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, 25,000 units were produced, requiring 100,000 pounds of materials and 50,000 hours of labor. An engineering efficiency study commissioned by the local university revealed that Carsen can produce the same 25,000 units of output using either of the following two combinations of inputs:

	F1	F2
Combinations:
Materials	78,000	84,600
Labor	31,000	33,200

The cost of materials is $7 per pound; the cost of labor is $12 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?

What is the total dollar value of the improvement?
$

Classify this as a technical or an allocative efficiency improvement.

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?

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

3. Compute the cost of producing 25,000 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?

Answer 1

ANSWER

1 Output - Input Ratio
	F1		Current
Material	25,000 /78,000	32.05%	25,000 /100,000	25%
Labor	25,000 /31,000	80.64%	25,000 /50,000	50%
Does this represent a productivity improvement over the current use of inputs?
Yes
What is the total dollar value of the improvement? $
	F1	Current	$ Improvement
Mat (Mat*7)	546,000	700,000	175,000
Lab (Hour*12)	372,000	600,000	228,000
Total	918,000	1,300,000	403,000
Technical Efficiency
2. Output-Input Ratio
	F2		Current
Material	25,000 /84,600	29.55%	25,000 /100,000	25%
Labor	25,000 /33,200	75.30%	25,000 /50,000	50%
	546,000		700,000
	372,000		600,000
Does this represent a productivity improvement over the current use of inputs?
Yes
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. $
	F1	F2	Diff
Mat (Mat*7)	546,000	592,200	46,200
Lab (Hour*12)	372,000	398,400	26,400
Total	1008000	990,600	72,600
YES