What does the total cost curve look like?

A total cost graph puts output on the horizontal axis and dollars on the vertical axis and usually shows three curves. Total fixed cost (TFC) is a flat horizontal line, because rent and equipment leases do not change with output. Total variable cost (TVC) starts at the origin, since producing nothing costs nothing in variable inputs, and rises as output grows. Total cost (TC) is TFC plus TVC, so it starts on the vertical axis at the level of fixed cost and runs above TVC everywhere. The vertical distance between TC and TVC at every quantity equals TFC, so TC is simply TVC moved straight up. That is why the two curves have the same shape: at any quantity they rise by the same amount, and both slopes equal marginal cost.

A cost table shows it. Suppose fixed cost is 60 dollars. At outputs of 0 through 6 units, TVC is 0, 20, 35, 45, 60, 85, and 120 dollars, so TC is 60, 80, 95, 105, 120, 145, and 180 dollars. Subtract TVC from TC on any row and you get 60 every time. Marginal cost, the change in TC from one row to the next, is 20, 15, 10, 15, 25, and 35 dollars. The changes in TVC are exactly the same numbers, because fixed cost never changes. You can check figures like these with the total cost calculator and the total variable cost calculator.

The bend in the curve comes from marginal cost, because the slope of TC at any point is MC. In the table, MC falls from 20 to 15 to 10 over the first three units, so TC climbs at a decreasing rate and gets flatter. After the third unit MC rises to 15, 25, and 35, so TC climbs at an increasing rate and gets steeper with every unit. The point where the curve switches from flattening to steepening is the output where MC is at its minimum. The rise in MC is caused by the law of diminishing marginal returns: with the factory fixed in the short run, each added worker contributes less extra output, so each extra unit needs more labor and costs more. TVC also rises with output for a simpler reason: more units need more variable inputs. Diminishing returns explain why it rises faster and faster.

The per-unit curves can be read straight off the total curves. Average total cost at any quantity is the slope of a straight line from the origin to that point on TC, and average variable cost is the slope of a line from the origin to the point on TVC. In the table, ATC is 80, 47.5, 35, 30, 29, and 30 dollars, lowest at 5 units, which is where a line from the origin just touches the TC curve. AVC is 20, 17.5, 15, 15, 17, and 20 dollars, lowest at 3 and 4 units, and the 4th unit's marginal cost of 15 matches it, just as MC crosses AVC at its minimum. The production costs sandbox draws those per-unit curves.

Three mistakes cost points. Starting TC at the origin forgets fixed cost in the short run, although in the long run every cost is variable and long-run TC does start at zero. Drawing TC as a straight line would mean marginal cost never changes, which ignores diminishing returns. Drawing TC and TVC so they move closer together or further apart breaks the rule that the gap is always TFC. For the full set of seven cost measures and how they connect, read the production costs guide, and compare the total and per-unit views in average variable cost vs total cost.