Cost Functions

A firm's cost function $TC(Q)$ specifies the total cost of producing each output level $Q$. It decomposes into explicit costs (cash outflows: wages, rent, materials) and implicit costs (opportunity costs with no money changing hands), and into fixed costs (independent of $Q$) and variable costs (rising with $Q$). The two textbook marginal-cost shapes are Type 1 (constant MC) — $TC = F + cQ$, so $MC = c$ is a horizontal line — and Type 2 (increasing MC) — convex $TC$, so $MC$ rises with output (diminishing marginal product of inputs).

When to use

Cost functions are the supply-side primitive behind every Topic 2 result: the monopolist solves $MR(Q) = MC(Q)$, so the shape of $MC$ determines whether the optimum is interior or at a capacity bound. The constant-MC case is the workhorse for closed-form linear-demand monopoly problems (see Solving a linear-demand monopoly). Increasing-MC cases show up in Cournot Competition with asymmetric costs — the firm with the lower MC schedule produces more in equilibrium. Always distinguish avoidable from sunk costs when computing forward-looking optima.