Question

Jameel runs a driver education school. The more driving instructors he hires, the more driving lessons he can sell. But because he owns a limited number of training automobiles, each additional driving instructor adds less to Jameel's output of driving lessons. The accompanying table shows Jameel's production function per day. Each driving lesson can be sold at \(\$ 35\) per hour. Determine Jameel's labor demand schedule (his demand schedule for driving instructors) for each of the following daily wage rates for driving instructors: \(\$ 160, \$ 180,\) \(\$ 200, \$ 220, \$ 240,\) and \(\$ 260\)

Short answer

Answer: To answer this question, refer back to the labor demand schedule obtained in step 4 of the solution. Find the number of driving instructors that maximize profit at a wage rate of 180.

Step-by-step solution

Identify variables in the problem

First, let's identify two important aspects of this exercise: the production function, which shows how many driving lessons Jameel can sell for different numbers of driving instructors, and the price per driving lesson (found to be \(35\) per hour). We also need to consider the different daily wage rates for the driving instructors as given in the exercise.

Define profit function

We need to calculate the profit for each level of driving instructors. To do that, we need to define a profit function as follows: Profit = (Number of driving lessons sold * Price per driving lesson) - (Number of driving instructors * Wage rate per driving instructor) Let's apply this formula to each level of driving instructors and calculate the profit for each wage rate given.

Calculate profit for each level of driving instructors and wage rates

Let's create a table with the number of driving instructors (from \(0\) to maximum given in the production function) and calculate the profit for each wage rate. Here, for each number of driving instructors, calculate Profit using the formula: Profit = (Number of driving lessons sold * 35) - (Number of driving instructors * Wage rate per driving instructor)

Determine labor demand schedule

After calculating the profit for each level of driving instructors and wage rates, we need to determine the labor demand schedule. This means finding the number of driving instructors that Jameel should hire for each given wage rate. For each wage rate, we should select the number of driving instructors that yield the highest profit. If multiple levels of driving instructors result in the same profit, Jameel can choose any of them (or choose the range between them). For each given wage rate (160, 180, 200, 220, 240, 260), find the number of driving instructors that maximize the profit based on the calculated profit table in step 3. This will give us the labor demand schedule for Jameel's driving education school.