Question

Productivity Measurement, Technical and Allocative Efficiency, Partial Measures

Carsen Company produces handcrafted pottery that uses two inputs: materials and labor. During the past quarter, 24,000 units were produced, requiring 96,000 pounds of materials and 48,000 hours of labor. An engineering efficiency study commissioned by the local university revealed that Carsen can produce the same 24,000 units of output using either of the following two combinations of inputs:

	Materials	Labor
Combinations:
F1	73,000	84,900
F2	35,000	33,500

The cost of materials is $7 per pound; the cost of labor is $16 per hour.

Required:

1. Compute the output-input ratio for each input of Combination F1. If required, round your answers to two decimal places.

Materials
Labor

Does this represent a productivity improvement over the current use of inputs?
Yes

What is the total dollar value of the improvement?
$

Classify this as a technical or an allocative efficiency improvement.
Technical efficiency

2. Compute the output-input ratio for each input of Combination F2. If required, round your answers to two decimal places.

Materials
Labor

Does this represent a productivity improvement over the current use of inputs?
Yes

Now, compare these ratios to those of Combination F1. What has happened?
F2 has lower productivity for materials and higher productivity for labor.

3. Compute the cost of producing 24,000 units of output using Combination F1.
$

Compare this cost to the cost using Combination F2.

Cost of Combination F1	$
Cost of Combination F2
Difference	$

Does moving from Combination F1 to Combination F2 represent a productivity improvement?
No

Answer 1

1. Output - Input ratio = Output/input

Materials (F1) = 24,000/73,000 = .33

Labour (F1) = 24,000/84,900 = .28

Current output-input ratio

Materials = 24,000/96,000 = .25

Labour = 24,000/48,000 = .50

Current cost of 24,000 units = (96,000 x 7) + (48,000 x 16) = 672,000 + 768,000 = $1,440,000

Cost of 24,000 units under F1 = (73,000 x 7) + (84,900 x 16) = 511,000 + 1,358,400 = $1,869,400

As F1 has higher cost than current use of inputs, F1 is less productive and has a higher cost by $429,400.

It has a higher productivity for materials but a ver low productivity for labour. the improvement in materials' productivity is allocative efficiency improvement.

2. Output-input ratio

Materials (F2) = 24,000/35,000 = .69

Labour (F2) = 24,000/33,500 = .72

This shows productivity improvement over current use of inputs.

F2 has better productivity than F1 for both the inputs.

3. Cost of combination F1 = $1,869,400

Cost of combination F2 = $781,000 {(35,000 x 7) + (33,500 x 16)}

Difference = $1,088,400

yes, Moving from F1 to F2 represents a productivity improvement.