Starbucks made the morning coffee jolt a bit more expensive in $2022.$ The price of a brewed tall $($small$)$ coffee is now $$2\mathrm{.}65,$ up $18$ percent from one year ago. The price increase for all its products averaged $8$ percent overall. Despite the price hikes, few customers have given up their Starbucks fix. As Professor David Reibstein of the Wharton Business School noted, $$they$$ve got so much customer loyalty that they$$re still able to keep their particular customer.$$ Starbucks reported a $1$ percent increase in unit sales for the year and an $11$ percent increase in total revenue.

According to Front Page Economics $$Starbucks Raises Prices Again,$$LO$12-2$

$($a$)$ By what percent did Starbucks increase the price of a tall cup of brewed coffee?

$($b$)$ Calculate the price elasticity of demand for a tall brewed coffee if there was a decline in sales for a tall brewed coffee by $3$ percent.

$($c$)$ Identify the relationship between price elasticity of demand and total revenue.