ST7.1 SOLUTION
A. The rule for an optimal combination of Testlogic1 (T) and Accutest3 (A) equipment is
This rule means that an identical amount of additional output would be produced with an additional dollar expenditure on each input. Alternatively, an equal marginal cost of output is incurred irrespective of which input is used to expand output. Of course, marginal products and equipment prices must both reflect the same relevant time frame, either hours or months.
B. On a per hour basis, the relevant question is
0.3 0.3
On a per month basis, the relevant question is
0.3 0.3
In both instances, the last dollar spent on each machine increased output by the same 0.3 units, indicating an optimal mix of testing machines.
C. The rule for optimal input employment is
MRP = MP MRQ = Input Price
This means that the level of input employment is optimal when the marginal sales revenue derived from added input usage is equal to input price, or the marginal cost of employment.
D. For each machine hour, the relevant question is
Testlogic-1
MRPT = MPT MRQ PT
27 $6 $18,000/(25 8)
$162 $90.
Accutest-3
MRPA = MPA MRQ PA
48 $6 $32,000/(25 8)
$288 $160.
Or, in per month terms:
Testlogic-1
MRPT = MPT MRQ PT
27 (25 8) $6 $18,000
$32,400 $18,000.
Accutest-3
MRPA = MPA MRQ PA
48 (25 8) $6 $32,000
$57,600 $32,000.
In both cases, each machine returns more than its marginal cost (price) of employment, and expansion would be profitable.
P7.6 SOLUTION
A. No. The rule for an optimal combination of newspaper (N) and magazine (M) ads is:
Here, the question is
6 8
In other words, the last dollar spent on newspaper ads attracted six inquiries, while the last dollar spent on magazine ads attracted eight inquiries. Therefore, the current ad combination is not optimal. More magazine ads and/or fewer newspaper ads should be run.
B. Currently, magazine ads return 33% (eight versus six) more inquiries per advertising dollar than do newspaper ads. Therefore, in order for the current ad mix to be optimal, inquiries generated by newspaper ads would have to increase by 33% from 3,000 to 4,000. To check:
=
8 8
P7.8 SOLUTION
A. The marginal product of advertising is given by the expression:
MPA = ΔS/ΔA
= $100 - A
B. The rule for determining the optimal amount of a resource to employ is:
MRPA = PA
The logic of this rule can be best understood by simply dissecting the above relations:
MRPA = PA
MPA MRQ = PA
=
=
ΔTR = ΔTC
Inflow = Outflow
C. The optimal advertising level is found where:
MRPA = PA
MPA MRQ = PA
(100 - A) $2 = $100
200 - 2A = 100
-2A = -100
A = 50