How does the price elasticity of demand affect total revenue for luxury goods when their prices increase, and how does this relate to cross-price elasticity with substitute goods?

Price elasticity of demand measures how much the quantity demanded of a good changes when its price changes. For luxury goods, demand is often elastic, meaning that when prices increase, people buy significantly less of them. This decrease in quantity sold can lead to a decrease in total revenue because the loss in sales outweighs the higher price per unit. For instance, if a luxury car's price goes up, many buyers might decide not to purchase it, leading to lower overall sales and revenue. Additionally, if there are substitute goods available, the cross-price elasticity comes into play, as consumers may turn to those alternatives, further reducing sales of the luxury item.