Question

Suppose a worker receives a wage of \(\$ 20\) per hour. Compute the real wage (money wage deflated by the price index) corresponding to each of the following possible price levels: \(85,95,100,110,120 .\) What do you notice about the relationship between the real wage and the price level? Relate your finding to the slope of the aggregate supply curve.

Short answer

Answer: The negative relationship between the real wages and price levels, as demonstrated by a decrease in real wages when price levels increase, is connected to the upward sloping aggregate supply curve. This indicates that when labor costs are lower, producers are more willing to supply goods and services due to reduced production costs and increased profitability. Therefore, higher price levels lead to lower real wages and increased production, resulting in an upward-sloping aggregate supply curve.

Step-by-step solution

Calculate the money wage

In this case, the worker receives a wage of $20 per hour. We'll use this value in our calculations for the real wage.

Calculate the real wage for each price level

To find the real wage, we need to divide the money wage by the price index and multiply by 100. We'll do this for each given price level: For \(P=85\): Real Wage = \(\frac{20}{85} \times 100 = 23.53\) For \(P=95\): Real Wage = \(\frac{20}{95} \times 100 = 21.05\) For \(P=100\): Real Wage = \(\frac{20}{100} \times 100 =20\) For \(P=110\): Real Wage = \(\frac{20}{110} \times 100 = 18.18\) For \(P=120\): Real Wage = \(\frac{20}{120} \times 100 = 16.67\)

Analyze the relationship between real wages and price levels

By looking at the results, we can see that as the price level increases, the real wage decreases. This implies a negative relationship between the real wage and the price level.

Relate the findings to the aggregate supply curve

The aggregate supply curve shows the relationship between the quantity supplied by all producers in the economy and the price level. If there are higher price levels, producers are willing to supply more goods and services. Our results show that as the price level increases, the real wages decrease. This indicates that producers are willing to supply more goods and services when the real wages are lower. This is because the labor costs are relatively lower which reduces the producers' costs of production. Lower labor costs result in a more profitable production, encouraging producers to increase their supply. This negative relationship between the real wage and the price level is reflected in the upward sloping aggregate supply curve.

Key concepts

Aggregate Supply Curve

The aggregate supply curve is a central concept in economics that depicts the total quantity of goods and services that producers are willing to supply at different price levels.

Simply put, it's a graph showing the relationship between the overall price level in the economy and the amount of output businesses are willing to produce. As price levels rise, businesses tend to supply more, which is visually represented by an upward sloping curve in the short run. This is because higher prices can lead to increased revenue for producers, assuming costs do not rise at the same pace.

In the context of real wages, as they decrease, the cost of employment to businesses is lower, which can spur production as businesses are more willing and able to hire labor at lower costs. This relationship underpins the classical view that in the short run, the supply of goods and services within an economy expands with the increase in price levels, making the aggregate supply curve upward sloping.

Real Wage Calculation

Real wage refers to the purchasing power of a worker's earnings, taking into account the effects of inflation or deflation. It’s a measure of how many goods and services wages can actually buy, rather than just the number on a paycheck.

To calculate the real wage, you divide the nominal or money wage by the price index (a measure of overall price levels in the economy) and then multiply by 100. The formula is: \[ \text{Real Wage} = \left( \frac{\text{Money Wage}}{\text{Price Index}} \right) \times 100 \]

Using this formula can give insight into the actual economic well-being of workers rather than just how much money they earn. It’s crucial to understand that a higher money wage doesn’t necessarily mean increased purchasing power if prices rise faster than wages.

Price Index

A price index is a statistical measure that shows changes in the price level of a market basket of consumer goods and services over time. It is used to measure the average change in prices experienced by consumers.

For instance, the Consumer Price Index (CPI) is a common price index that indicates the cost of living by measuring changes in the price of a set basket of goods and services purchased by households. The CPI helps to adjust money wage into real wage. When we talk about deflating a wage, we are using the price index to account for inflation and provide a clearer picture of the purchasing power over time. If the price index rises, it typically signals inflation, meaning that your money wage can buy less than it did previously.

Money Wage

Money wage, also known as nominal wage, is the amount of money a worker is paid per hour or per work unit, before accounting for inflation. It’s the figure you see in your employment contract or pay slip.

Money wages can be misleading when looked at alone because they don’t take into account the cost of living, which can dramatically influence what you can actually afford with that wage. This is why economists use real wages for a more accurate picture of economic well-being. As prices rise (inflation), the value of the money wage falls unless wage increases keep up with inflation, thereby maintaining or increasing the real wage.