production function

Question No. 1 P: 219
Explain the difference between short run and long run production function; cite one example of this difference in a business situation.
The short run production function shows the maximum quantity of a good or service that can be produced by a set of inputs, assuming the amount of at least one of the inputs used remains unchanged.
While a long run production function shows the maximum quantity of a good or service that can be produced by a set of inputs, assuming the firm is free to vary the amount of all the inputs being used.
Example for this difference
At furniture Manufacturer Company, the variable inputs are labor and row material while the fixed input is the machinery.
It is a short-run production functions if the company change only the variable inputs but if the company change all the inputs including the fixed one it’s called a Long-run Production function.

Question No. 2 P: 219
Define the Law of diminishing returns. Why this law is considered a short-run phenomenon?
The law of diminishing stated that: As additional units of a variable input are combined with a fixed input, at some point the additional output starts to diminish. And it’s a short-run phenomenon because as stated earlier one of the inputs is fixed.

Question No. 3 P: 219
What are the key points in a short-run production function that delineate the three stages of production? Explain the relationship between the law of diminishing returns and the three stages of production?
Stage I occur at the range from zero to where the Average Product reaches its maximum where AP = MP. Also the diminishing of return take effect when MP reaches its maximum at stage one.
Stage II occur at the range from the last of stage I to the point where Total Product is maximized and MP = 0.
Stage III continues on from the last of stage II.

Problem No. 1 P: 220
Indicate whether each of the following statement is true or false. Explain why.
a. When the law of diminishing return takes effect as firm's average product will start to decrease
(False) When the law of diminishing return takes effect, Average product will keep increasing until AP = MP “The end of stage I at diminishing return”

b. Decrease in return to scale occurs when a firm has to increase all its inputs at an increasing rate to maintain a constant rate of increase in its output.
(True) because eventually the proportional increase in output will become less than the proportional increase in inputs as of the coefficient of output elasticity will be Eq < 1

c. A linear short run production function implies that the law of diminishing return does not take effect over the range of output being considered.
??? (I do not know the answer)

d. Stage one of production processes ends at the point where the low diminishing return occur
(False) Stage one of Production Processes ends where the Average Product reaches its maximum as of AP = MP. After the law of diminishing take effect.

Problem No. 2 P: 220
The oceanic Pacific fleet has just decided to use a pole-and-Line method of fishing instead of gill netting to catch tuna. The latter method involves the use of miles of nets strung out across the ocean and therefore entraps other sea creatures besides tuna. Concern for endangered species was one reason for this decision, but perhaps more important was the fact that the major tuna canneries in the United States will no longer accept tuna caught by gill netting.
Oceanic Pacific decided to conduct a series of experiments to determine the amount of tuna that could be caught with different crew sizes. The results of these experiments follow.
a. Determine the point at which diminishing returns occurs.
Number of
Fishermen
Daily Tuna
Catch (lb)
MP
0
0

1
50
50
2
110
60
3
300
190
4
450
150
5
590
140
6
665
75
7
700
35
8
725
25
9
710
(15)
The point at which diminishing returns Occurs when the third Fishermen employed and the MP = 190

Number of
Fishermen
Daily Tuna
Catch (lb)
MP
AP
0
0

1
50
50
50
2
110
60
55
3
300
190
100
4
450
150
112.5
5
590
140
118
6
665
75
110.8
7
700
35
100
8
725
25
90.6
9
710
(15)
78.9
b. Indicate the points that delineate the three stages of production.
Stage I occur at range from 0 – 5 fishermen employed where the AP reach its maximum, AP = 118.
Stage II occur from where stage I end until TP reach its maximum, TP = 725.
Stage II continues on from where stage II end.

c. Suppose the market price of tuna is $ 3.50/pound. How many fishermen should the company use if the daily wage rate is $ 100?
Number of
Fishermen
Daily Tuna
Catch (lb)
MP
AP
TRP
at $ 3.5/lb
MRP
TLC
MLC
TRP-TLC
MRP-MLC
0
0

1
50
50
50
175
175
100
100
75
75
2
110
60
55
385
210
200
100
185
110
3
300
190
100
1050
665
300
100
750
565
4
450
150
112.5
1575
525
400
100
1175
425
5
590
140
118
2065
490
500
100
1565
390
6
665
75
110.8
2327.5
262.5
600
100
1727.5
162.5
7
700
35
100
2450
122.5
700
100
1750
22.5
8
725
25
90.6
2537.5
87.5
800
100
1737.5
-12.5
9
710
-15
78.9
2485
-52.5
900
100
1585
-152.5

The Company should use seven Fishermen only because adding more Fishermen will cause the Marginal revenue product to be less than the Marginal Labor Cost.

d. Suppose a glut in the market for tuna causes the price to fall to $ 2.75/pound. What effect would this have on the number of fishermen used per boat?
Number of
Fishermen
Daily Tuna
Catch (lb)
MP
AP
TRP
at $ 2.75/lb
MRP
TLC
MLC
TRP-TLC
MRP-MLC
0
0

1
50
50
50
137.5
137.5
100
100
37.5
37.5
2
110
60
55
302.5
165
200
100
102.5
65
3
300
190
100
825
522.5
300
100
525
422.5
4
450
150
112.5
1237.5
412.5
400
100
837.5
312.5
5
590
140
118
1622.5
385
500
100
1122.5
285
6
665
75
110.8
1828.75
206.25
600
100
1228.75
106.25
7
700
35
100
1925
96.25
700
100
1225
-3.75
8
725
25
90.6
1993.75
68.75
800
100
1193.75
-31.25
9
710
-15
78.9
1952.5
-41.25
900
100
1052.5
-141.25

The number of Fishermen will decrease to six Fishermen maximum per boat as of adding more Fishermen will cause the Marginal revenue product to be less than the Marginal Labor Cost.

_ Suppose the price rose to $ 5.00/pound. What effect would this have on its hiring decision?
Number of
Fishermen
Daily Tuna
Catch (lb)
MP
AP
TRP
at $ 5/lb
MRP
TLC
MLC
TRP-TLC
MRP-MLC
0
0

1
50
50
50
250
250
100
100
150
150
2
110
60
55
550
300
200
100
350
200
3
300
190
100
1500
950
300
100
1200
850
4
450
150
112.5
2250
750
400
100
1850
650
5
590
140
118
2950
700
500
100
2450
600
6
665
75
110.8
3325
375
600
100
2725
275
7
700
35
100
3500
175
700
100
2800
75
8
725
25
90.6
3625
125
800
100
2825
25
9
710
-15
78.9
3550
-75
900
100
2650
-175

The number of Fishermen will increase to eight Fishermen maximum per boat as of adding more Fishermen will cause the Marginal revenue product to be less than the Marginal Labor Cost.

e. Suppose the firm realizes that to keep up with the demand for tuna caught by the more humane pole-and-line method of fishing, each of its boats must catch at least 1,000 pounds of fish per day. Given the preceding data, what should it consider doing? Explain.
Because the maximum catch in the short run for the boat is 725 pounds, the company would have to consider certain long-term solutions like
1. Hire more skilled fisherman.
2. Up skill the current crew to be more productive.
3. Find out more abundant fishing areas.
4. Buy bigger or more modern boats.
5. Buy modern electronics equipment such as radar to find the fish more rapidly.