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# How to calculate a demand function

Knowing the demand function calculation can give you an insight into the demand and optimal sale price for a given product based on consumer’s behavior. It doesn’t always follow that the cheapest price will give you the best sales volume, the same applies with high prices. Calculating the demand function can save you from costly market testing at numerous different prices as with just a few price tests you can do the relevant calculation to plot the rest of the graph based on known demand curves in economics.

Collect the data you have for a given product sold at varying prices. You will need to create an individual graph for each product as different products will produce different results.

Draw a graph with sales prices listed on the vertical Y axis. Label the horizontal X axis "Quantities Sold."

Plot the data you have collected on the graph and draw a line showing the general direction the group of points seem to be heading, this is known as the line of best fit. If you are looking for a more accurate line of best fit then you will need to calculate the linear regression.

Calculate the rise over run of the slope by dividing the rise where the line of best fit crosses the X Axis and run being where it crosses the Y Axis. This must be shown as a negative figure (Call it a).

Find the figure for the sales price where the line of best fit crosses the X axis (Call it b).

Choose the quantity along the purchases Y axis and put it into the following equation to calculate the demand function X=aY+b (price = a multiplied by purchases plus b).

#### Tip

The calculation for linear regression is Y=a+bX, where “a” is the intercept of y when x equals 0 and “b” is the rise over run of the slope. The more data you can gather to plot on the graph the more accurate your demand function calculation will be.

• Graph Paper
• Pen
• Calculator