Production and cost theory models a firm's decisions as its own optimisation problem, choosing exactly how much labour, capital and other inputs to combine in order to produce a given quantity of output at the lowest possible total cost, the direct producer-side mirror of consumer theory's utility maximisation on the buyer's side. Where a consumer chooses among goods to maximise satisfaction within a budget, a firm chooses among inputs to minimise cost while hitting a production target, and the resulting cost curves are exactly what determine how much a firm is actually willing to supply at any given price.
A firm has to choose how to combine inputs, not just how much of each to buy in isolation
A given quantity of output can typically be produced through several different combinations of labour and capital, more workers and less machinery, or more machinery and fewer workers, and production theory models exactly how a firm chooses among these combinations, weighing each input's productivity against its price to find the combination that produces the required output at the lowest possible total cost. This mirrors consumer theory's own trade-off logic closely, just applied to inputs a firm buys to produce something rather than to goods a consumer buys to directly consume.
The resulting cost curves are what actually drive a firm's real supply decisions
Once a firm's cost-minimising input combination is worked out for each possible output level, the resulting cost curve, showing total cost at every quantity a firm might choose to produce, is exactly what a firm actually consults when deciding how much to supply at a given market price, producing more only as long as the additional revenue from selling one more unit still exceeds the additional cost of producing it. This connection is precisely why production and cost theory sits underneath supply curves the same way consumer theory sits underneath demand curves, each supplying the underlying optimisation logic for one side of a market.
What we're still unsure about
That cost-minimising input choice provides a mathematically coherent framework for deriving a firm's supply behaviour is well established, foundational microeconomic theory taught consistently for over a century. What's more genuinely an ongoing empirical question is exactly how accurately this cost-minimisation model actually describes real firms' decision-making, since real firms often work with imperfect information about input productivity, face genuine adjustment costs when changing their input mix, and don't necessarily recalculate an optimal input combination continuously the way the pure theoretical model assumes, and economists continue to study exactly how closely real firm behaviour tracks the theoretical cost-minimising benchmark across different industries.
This sits inside Production & Cost Theory, one of eight topics in Microeconomics, one of five domains in Economics, one of seventeen subjects the app can quiz you on.