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, 20,000 units were produced, requiring 80,000 pounds of materials and 40,000 hours of labor. An engineering efficiency study commissioned by the local university revealed that Carsen can produce the same 20.000 units of output using either of the following two combinations of Inputs: Combinations: Materials 70,000 $4,600 Labor 38,000 33,500 The cost of materials is $10 per pound; the cost of labor is $15 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? 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 20,000 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	20,000/70,000	28.57%	20,000/80,000	25%
Labor	20,000/38,000	52.63%	20,000/40,000	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*10)	700,000	800,000	100,000
Lab (Hour*15)	570,000	600,000	30,000
Total	1,270,000	1,400,000	130,000
Technical Efficiency
2. Output-Input Ratio
	F2		Current
Material	20000/84,600	23.64%	20000/80,000	25%
Labor	20000/33,600	59.52%	20000/40,000	50%
	700,000		800,000
	570,000		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*8)	700,000	846,000	146,000
Lab (Hour*12)	570,000	403200	-166,800
Total	1,270,000	1,249,200	-20,800
YES

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