Question

Let's assume that each person in the United States consumes an average of 37 gallons of soft drinks (nondiet) at an average price of $$ 2$ per gallon and that the U.S. population is 294 million. At a price of $$ 1.50 per gallon, each individual consumer would demand 50 gallons of soft drinks. From this information about the individual demand schedule, calculate the market demand schedule for soft drinks for the prices of $$ 1.50 and $$ 2 per gallon.

Short answer

The market demand at \(2 per gallon is 10,878 million gallons (37 * 294 million), and at \)1.50 per gallon, it is 14,700 million gallons (50 * 294 million).

Step-by-step solution

Initial Data Review

Review the data provided: At a price of \(2 per gallon, each person consumes 37 gallons of soft drinks and the US population is 294 million. At a price of \)1.50 per gallon, consumption would increase to 50 gallons per person.

Calculate Market Demand at \(2 per Gallon

Multiply the average consumption per person at \)2 per gallon by the total population to get the market demand. Market demand at \(2 per gallon = 37 gallons/person * 294 million people.

Calculate Market Demand at \)1.50 per Gallon

Multiply the average consumption per person at \(1.50 per gallon by the total population to get the market demand. Market demand at \)1.50 per gallon = 50 gallons/person * 294 million people.

Perform the Calculations

For the price of \(2/gallon: Market demand = 37 * 294,000,000 gallons. For the price of \)1.50/gallon: Market demand = 50 * 294,000,000 gallons. Execute the multiplication to get the final values.

Key concepts

Demand Curve

Understanding the demand curve is crucial when studying market behaviors. It represents the relationship between the price of a good and the quantity demanded by consumers. In graphical terms, the demand curve is typically downward sloping, indicating that as the price of a product decreases, the quantity demanded increases, and vice versa.

In our exercise, two points on the demand curve for soft drinks can be plotted using the provided data. At a price of \( \$2 \) per gallon, the quantity demanded is 37 gallons per person, and at \( \$1.50 \) per gallon, it rises to 50 gallons. This inverse relationship between price and quantity demanded is a classic example of the law of demand and is visually represented by the demand curve.

Price Elasticity of Demand

The price elasticity of demand measures how sensitive the quantity demanded of a good is to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. If the quantity demanded changes significantly with a small change in price, the demand is described as elastic. Conversely, if quantity demanded is relatively unresponsive to price changes, it is inelastic.

Considering our soft drink example, a reduction in price from \( \$2 \) to \( \$1.50 \) leads to a significant increase in demand from 37 to 50 gallons per person, suggesting that the demand for soft drinks might be relatively elastic. However, calculating the precise elasticity would require using the formula for elasticity and additional points on the demand curve.

Consumer Behavior

Consumer behavior examines how individuals make decisions to spend their available resources (time, money, effort) on consumption-related items. This includes what they buy, why they buy it, how much they buy, when they buy it, and how often they use it. In this context, the consumption of soft drinks can be influenced by factors such as price, income level, personal preferences, health concerns, and advertising.

From the exercise, we can infer that when the price drops, people are willing to consume more soft drinks, which could be due to the lower cost or increased perceived value at a lower price. This behavior reveals the importance of pricing strategies in influencing consumer purchasing patterns.

Equilibrium Price

The equilibrium price, also known as the market-clearing price, is the price at which the quantity demanded by consumers equals the quantity supplied by producers. At this point, there is no excess supply or demand, and the market is stable. The equilibrium price is determined by the intersection of the supply and demand curves.

In real-world markets, finding the equilibrium price helps businesses determine the optimal price for their products, ensuring they sell their entire stock without under or overcharging. This exercise does not provide data on supply or the equilibrium point, but understanding that at a lower price, demand increases, helps infer that if the supply remains constant, the equilibrium price could be lower than \( \$2 \) per gallon for soft drinks.