Question

Mr. Mavis runs a beer distributorship and currently sells a case of beer for \(\$ 4.00\). In an informal study of 61 customers in his store one day, Mr. Mavis determined that above the price of \(\$ 4.00\), demand is slightly inelastic, while below the price of \(\$ 4.00\), demand is slightly elastic. If Mr. Mavis wishes to maximize total revenue, should he raise or lower price?

Short answer

To maximize total revenue, Mr. Mavis should lower the price from \(4.00 because demand is elastic below this price point. By lowering the price, the increase in quantity demanded will more than offset the decrease in price, leading to a higher total revenue. If he increases the price, demand is inelastic, and the decrease in quantity demanded won't offset the higher price, resulting in a smaller increase in total revenue.

Step-by-step solution

Understanding Elasticity

Elasticity is a measure of the responsiveness of quantity demanded to a change in price. If demand is elastic, the percentage change in quantity demanded will be greater than the percentage change in price, meaning that a decrease in price will lead to an increase in total revenue. If demand is inelastic, the percentage change in quantity demanded will be smaller than the percentage change in price, indicating that increasing the price will increase total revenue.

Maximizing Total Revenue

To maximize total revenue, Mr. Mavis needs to find the optimal price point where raising or lowering the price wouldn't lead to further changes in total revenue. Since the demand is elastic for prices below \(4.00 and inelastic for prices above \)4.00, we can derive the following information: 1. If the price is lowered (below $4.00), the increase in quantity demanded will more than offset the lower price, and total revenue will increase. 2. If the price is raised (above $4.00), the decrease in quantity demanded will be less than the increase in price, and total revenue will still increase.

Deciding the optimal price

From the above information, we can conclude that Mr. Mavis should reduce the price from \(4.00 to maximize total revenue. This is because demand is elastic below the \)4.00 price point, meaning that the increase in quantity demanded will outweigh the decrease in price, resulting in an overall increase in total revenue. If he increases the price, the decrease in quantity demanded will not be enough to offset the higher price, which in turn leads to a smaller increase in total revenue.

Key concepts

Elastic Demand

When we talk about elastic demand, we're looking at how sensitive consumers are to price changes. If demand is elastic, it means that even a small change in price can lead to a significant change in the quantity of a product that consumers are willing to buy. Simply put, if you lower the price a bit, you'll sell a lot more, and if you raise the price a bit, you'll sell a lot less. This happens because consumers have plenty of alternatives or because the product isn't a necessity, so they easily switch to something else if the price goes up.
For Mr. Mavis, the beer is in elastic demand when its price drops below $4.00. As he decreases the price, more customers will buy, and the increased sales volume will compensate for the lower price per case, boosting his total revenue.

Inelastic Demand

Inelastic demand describes a situation where changes in price have little effect on the quantity demanded. This typically occurs with essential goods or products with few substitutes, where consumers will continue buying regardless of price increases. This means, for products with inelastic demand, raising prices will usually increase total revenue.
For Mr. Mavis, when beer is priced above $4.00, the demand becomes inelastic. Raising the price won't cause a significant drop in the number of cases sold, so the total revenue will increase. The higher price per case more than offsets the slight decrease in sales, leading to an overall gain in revenue.

Total Revenue Maximization

Maximizing total revenue involves finding the price point where increasing or decreasing the price results in no additional gain in revenue. It's about hitting that sweet spot where you're making as much money as possible without losing customers due to high prices or losing profit margin due to low prices.
In Mr. Mavis's case, to maximize total revenue, he needs to focus on pricing strategies that take advantage of demand elasticity. Since demand below $4.00 is elastic, by reducing the price slightly, he can increase sales enough to boost overall revenue. If he were to raise the price above $4.00, the demand becomes inelastic, and total revenue could still increase but is less optimal compared to taking advantage of the elastic nature below $4.00. Therefore, Mr. Mavis should lower his prices to effectively capitalize on the elastic demand and maximize his total revenue.