Supply, Demand,
& Elasticity Newsletter

Price Elasticity of Demand

Economics and Financial Decision Making

We can conceptualize the ideas of demand and supply in an industry. Through economic theory we can even predict the equilibrium price in the market through "the intersection of the supply and demand curves".

In practice we must work with elasticity in order to really use the information as opposed to just seeing what happened. As the quantity produced by an industry (or company) increases, total sales revenue (and profit) may increase, decrease, or stay the same. This exact relationship is explained with the price elasticity of demand: the percent change in quantity of a good demanded divided by the percent change in its price. We generally measure this by changing the price by 1% and observing the resulting change in quantity.

Demand curves are almost always downward sloping, thus an increase in price results in a decrease in quantity. Price elasticity of demand is therefore a negative number.

By defining variables:

Then we can calculate point elasticity by substituting as follows:
By reordering the variables we can manipulate this into something a little more useful:

From a manager's point of view, we like to operate in the "elastic" range of the demand curve because increasing sales quantity results in increased total revenue. When we operate in the inelastic region of the demand curve and increase in sales quantity results in decreased sales value. What is an example of a perfectly elastic demand curve (within reason). How about an iron lung? Or a heart operation, or oxygen at the International Space Station?

Consider the following demand curve:
P = $120 - 0.5Q

We can calculate the point elasticity of demand at some point, say where price equals $115/M3.

We should start with what we know:

Point elasticity = -23.0
We would interpret this by stating that at $115/M3, for every 1% increase in price, there will be a 23% decrease in quantity demanded in the market. Or for each $1.15 raise (drop) there is a 23% drop (raise) in quantity demanded in the market. So, if price decreased by $1.00 (from $115 to $114 (0.99%)) we would expect the quantity demanded in the market to increase by about 2,280 cubic meters a day.

We can calculate the average or arc elasticity of demand between $116/M3 and $114/M3.

When the demand curve is a straight line, the two methods, "arc" and "point" will always give you the same answer. However, the graph of a actual demand curve is generally curved; steep at low volumes and flat at higher volumes. The general mathematical expression of a demand curve is as follows:
(C), click to see larger imageIn the case of the West Coast of the Japanese log market for spruce the demand curve in July of 1998 was approximated by the following equation:
We can calculate the arc elasticity but the point elasticity is a little more difficult because the equation is not linear. In trigonometry we learned to take the derivative of an equation in order to get the slope at a certain point. The calculation looks like this:

Therefore, at a price of $115/M3 and volume of 11 thousand cubic meters a day, a 1% increase in price ($1.15/M3) will result in a 0.3125% decrease (3,438 cubic meter) in demand for logs. More precisely, a $0.10 increase in price (to $115.10/M3) will result in a 300 cubic meter drop in volume demanded to 10,700 cubic meters.

Applying the Concepts

For the most part, private forestland owners will not be in a position to supply sufficient quantity to a region to change the price in the market. We are in a position however, to observe how other forestland owners are reacting to conditions in the local market and recognize how major events will impact price and quantity in the market. For instance, in the Intermountain West Region (Idaho, Montana, Eastern Washington) high amounts of snow accumulation in the winter are common. Most of the high elevation forestlands are out of reach during the winter. Sawmills are faced with the challenge of purchasing sufficient log volumes in the late summer and fall to cut during the winter when processing volume often exceeds purchases.

During the summer of 2000, wildfires ravaged the region and closed the woods to logging. Sawmills were unable to purchase enough log volume in the summer and fall from the local region to sustain their production through the winter. As a result, quantity went down and their willingness to pay (price) went up considerably. Those forestland owners who could access their timberlands in the late fall and winter received higher than average prices.

Although it may be impossible (or improbable) to plan for such events, it is not out of reason to take advantage of those events when they occur. The key is to understand the overall relationship between supply and demand in the market, and how prices react to changes in the market.

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© 2007 Kamiak Econometrics, a Division of Kamiak Ridge, LLC
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Kamiak Econometrics, a Division of Kamiak Ridge, LLC