Question

Assume:         PQ = $4.00                  PL = $2.00                               PK = $4.00

K         MPK    MP/PK            MRP/PK          L          MPL      MP/PL                   MRP/PL

1          28        7          28                    1          15        5                      20

2          24        6          24                    2          12        4                      16

3          20        5          20                    3          9          3                      12

4          12        4          16                    4          6          2                      8

5          8          2          8                      5          3          1                      4

6          4          1          4                      6          1          0.5                   2

7          2          0.5       2                      7          0.5       0.25                 1

8          1          0.25     1                      8          0.25     0.13                 0.52

9          0.5       0.125   0.5                   9          0.125   0.06                 0.24

The least cost combination of capital and labor to produce 134 units of output.

Answer 1

Total cost (TC) = L x PL + K x PK

Cost is minimized when (MPL / PL) = (MPK / PK) which holds true for following bundles.

(1) The ratio is 20, L = 15, K = 3 and TC = 2 x 15 + 4 x 3 = 30 + 12 = 42

(2) The ratio is 16, L = 12, K = 4 and TC = 2 x 12 + 4 x 4 = 24 + 8 = 32

(3) The ratio is 8, L = 6, K = 5 and TC = 2 x 6 + 4 x 5 = 12 + 20 = 32

(4) The ratio is 4, L = 3, K = 6 and TC = 2 x 3 + 4 x 6 = 6 + 24 = 30

(5) The ratio is 2, L = 1, K = 7 and TC = 2 x 1 + 4 x 7 = 2 + 28 = 30

(6) The ratio is 1, L = 0.5, K = 8 and TC = 2 x 0.5 + 4 x 8 = 1 + 32 = 33

Therefore, cost is minimized (= 30) when Either L = 3 & K = 6, or L = 1 and K = 7.