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The supply curve is mathematically represented as Qs = mP + b, where Qs is quantity supplied, P is price, m is the slope showing quantity change per unit price change, and b is the quantity supplied at zero price. This linear function models the law of supply and helps predict producer behavior in response to price changes.

The slope (m) of a supply curve represents the quantity change per unit price change. For example, if the slope is 200, the quantity supplied increases by 200 pounds for every additional dollar in price. This positive slope reflects the law of supply, showing that producers supply more at higher prices.

The inverse supply function rearranges the standard supply equation to express price as a function of quantity supplied instead of quantity as a function of price. For a supply function Qs = 200P - 200, the inverse shows the minimum price producers require to supply goods, revealing the supply choke price threshold.

The supply choke price is the vertical intercept (b) on the supply curve where quantity supplied equals zero. It represents the minimum price below which producers will not supply any quantity of the good because it becomes unprofitable or infeasible. At this threshold, supply is effectively choked off due to cost considerations.

The intercept (b) in the supply equation Qs = mP + b indicates the quantity supplied when price is zero. A negative intercept, like -200 in the tomato example, means producers require a minimum price before supplying any quantity. This intercept directly determines the supply choke price and shifts the entire supply curve vertically.

Understanding the mathematical supply function enables economists to predict how producers respond to price changes and forecast market behavior. By analyzing the slope and intercept, economists can determine production thresholds, identify profitability levels, and model supply responses to various economic conditions affecting producer decisions.

To calculate quantity supplied at a specific price, substitute the price value into the supply equation Qs = mP + b. For the tomato example with Qs = 200P - 200, at a price of $2 per pound, quantity supplied equals 200(2) - 200 = 200 pounds. This direct calculation shows the relationship between price and quantity supplied.