Diminishing Returns To Scale

Part A

K=

L= 0
1
2
3
4
5
6
7

10
0
9
11
13
15
16
17
19

9
0
8
10
12
14
15
16
17

8
0
7
10
11
13
14
15
16

7
0
7
9
10
12
13
14
14

6
0
6
8
9
10
11
12
13

5
0
5
7
8
9
10
11
11

4
0
4
6
7
8
9
9
10

3
0
4
5
6
6
7
8
8

2
0
3
4
4
5
5
6
6

1
0
2
2
3
3
3
3
4

0
0
0
0
0
0
0
0
0

Used formula N (boats) = 1.7(K^0.7)*(L^0.4). The production function implies diminishing returns to scale. The function is a Cobb Douglas production function because it is in the form: N=C*L^g*K^b. You can tell the function has diminishing returns to scale because it g and b values add up to more than 1. In this case: 0.7+0.4= 1.1. 1.1>1 therefore diminishing returns.

Part B
Used Part (A) as estimation for Estimated Isoquant Line for 7 boats. Points used (in the order labour, machines): (1,7.5), (2,5), (3,4) (5,3)
This line is drawn by plotting the labour and machine coordinates that produce approximately 7 boats on the edgeworth box diagram and using these points to estimate an isoquant line for 7 boats.
Points used for Estimated Isoquant Line for 11 boats: (2,10), (3,8), (5,6), (6,5), (7,5)

Part C

K=

L= 0
1
2
3
4
5
6
7

10
0
13
15
17
18
19
20
21

9
0
12
14
16
17
18
19
20

8
0
11
14
15
16
17
18
19

7
0
11
13
14
15
16
17
18

6
0
10
12
13
14
15
16
16

5
0
9
11
12
13
14
14
15

4
0
8
10
11
11
12
13
13

3
0
7
8
9
10
11
11
11

2
0
6
7
8
8
9
9
9

1
0
4
5
5
6
6
6
7

0
0
0
0
0
0
0
0
0

Points used for 10 van isoquant estimation: (1,6),(2,4),(4,3)
Points used for 14 van isoquant estimation: (2,8.5),(3,7),(4,6),(5,5),(6,5)
This edgeworth box shows efficient combinations of people and machines because the points where the isoquants for vans and boats are at a tangent (touching) with each other are efficient.
Part D There could be a better allocation of resources in Eurcadia if 1 employee and 7 machines were making vans. This is because the point is not on the contract curve, which is formed of the points where the two isoquants are at a tangent to each other, which shows the most efficient combinations of people and machines.
Part E
It is possible to rearrange the equation in order to get a more accurate isoquant line. The rearrangement for the 7 boats isoquant line is as follows:
N (boats)= 1.7* (Machines^0.7)*(Labour^0.4)
Machines^0.7=N/1.7*(Labour^0.4)
Machines=(N/1.7*(Labour^0.4))^(10/7)
From there you obtain the line by substituting whatever number of goods you want the isoquant line to depict for N (in this case 7 boats) and the corresponding Labour value along the X-axis for L.
The Algebra used for the other Isoquant Lines is as shown:
Algebra used for Isoquant Line for 11 Boats: N=1.7*(K^0.7)*(L^0.5) K^0.7=N/1.7*(L^0.5) K=(N/1.7*(L^0.5))^(10/7) Where N=11

10 Vans Isoquant:

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