Question

Consider the following price information: $$ \begin{array}{lll} & \text { Year 1 } & \text { Year 2 } \\ \cline { 2 - 3 } \text { Cup of coffee } & \$ .50 & \$ 1.00 \\ \text { Glass of milk } & \$ 1.00 & \$ 2.00 \\ \hline \end{array} $$ a. Based on the information given, what was the inflation rate between year 1 and year 2? b. What happened to the price of coffee relative to that of milk between year 1 and year 2?

Short answer

Answer: The inflation rate between year 1 and year 2 is 100%. The relative price of coffee to that of milk did not change between the two years, as the ratio remained at 0.50 in both years.

Step-by-step solution

Calculate the percentage change in the prices of coffee and milk

First, we need to calculate the percentage change in the price of each item between year 1 and year 2: Percentage change in the price of coffee: $$ \frac{\text{Price in Year 2} - \text{Price in Year 1}}{\text{Price in Year 1}} \times 100 $$ $$ \frac{1 - 0.50}{0.50} \times 100 = 100\% $$ Percentage change in the price of milk: $$ \frac{\text{Price in Year 2} - \text{Price in Year 1}}{\text{Price in Year 1}} \times 100 $$ $$ \frac{2 - 1}{1} \times 100 = 100\% $$

Calculate the inflation rate

Now we can find the average percentage change in the prices of the two items to calculate the inflation rate: $$ \text{Inflation rate} = \frac{(\text{Percentage change in coffee price} + \text{Percentage change in milk price})}{2} $$ $$ \text{Inflation rate} = \frac{(100\% + 100\%)}{2} = 100\% $$ The inflation rate between year 1 and year 2 is 100%.

Calculate the ratio of the price of coffee to the price of milk in both years

We can now find the ratio of the price of coffee to the price of milk in both years: Year 1: $$ \frac{\text{Price of coffee}}{\text{Price of milk}} = \frac{0.50}{1} = 0.50 $$ Year 2: $$ \frac{\text{Price of coffee}}{\text{Price of milk}} = \frac{1}{2} = 0.50 $$

Compare the two ratios

The ratio of the price of coffee to the price of milk in year 1 is 0.50, and the ratio in year 2 is also 0.50. Since the two ratios are equal, it appears that the relative price of coffee to that of milk did not change between year 1 and year 2.

Key concepts

Price Level Changes

In economics, understanding how prices change over time is vital as it affects both consumers and businesses. The example of prices for a cup of coffee and glass of milk from one year to another illustrates this point effectively.

When we see that the price of coffee has risen from \(0.50 to \)1.00, and similarly that milk has gone from \(1.00 to \)2.00, we're witnessing price level changes. These changes are indicative of variations in purchasing power and cost of living.

A crucial metric to consider in such cases is the inflation rate, which broadly reflects the average increase in prices across a range of goods and services. In our exercise, the double price for both coffee and milk suggests a high inflation rate, assuming these items represent a broader basket of goods.

Percentage Change Formula

The percentage change formula is a mathematical way to express the degree of change over time. This is important not just for economists, but for anyone wanting to understand shifts in cost, sales, population, or any variable that changes in quantity.

To calculate this change, we use the formula: \[ \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100 \].

For the coffee and milk prices, the calculation would demonstrate a 100% increase for both. This stark increase is indicative of hyperinflation if it represents a consistent trend across various goods and services.

Understanding how to properly compute the percentage change is crucial, as it lays the groundwork for analyzing economic health and making informed decisions whether you're a policymaker, business owner, or a consumer trying to budget.

Economic Indicators

Economic indicators are statistics that help us assess the health of an economy. They come in various forms, such as GDP, unemployment rates, and inflation rates.

In the context of our exercise, inflation is the economic indicator in question. The inflation rate is especially significant as it directly impacts the cost of living, savings, and investment returns.

While the calculated 100% inflation rate in our example is a simplification for illustrative purposes, real-world inflation rates are key figures in economic policy, business planning, and personal finance. They help predict future price levels, indicate stability, and can signal if corrective measures are needed in economic policy.

Understanding economic indicators like the inflation rate allows for better financial planning and enables a broader discussion on economic policies and their impacts on daily life.