Question

Suppose that a car dealership wishes to see if efficiency wages will help improve its salespeople's productivity. Currently, each salesperson sells an average of one car per day while being paid $$\$ 20$$ per hour for an eight- hour day. \(L O 17.8\) a. What is the current labor cost per car sold? b. Suppose that when the dealer raises the price of labor to $$\$ 30$$ per hour the average number of cars sold by a salesperson increases to two per day. What is now the labor cost per car sold? By how much is it higher or lower than it was before? Has the efficiency of labor expenditures by the firm (cars sold per dollar of wages paid to salespeople) increased or decreased? c. Suppose that if the wage is raised a second time to $$\$ 40$$ per hour the number of cars sold rises to an average of 2.5 per day. What is now the labor cost per car sold? d. If the firm's goal is to maximize the efficiency of its labor expenditures, which of the three hourly salary rates should it use: $$\$ 20$$ per hour, $$\$ 30$$ per hour, or $$\$ 40$$ per hour? e. By contrast, which salary maximizes the productivity of the car dealer's workers (cars sold per worker per day)?

Short answer

a. $160 per car; b. $120 per car, efficiency increased with labor cost decrease of $40; c. $128 per car; d. $30/hr maximizes efficiency; e. $40/hr maximizes productivity.

Step-by-step solution

Calculate Current Labor Cost per Car Sold

Currently, each salesperson sells 1 car per day and is paid $20 per hour for an 8-hour day. Calculate daily wages: \[ \text{Daily Wage} = 20 \times 8 = 160 \text{ dollars} \] Since a salesperson sells 1 car per day:\[ \text{Labor Cost per Car} = \text{Daily Wage} = 160 \text{ dollars} \]

Calculate New Labor Cost per Car Sold After Wage Increase to $30/hour

When the labor cost increases to \(30 per hour, the number of cars sold increases to 2 per day.Calculate new daily wages:\[ \text{Daily Wage} = 30 \times 8 = 240 \text{ dollars} \]With 2 cars sold per day:\[ \text{Labor Cost per Car} = \frac{240}{2} = 120 \text{ dollars} \]Compare with previous: \[ 160 - 120 = 40 \text{ dollars decrease} \]The labor cost per car sold is \)40 less, meaning the efficiency (cars sold per dollar of wages) has increased.

Calculate Labor Cost per Car Sold After Further Wage Increase to $40/hour

If the wage is increased to $40 per hour, the average number of cars sold rises to 2.5 per day.Calculate new daily wages:\[ \text{Daily Wage} = 40 \times 8 = 320 \text{ dollars} \]With 2.5 cars sold per day:\[ \text{Labor Cost per Car} = \frac{320}{2.5} = 128 \text{ dollars} \]

Determine Best Wage for Efficiency of Labor Expenditures

Efficiency is measured by cars sold per dollar of wages. Compare labor cost per car sold at different wages: - $20/hr: $160 per car - $30/hr: $120 per car - $40/hr: $128 per car The wage of $30/hr has the lowest labor cost per car, maximizing efficiency.

Determine Salary That Maximizes Productivity

Productivity is measured by cars sold per salesperson per day. - $20/hr: 1 car/day - $30/hr: 2 cars/day - $40/hr: 2.5 cars/day The wage of $40/hr maximizes productivity at 2.5 cars per day.

Key concepts

Labor Cost Analysis

The concept of labor cost analysis involves understanding how much money is spent per unit of output—in this case, cars sold by salespeople. It's critical for businesses to know this to efficiently allocate resources and maintain profitability. Let's break down the labor costs from the exercise above to better grasp this concept.

Initially, each salesperson is paid $20/hour, working eight hours daily, which sets the labor cost per car at 160 dollars since they sell one car per day. Upon increasing the wage to $30/hour, the labor cost per car reduces to 120 dollars, as sales improve to two cars a day. This change indicates an improved cost efficiency. Finally, raising wages again to $40/hour results in a slightly increased labor cost of 128 dollars per car, while sales go up to 2.5 cars per day.

Analyzing these numbers allows the dealership to understand the trade-off between higher wages and output levels. The most efficient wage per car sold is found at $30/hour, making it crucial to find that balance in wage settings. This analysis helps companies make informed decisions about employee compensation and expenditure effectiveness.

Productivity Measurement

Productivity measurement involves calculating the output each employee generates within a specified duration—in this scenario, the number of cars sold per day by each salesperson. This measure is key to understanding the impact of wages on sales performance.

Here’s how the dealership's productivity changes with different wages:

• At $20/hour, each salesperson sells 1 car per day, translating to the base productivity level.
• Increasing the wage to $30/hour doubles the daily sales to 2 cars per salesperson, showing a significant productivity boost.
• Further increasing the wage to $40/hour results in 2.5 cars per day, slightly enhancing productivity even more.

This rising trend indicates that higher wages might be motivating salespeople to work harder or perhaps attract more skilled workers. Measuring productivity helps businesses understand the correlation between wage changes and employee performance.

Wage Impact on Productivity

The impact of wages on productivity looks at how changes in compensation affect employee output. The exercise above shows a clear pattern: as wages increase, so does productivity, up to a certain point.

Initially, with a wage of $20/hour, the productivity is at its base level of 1 car per day. When the wage rises to $30/hour, productivity doubles to 2 cars per day, demonstrating that offering higher wages can lead to more motivated or capable employees. This increase, however, is not linear. When the wage is further raised to $40/hour, productivity grows to only 2.5 cars per day.

This exercise illustrates that while appropriately set efficiency wages can boost productivity, there are diminishing returns after a certain threshold. Businesses need to identify this balance to avoid excessive costs without corresponding increases in output. Understanding the wage-productivity relationship helps in designing wage structures that maximize both employee satisfaction and organizational efficiency.