In 2007, Hepworth Products, Inc., used the following input combination to produce 8,000 units of output:
Materials 17,600 lbs.
Labor 16,000 hrs.
The following combination is optimal for an output of 8,000 units (but unknown to Hepworth Products):
Materials 8,000 lbs.
Labor 32,000 hrs.
The cost of materials is $40 per pound, and the cost of labor is $10 per hour. These input prices hold for 2007 and 2008. In 2008, Carson Products again produced 8,000 units, with the following input combination:
Materials 9,600 lbs.
Labor 50,000 hrs.
Required
1. Compute the partial productivity ratios for each of the following:
a. The actual inputs used in 2007.
b. The actual inputs used in 2008.
c. The optimal input combination.
Did productivity increase in 2008-as measured by the partial ratios?
2. Compute the cost of 2007's productive inefficiency relative to the optimal input combination.
3. By how much did profits increase because of improvements in productive effi- ciency from 2007 to 2008?
4. How much additional improvement in profits is possible after 2008 (assuming input costs remain the same and output doesn't change)?