## Section5.3Elasticity

Elasticity of demand is a concept from economics that looks at relative rate of change rather than rate of change. We want to look at how we express this as a variant of the derivative.

##### 11.

List 3 items where you would expect the demand price to be elastic and 3 items where you would expect the demand price to be inelastic. Explain why you have put each item into its category.

Solution.

Hint:

Elastic ($$E \gt 1$$) The book mentions an elastic market points to something that can be easily substituted and where revenue goes up when prices go down. Examples are a particular cut of meat and for instance a brand of clothes. If there is a sale we would choose the cheaper item. What else falls into this category?

Inelastic ($$E \lt 1$$) This is something where an increase in price would not decrease revenue. One situation would be items that are not easily substituted. For example wedding rings or life saving medication. What else falls into this category?

##### 12.

Give reasons why a vendor might set a price that does not maximize revenues.

##### 13.

If the short-term elasticity for widgets is 2.5 and the price is raised by 10%, find the percent change in quantity and revenue.

Solution.
\begin{equation*} E=-\frac{\text{percent change in quantity}}{\text{percent change in price}} \end{equation*}

So we have $$2.5=\frac{-\text{percent change in quantity}}{10 \text{ percent}}\text{,}$$ and thus $$\text{change in quantity}=-25\%\text{.}$$

And $$\text{new revenue}=(1.10\text{ old price})(0.75\text{ old quantity})=.8250\text{ old price}\text{.}$$

Hence we have a $$-17.5\%$$ change in revenue.

##### 14.

If the short-term elasticity for thingamabobs is 0.8 and the price is raised by 10%, find the percent change in quantity and revenue.