Question

Suppose you are currently carning \(\$ 15\) an hour. If the inflation rate over the current year is 10 percent and your firm provides a cost-of-living raise based on the rate of inflation, what would you expect to carn after your raise? If the cost-of-living raise is always granted on the basis of the past year's inflation, is your nominal income really kecping up with the cost of living?

Short answer

Answer: The expected hourly wage after receiving the 10% cost-of-living raise is $16.50. It is difficult to determine if this raise is keeping up with the cost of living without information about the current year's inflation rate. The raise helps maintain purchasing power based on the previous year's inflation, but discrepancies may occur if the current year's inflation rate is different.

Step-by-step solution

Calculate the Raise

The cost-of-living raise is based on the inflation rate, which is 10 percent in this case. To calculate the raise, multiply the current hourly wage by the inflation rate: Raise = (Current hourly wage) × (Inflation rate) Raise = $15 × 0.10 = \$1.50

Compute the New Hourly Wage

Now, we will add the cost-of-living raise to the current hourly wage to compute the new expected wage after the raise: New hourly wage = (Current hourly wage) + (Raise) New hourly wage = $15 + \$1.50 = \$16.50

Analyze if the Nominal Income is Keeping Up with the Cost of Living

Receiving a cost-of-living raise based on the previous year's inflation helps to maintain the purchasing power of the income, meaning it aims to keep the real income unchanged. However, it's important to consider that the base for this cost-of-living raise is the previous year's inflation, which means there may be discrepancies if the current year's inflation is different. In this case, there is no information about the current year's inflation, so it is impossible to determine if the nominal income is truly keeping up with the cost of living. If the current year's inflation rate remains constant at 10%, then the raise would adjust the income to be in line with the cost of living. However, if the current year's inflation rate is higher or lower than 10%, the nominal income might not perfectly align with the cost of living. In conclusion, the cost-of-living raise can help to keep up with the cost of living, but discrepancies may occur if there are changes in the inflation rate.

Key concepts

Inflation Rate

Understanding the inflation rate is crucial as it signifies the rate at which the general level of prices for goods and services is rising, and, subsequently, how it erodes the purchasing power of money. It's typically expressed as a percentage, indicating the annual change in the cost of living. For instance, an inflation rate of 10% means that what cost \(100 a year ago now costs \)110.

In the context of salary adjustments, the inflation rate is used to calculate cost-of-living raises. This aims to ensure that employees' wages increase proportionately to the inflation rate so that their purchasing power remains stable. However, if the cost-of-living adjustment is based on past inflation data, there may be a lag, and the adjustments might not fully match real-time changes in the cost of living.

Nominal Income

Nominal income refers to the amount of money paid to an individual or employees without adjusting for inflation. For example, if you earn \(15 per hour and receive a raise that brings your compensation to \)16.50 per hour, your nominal income has increased.

However, nominal income doesn't provide a complete picture because it doesn't account for the change in the value of money due to inflation. It's important to distinguish between nominal income and real income, where the latter is adjusted for inflation and reflects actual purchasing power. When evaluating whether wages are keeping up with the cost of living, it's essential to look at the real income rather than just the nominal figures.

Purchasing Power

Purchasing power refers to the quantity of goods or services that one unit of money can buy. Inflation erodes purchasing power since the value of money decreases as prices rise. This is a critical concern for workers and their salaries.

A cost-of-living raise, if precisely aligned with the actual inflation rate, helps maintain purchasing power. However, discrepancies arise if the inflation rate accelerates beyond the raise or if the raise is benchmarked against historical, not current, inflation data. For example, if the actual inflation rate were to increase to 12% after you've received a 10% raise based on last year's figures, your purchasing power would effectively decrease, despite the nominal increase in your wage. Therefore, for nominal income to genuinely keep pace with the cost of living, cost-of-living raises would need to be reflective of real-time changes in the inflation rate.