## 9/7/15

### What is a price function?

Sometimes you will be asked to define a price function. When you receive such a question, it is probably in regards to a supply and demand graph, and you will be asked to graph said price function. The three components of a price function include: price (as you probably expected), an intercept, and quantity. It is also possible for a price function to include many other variables such as preferences, prices of related goods, income, number of buyers, etc. but this is for more complicated price functions (and upper division style classes).

A price function generally looks like:

P=f(Q)

Where price is stated to be a function of quantity. This means that price is only depended on quantity.
For example, we could have a price function that looks like:

P=10-2Q

Is this example, 10 represents the intercept, and the coefficient on quantity is 2. Price will be equal to 10 if quantity is equal to 0. As quantity rises, we see that price will go down. Eventually as quantity equals 5, we see that the price will be 0.

Price functions can also be called inverse demand functions. This is because a demand function has quantity as a function of price, but through simple algebra, we can solve for p to get the price function. This is a necessary step if you intend to graph the function, but price is on the y-axis.

Typically, you will be given problems that give you a supply or demand function. You can obtain the price function (for either the consumers or producers) by solving for price. Consider the example below:

Originally you are given a demand function:

Qd = 500 - 10P

We can see that quantity is dependent on price, however, in order to graph this on a typical supply and demand graph we need to find the inverse demand function (or price function). We can do this by dividing both sides by 10 to get:

Qd/10 = 50 - P

Now subtract Qd/10 from both sides, and add P to both sides. This gives us:

P = 50 - Qd/10

Note that P is solved for, and is dependent on an intercept (50) and quantity (with the coefficient of 1/10). This gives us the price function (or inverse demand function) that can now be visually represented in a graph.

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