the true economic cost of its use is an opportunity cost. This cost equals the amount the firm could have received by renting the capital to someone else.
Short-run cost: one variable input
In the short run, if a firm has just one variable input, we can find the firm's short-run variable cost curve by "flipping" the production function, plotting output on the horizontal axis and variable cost (the input price times the input level) on the vertical axis.
The short-run variable cost function can be determined mathematically by using the production function to solve for the amount of variable input needed at each level of output and multiplying by the input's price. The firm's total cost is equal to this variable cost plus its fixed cost.
Long-run cost: cost minimization with two variable inputs
When a firm has more than one variable input, the least-cost production method for producing Q units is the point on the Q-unit isoquant that lies on the lowest possible isocost line, which is equivalent to satisfying the no-overlap rule.
If the least-cost production method is an interior solution, it must satisfy the tangency condition: the MRTS—the ratio of marginal products—equals the input price ratio.
If the least-cost input combination is a boundary solution, then the relationship between the MRTS and the input price ratio may instead satisfy an inequality condition.
If the firm's isoquants have a declining MRTS, then any interior input combination that satisfies the tangency condition (so that the ratio of marginal products equals the input price ratio) is a least-cost input combination.
The firm's output expansion path contains the least-cost input combinations at various levels of output at given input prices. The firm's cost function gives the cost of the input combinations along the firm's output expansion path.
Average and marginal costs
Average cost is total cost divided by the number of units produced: AC = C/Q.
Marginal cost is the extra cost associated with the ΔQ marginal units of output, measured on a per-unit basis: MC = [C(Q) - C(Q - ΔQ)]/ΔQ.
When output is finely divisible, marginal cost at Q units of output equals the slope of the line drawn tangent to the cost curve at Q, while average cost equals the slope of the line from this point on the cost curve to the origin.
A firm's average cost curve is downward sloping where marginal cost is less than average cost; upward sloping where marginal cost is greater than average cost; and neither rising nor falling where marginal cost equals average cost. The marginal cost curve crosses the average cost curve from below at the efficient scale of production. The same is true of the relationship between marginal cost and average variable cost.
Effects of input price changes
When the price of an input increases (decreases), the least-cost production method uses less (more) of that input, or remains unchanged.
Short-run versus long-run costs
If a firm cannot adjust one of its inputs in the short run but can do so over the long run, its costs when its output level changes will be higher in the short run than in the long run.
The long-run average cost curve is the lower envelope of the firm's short-run average cost curves.
Starting at any initial output level, the firm's short-run marginal cost curve is steeper than its long-run marginal cost curve. It crosses the long-run marginal cost curve at the initial output level.
Economies and diseconomies of scale
A firm enjoys economies of scale if its average cost decreases as the quantity produced increases. It suffers diseconomies of scale if its average cost increases as the quantity produced increases.
A firm whose technology has increasing returns to scale will enjoy economies of scale when input prices are unaffected by the firm's output level, while a firm with decreasing returns to scale will have diseconomies of scale.
Multiproduct firms and economies of scope
Most firms produce many products. One reason they do so is to take advantage of economies of scope, which arise when the cost of producing products together is lower than the cost of producing them in separate firms.
When firms experience diseconomies of scope, it is cheaper to produce different products in separate firms.
