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In the world of economics, understanding the interplay between price and quantity is vital. When we alter the price of a product, it inevitably affects the quantity of that product that consumers are willing to purchase. This relationship is often depicted in demand curves, where typically, a lower price leads to higher quantity demands, and vice versa.

In our candy-selling scenario, as prices increase from $1.00 to $2.50, the quantity sold decreases incrementally. For example, when the price is low at $1.00, the highest quantity of candy, 2765, is sold. However, as the price rises to $2.50, only 430 candies are sold. This inverse relationship between price and quantity is a clear representation of the law of demand:

• Higher prices mean fewer consumers will buy the product.
• Lower prices generally increase consumer purchase.

Keeping this relationship in mind helps businesses and economists predict consumer behavior. Adjusting price points strategically allows maximizing sales volume or revenue under certain economic conditions.

Understanding the concept of inelastic and elastic demand is crucial in economics. Elasticity of demand indicates how sensitive quantity demanded is to a change in price. If demand is elastic, a small change in price leads to a large change in the quantity demanded. Conversely, inelastic demand means consumers are less responsive to price changes.

In our exercise, at a price of $1.00, the elasticity was calculated as approximately -0.93, which is less than 1. This indicates inelastic demand, meaning consumers do not significantly change their purchase quantities with price changes.

• Inelastic Demand ( |E| < 1 ): Consumers are not sensitive to price changes.
• Elastic Demand ( |E| > 1 ): Consumers are sensitive to price changes.
• Unit Elasticity ( |E| = 1 ): Proportional response to price changes.

As price increases along the table, the demand becomes more elastic, suggesting consumers become more price-sensitive at higher price points. This switch occurs because a higher price makes the relative cost difference more noticeable to a buyer.

Total revenue is a key metric for businesses to evaluate their financial performance, especially when considering price changes. It is calculated as the product of the price per unit and the quantity sold \[ R = p \times q \].

In the exercise, you see how total revenue changes with different prices for the candy:

• For a price of \(1.00, total revenue is 2765.
• As the price increases to \)2.00, total revenue also increases, but then it starts declining from this point as prices get higher.

This showcases an important insight: total revenue first increases as prices rise, but after reaching a particular point (where elasticity is close to 1), it starts decreasing. The idea is to maximize revenue where elasticity is unitary (|E|=1), avoiding the extremes where significant drops in quantity sold can adversely affect revenue.

To determine elasticity, we often use the midpoint formula. It provides a more precise measure compared to simple percentage changes because it takes into account the average percent changes in both quantity and price.

The formula is given by:

\[ E = \frac{(q_2 - q_1) / ((q_1 + q_2)/2)}{(p_2 - p_1) / ((p_1 + p_2)/2)} \]
• \(q_1\) and \(q_2\) are initial and final quantities.
• \(p_1\) and \(p_2\) are initial and final prices.

This formula is especially useful in avoiding the discrepancies that arise when using standard percentage change calculations. Instead of basing the percentage change off the initial or final values alone, the midpoint formula uses the average values, giving a more balanced elasticity estimate. This nuanced calculation is essential for better understanding consumer reactions to price changes over a range of price points.