Question

The case of Fina Auto Speed and Quality Auto Inc., modifies 375 autos per year. The manager is interested in obtaining a measure of overall performance. He asked you to provide him with productivity measures of last year's performance as a benchmark for future comparison. You have assembled the following data: resource inputs were labour, 10,000 hours; 500 suspension and engine modification kits; and energy 100,000 kw-hours. Average labour cost last year was 2000-cent per hour, kits cost $1000 each, and energy costs were $3 per kw-hour.

a. What is the labour productivity?
b. What is the multi-factor productivity?
c. Assume that after receiving the first productivityrelated report, the manager has increased the modified auto number to 420 . Also, he has purchased a new machine by investing $1000 which in turn reduces the energy costs to $1 per kw-hour. No more changes have been made. Considering all of these, calculate the new multi-factor productivity.
d. Calculate the preductivity growth rate in multifactor productivity.
e. Plot the MFP figures on a graph.
f. Explain the scenario briefly considering each section.

Answer 1

a. The labor productivity is 0.0375 autos per hour. b. The multi-factor productivity is 0.000875 autos per dollar of input. c. The new multi-factor productivity is 0.000952 autos per dollar of input. d. The productivity growth rate is 8.8%. e. The MFP figures can be plotted on a graph. f. The scenario involves measuring productivity and analyzing its changes.

Step-by-step explanation:

a. To calculate labor productivity, we need to divide the total output by the total number of hours worked. In this case, the total output is 375 autos and the total hours worked is 10,000 hours. Therefore, the labor productivity is 375 autos / 10,000 hours = 0.0375 autos per hour.

b. To calculate multi-factor productivity, we need to divide the total output by the total value of all inputs. In this case, the total output is 375 autos, the total labor cost is 10,000 hours * $20 per hour = $200,000, the total kit cost is 500 kits * $1000 per kit = $500,000, and the total energy cost is 100,000 kw-hours * $3 per kw-hour = $300,000. Therefore, the multi-factor productivity is 375 autos / ($200,000 + $500,000 + $300,000) = 0.000875 autos per dollar of input.

c. With the increased modified auto number to 420 and the reduced energy cost to $1 per kw-hour, the new multi-factor productivity can be calculated using the same formula as in part b. The total output is now 420 autos and the total energy cost is 100,000 kw-hours * $1 per kw-hour = $100,000. Therefore, the new multi-factor productivity is 420 autos / ($200,000 + $500,000 + $100,000) = 0.000952 autos per dollar of input.

d. The productivity growth rate in multi-factor productivity can be calculated by subtracting the initial multi-factor productivity from the new multi-factor productivity and dividing the result by the initial multi-factor productivity. In this case, the initial multi-factor productivity is 0.000875 and the new multi-factor productivity is 0.000952. Therefore, the productivity growth rate is (0.000952 - 0.000875) / 0.000875 = 0.088 (or 8.8%).

e. To plot the MFP figures on a graph, we can use a line graph with time (in years) on the x-axis and MFP (autos per dollar of input) on the y-axis. We can plot the initial MFP and the new MFP numbers for each year to visualize the change in productivity over time.

f. In this scenario, the manager is interested in measuring the overall performance of the company in terms of productivity. The labor productivity (a) measures the number of autos modified per hour of labor, while the multi-factor productivity (b) measures the number of autos modified per dollar of input (including labor, kits, and energy). The manager then increases the modified auto number and purchases a new machine, which affects the multi-factor productivity (c). The productivity growth rate (d) indicates the rate of change in multi-factor productivity over time, and plotting the MFP figures on a graph (e) allows for visualizing the productivity trend.