questionBig Winner is debating decreasing the price of its rooms to $175 per night. Under the initial demand conditions, you can see that this would cause its total revenue to DECREASE. Decreasing the price will always have this effect on revenue when Big Winner is operating on the INELASTIC portion of its demand curve.
answerWhen the Big Winner charges $200, it can fill 300 rooms at that price.
Total revenue is equal to price times quantity. Therefore, you can compute Big Winner's revenue at this price in the following way:
Total Revenue = PriceĂ—Quantity
$200*300 = 60000
By lowering its price to $175, Big Winner can fill 325 rooms. In this case, total revenue is $175 per room per nightĂ—325 rooms=$56,875 per night$175 per room per nightĂ—325 rooms=$56,875 per night, a decrease of $3,125.
When demand is inelastic, you know that the percentage change in price is larger than the percentage change in quantity. This means that total revenue will move in the same direction as the price change. Thus, when price increases, so does total revenue; when price decreases, total revenue decreases as well.
When demand is elastic, you know that the percentage change in price is smaller than the percentage change in quantity, because consumers are highly sensitive to changes in price. This means that price and total revenue move in opposite directions. Thus, when price decreases, total revenue increases; when price increases, total revenue decreases.
Because total revenue decreases when Big Winner decreases its price, it must be operating on the inelastic portion of its demand curve.
Another way to confirm this is by directly examining the price elasticity of demand for Big Winner's rooms. The price elasticity of demand measures the responsiveness of consumers to changes in price. For example, if consumers change their purchasing behavior very little in response to a drastic change in price, demand is said to be inelastic; if consumers change their purchasing behavior a lot in response to a small change in price, demand is said to be elastic.
The price elasticity of demand is the percentage change in quantity divided by the percentage change in price. If the Big Winner drops its price from $200 to $175 per night—a decrease of 12.5%—the quantity of rooms demanded increases from 300 to 325, an increase of about 8.3%:
Price Elasticity of Demand = Percentage Change in Quantity / Percentage Change in Price
Since the percentage change in quantity demanded is less than the percentage change in price, the price elasticity of demand is less than 1, and demand is inelastic in this region. (Note: The percentage change calculations in this problem do not use the midpoint method. )