A supply curve shows the relationship between the price of a good and the quantity a firm is willing to produce and sell, holding input prices and technology constant. Supply curves typically slope upward: higher prices make production more profitable, incentivizing greater output. Supply reflects firms' production and pricing decisions.
Your prerequisite — scarcity, choice, and production tradeoffs — established that producing more of anything means using resources that have alternative uses. The supply curve makes this intuition precise: it translates the production tradeoff into a specific price-quantity relationship that describes a firm's willingness to produce.
Think about a simple case: a bakery. To produce ten loaves a day, the baker uses an oven, flour, and labor at a certain cost. To produce twenty loaves, she needs more flour, more labor hours, and perhaps overtime. The cost of each additional loaf — the marginal cost of production — tends to rise as output expands, because the baker must use inputs (her own time, specialized labor) that become increasingly scarce. This rising marginal cost is the underlying engine of the upward-sloping supply curve. The firm will produce an additional unit whenever the price it receives for that unit at least covers the marginal cost of producing it. So at a low price, only the cheapest units are worth producing; at a higher price, it's profitable to expand output further. Mapping out "how much would we produce at each possible price?" traces the supply curve.
The supply curve as a marginal cost curve is a key insight. For a competitive firm (one that cannot affect the market price), the supply curve is literally the firm's marginal cost curve above the point where price covers variable costs. At a price of $2 per loaf, she produces where MC = $2. At $3, she expands until MC = $3. This equivalence — supply = MC — is what links the supply curve you see in market diagrams to the cost structure you study in firm-level analysis. It also explains *why* supply curves shift: if input prices fall (cheaper flour), marginal cost falls at every output level, and the firm is willing to supply more at every price — a rightward shift. If input prices rise, the curve shifts left.
The supply curve holds many things constant — technology, input prices, expectations, and the number of producers. These ceteris paribus conditions define what counts as a shift versus a movement. A price change for the firm's own output causes movement *along* the existing curve — quantity supplied changes, but supply itself does not. A change in input prices, technology, or regulatory environment shifts the entire curve. This distinction — which you've already seen on the demand side — is equally important for supply. The supply curve is not a fixed physical fact about the world; it is a summary of cost conditions at a point in time, and it changes whenever those conditions change.