show working production function: q = 6l – 0.5l2 where q = number of car washes per hour and l = number of workers. a) generate a schedule showing total product, average product and marginal product. (5 marks) b) the price of a basic car wash is $50. how many workers should he hire if each worker is paid $60/hour? (3 marks) c) he is considering hiring students on a part–time basis for $40/hour, do you think he should do so? explain. (2 marks)
a) To generate a schedule showing total product, average product, and marginal product, we need to calculate the values for each level of workers (l) and plug them into the given production function formula.
Total product (TP) is the total number of car washes per hour. We can calculate TP by substituting the values of l into the equation q = 6l – 0.5l^2.
Average product (AP) is the average number of car washes per hour per worker. It is calculated by dividing total product by the number of workers (l).
Marginal product (MP) is the additional output produced by each additional worker. It is calculated by finding the difference in total product when the number of workers increases by one.
Let's calculate the values for each level of workers (l = 1, 2, 3, 4, 5).
For l = 1:
TP = 6(1) - 0.5(1^2) = 6 - 0.5 = 5.5
AP = TP / l = 5.5 / 1 = 5.5
MP = TP for l = 1 - TP for l = 0 = 5.5 - 0 = 5.5
For l = 2:
TP = 6(2) - 0.5(2^2) = 12 - 2 = 10
AP = TP / l = 10 / 2 = 5
MP = TP for l = 2 - TP for l = 1 = 10 - 5.5 = 4.5
Similarly, calculate TP, AP, and MP for l = 3, l = 4, and l = 5.
b) To determine how many workers he should hire, we need to find the level of workers (l) where the marginal cost of hiring an additional worker is equal to the marginal benefit (price of a basic car wash).
In this case, the price of a basic car wash is $50.
The marginal benefit is the revenue generated by hiring an additional worker, which is the price ($50) multiplied by the marginal product (MP) of the last worker.
For each level of workers (l), calculate the MP and multiply it by the price ($50) to get the marginal benefit (MB).
Compare the marginal benefit (MB) to the wage paid per worker ($60/hour). If the wage is greater than the marginal benefit, it is economically inefficient to hire an additional worker.
Find the level of workers where the wage paid is equal to or slightly greater than the marginal benefit. This will be the optimal number of workers to hire.
c) To determine if he should hire students on a part-time basis for $40/hour, compare the wage ($40/hour) to the marginal benefit (MB) calculated in part (b).
If the wage is less than the marginal benefit, hiring students on a part-time basis would be more economically efficient as it would result in a higher profit.
If the wage is greater than the marginal benefit, it would be more efficient to stick with the current number of workers and not hire additional part-time students.