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The supply function is a mathematical equation that connects the quantity of supply of a good with its determining factors. Determinants include its own price, wages, energy costs, raw material prices, taxes, the selling price expectation, subsidies, and so on.

## How the supply function works

Usually, economists use several variables to explain how they affect supply. They assume other factors do not change or ceteris paribus.

For example, the supply function equation is** QS = a + bP – cW.**

Where

- Qs is the quantity (unit)
- P is the price of goods (Rp)
- W is wage (Rp)
- b and c are coefficients, each representing the magnitude of the effect of prices and wages.

From the equation, we say that supply quantity is a function of price and wages. The positive coefficient sign of the price shows a positive relationship between the price and the quantity supplied, as per the law of supply. A price increase of Rp1 increases the amount supplied by b units.

Conversely, supply quantity has an inverse relationship with wages. Higher wages increase production costs, disincentivizing producers to produce. If wages rise by Rp1, the supply quantity decreases c units.

## Convert the demand function into a demand curve

Because many factors affect the quantity of supply, it is difficult to illustrate all of them in the graph. To simplify the illustration, economists isolate factors other than the price of goods.

**Why the price?**

Price signals the company when it decides to produce and sell products. And economists agree that the price of goods is the most fundamental determinant of supply. Therefore, in a simple supply curve, economists only illustrate the relationship between the price of goods and the quantity supplied.

Remember, in the graph, the x-axis represents the quantity supplied, and the y-axis represents the price of the goods. That means, price is a function of quantity, not vice versa, as in the supply function.

To get the slope of the curve, we need to determine the inverse supply function. Let’s ignore wages, so the previous function becomes **QS = a + bP.** To reverse this function, we move the price variable (p) to the left of “=.” So, the inverse function becomes: **P = (1/b) Qs – (a/b).** The value **1/b** represents the slope, and **a/b **represents the intercept of the curve.