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When we solve this for b (i.e., the x-intercept), we find that in this case, b = 0. This leaves us with the following equation: 500 = 250*2 + b.
#Equation maker out of ordered pairs update#
Revisiting our example, we can update the initial linear function to include the slope (i.e., Q s = 250P + b). Next, we replace P and Q s with the values of our first ordered pair (2, 500). Again, please note we are using the x-intercept because the axes are flipped. Then all we need to do is plug in the values of one ordered pair, which allows us to calculate the x-intercept of the function (by solving the equation for b). Now that we have calculated the slope of the function, we can plug that value into the initial function (instead of m).
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4) Calculate the x-Intercept of the Supply Function That means, they slope upwards from left to right. Please note that, unlike most demand functions, supply functions usually have a positive slope. That means the formula looks as follows: (250-500)/(1-2), which results in a slope of 250 (i.e., 250/-1). In the case of our example, the two ordered pairs are (2, 500) and (1, 250). Thus, we can use the following formula to calculate the slope: m = ( x 2 – x 1)/(y 2 – y 1). However, in this case, we need the inverse slope because our axes are flipped, as explained above. The slope is defined as the change in price divided by the change in quantity supplied between two points (i.e., the two ordered pairs). With the two ordered pairs and the basic linear function, we can now calculate the slope of the supply function. With this information, we can create two ordered pairs (500,2) and (250,1).ģ) Calculate the Slope of the Supply Function
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Meanwhile, at USD 1.00, the company only sells 250 bars. You will usually find the information needed to create these ordered pairs in statements like “at a price of y, sellers are willing and able to sell x units of good A” or “when the price rises to y, the supply of good B increases to x.” Going back to our example, we’ll assume that at USD 2.00, SuperCandy is willing to sell 500 candy bars. Note that each of these pairs represents the x and y coordinates of a point in the supply and demand diagram. This allows us to create what we call two ordered pairs (x 1,y 1) and (x 2, y 2). To calculate a linear supply function, we need to know the quantities supplied for at least two different prices. 2) Find Two Ordered Pairs of Price and Quantity Hence, the basic linear function in our example can be written as Q s = mP + b. We will call the function Q s, with P being the price of candy bars in the market. For now, let’s start with the supply function of an imaginary candy bar factory, called SuperCandy. Therefore, we’ll have to make some adjustments as we move along. That means we have the independent variable (i.e., price) on the y-axis and the dependent variable (i.e., quantity) on the x-axis.
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However, please note that in the supply and demand diagram, the two axis are flipped (for whatever reason). Meanwhile, m shows the slope of the function, and b represents its y-intersect (i.e., the point where the function intersects the y-axis). In this case, x and y represent the independent and dependent variables. In its most basic form, a linear supply function looks as follows: y = mx + b. Fortunately, we can use the same four-step process we use to calculate a linear demand function, with a few subtle differences: (1) Write down the basic linear function, (2) find two ordered pairs of price and quantity, (3) calculate the slope of the supply function, and (4) calculate its x-intercept.
#Equation maker out of ordered pairs how to#
Thus, in the following paragraphs, we will take a closer look at how to calculate a linear supply function. For the sake of simplicity, we often assume them to be linear, which makes it much easier to calculate them. They help us analyze and understand the most fundamental economic concepts and issues (e.g., the law of supply and demand, calculating producer surplus). Supply and demand functions play a crucial role in economics. By Raphael Cedar | Updated (Published Feb 14, 2018)