Question

A statistician in the Department of Agriculture observed that every year the temperature in Florida dropped below \(20^{\circ} \mathrm{F}\), the price of oranges was above normal while the quantity sold was below normal. He concluded that Florida oranges did not obey the law of supply. Is he correct?

Short answer

The statistician's conclusion that Florida oranges do not obey the law of supply is not accurate, as he focuses on the relationship between price and quantity sold, while the law of supply concerns the relationship between price and quantity supplied. Cold temperatures can damage orange crops, causing reduced production, resulting in higher prices and fewer oranges to sell. To draw a valid conclusion, data on the relationship between the price of oranges and the quantity supplied, as well as the impact of cold temperatures on orange production, must be considered.

Step-by-step solution

Review the Law of Supply

The law of supply states that there's a positive relationship between a product's price and the quantity supplied, meaning that an increase in price will lead to an increase in quantity supplied, and vice versa. The law is based on the premise that higher prices provide incentives for producers to produce more.

Evaluate the Statistician's Observation

The observed data covers only years when the temperature dropped below \(20^{\circ}\mathrm{F}\). In those years, the price of oranges was higher while the quantity sold was lower. It's important to consider that we don't have any information about the quantities supplied in those years, just the quantity sold.

Determine the Role of External Factors

Cold temperatures could damage orange crops and lead to reduced production, which could result in higher prices due to scarcity. Since reduced production means fewer oranges to sell, this would lead to a lower quantity being sold. So, the reduced quantity sold is a result of real-world factors (cold temperatures) rather than a violation of the law of supply.

Analyze the Conclusion

The statistician's conclusion is not accurate because he associates the price with the quantity sold, not the quantity supplied. The law of supply refers to the relationship between the price and quantity supplied, whereas the observed relationship is between price and quantity sold. There's simply is no contradiction between the law of supply and the observed data, which relates to the quantity sold, not quantity supplied.

Final Thought

The observed relationship between price, quantity sold, and cold temperatures is not enough evidence to conclude that Florida oranges do not obey the law of supply. In order to draw a valid conclusion, we would need data on the relationship between the price of oranges and the quantity supplied, and to consider factors like the impact of cold temperatures on orange production.

Key concepts

Supply and Demand

Understanding the dynamics of supply and demand is fundamental to grasping economic principles. This concept explains how the quantity of a product that producers are willing to supply at different prices interacts with the quantity that consumers are willing to buy. When prices rise, producers are generally more inclined to increase production and supply more of the good because they can potentially earn more revenue. Conversely, higher prices may deter some consumers from purchasing as much of the good, decreasing the quantity demanded.

The interplay between supply and demand determines the price and quantity of goods sold in markets. If we look at the exercise regarding Florida oranges, we see an unusual situation where a decrease in temperature, an external factor, leads to higher prices and lower quantities sold. While this may seem counterintuitive, it's essential to recognize the role of external factors that can affect supply (such as weather conditions), which subsequently impacts the prices and quantities that appear in the market.

Price Elasticity

Price elasticity is a concept that measures how responsive the quantity demanded of a good is to a change in its price. Essentially, it gauges whether a rise or decline in price will significantly affect the quantity that consumers buy. The elasticity of a product can be described as elastic, inelastic, or unitary elastic.

An elastic good means that a small change in price leads to a large change in quantity demanded. For instance, if luxury goods become slightly more expensive, people may choose not to buy them, showing high elasticity. In contrast, an inelastic good means that changes in price have little impact on the quantity demanded. Essential items like medication often exhibit inelasticity because people need them regardless of the cost.

When applying these principles to the case of the Florida oranges, the temperature drop caused a shortage that led to higher prices. Since oranges have few substitutes, the demand may be relatively inelastic in the short term, which allows the price to rise without a significant drop in quantity demanded. Consumers still need to purchase oranges, despite the higher cost, up to a certain point.

Market Equilibrium

Market equilibrium occurs when the quantity of a good that consumers are willing to buy equates to the quantity that producers are willing to sell, at a certain price level. This balance is where supply equals demand, often visualized where the supply and demand curves intersect on a graph. At this point, there is no inherent tendency for the price to change, because the market forces are in harmony.

However, equilibrium can be disrupted by external factors, as evidenced in the orange market example. The cold snap in Florida likely decreased the supply of oranges, shifting the supply curve to the left and creating a new, higher equilibrium price with a lower equilibrium quantity. This adjustment reflects how markets react to external shocks, striving to find a new balance point in response to changing conditions.

It is important to note that market equilibrium is a theoretical state where all else is held constant; in reality, markets are dynamic and constantly adjusting to new information and conditions, such as weather changes affecting crop yields.