Explain the rule for determining the optimal use of a multiple resources when minimizing costs, then...

Explain the rule for determining the optimal use of a multiple resources when minimizing costs, then determine the least cost manner of producing 138 units of output given that the price of labor is $4 and the price of capital is $8

Labor	MP_L	MP_L /P_L	Capital	MP_K	MP_K /P_K
1	24		1	40
2	16		2	30
3	12		3	28
4	8		4	10
5	4		5	5

Expert Solution

Given, PL = $4 and PK = $8

Required rule is as below:

(MPL / PL) = (MPK / PK)

If the above equality is not maintained exactly, the difference must be close.

The table should be completed as below:

Labor	TPL	MPL	MPL/PL	Capital	TPK	MPK	MPK/PK
1	24	24	24/4 = 6	1	40	40	40/8 = 5
2	24 + 16 = 40	16	16/4 = 4	2	40 + 30 = 70	30	30/8 = 3.75
3	40 + 12 = 52	12	12/4 = 3	3	70 + 28 = 98	28	28/8 = 3.5
4	52 + 8 = 60	8	8/4 = 2	4	98 + 10 = 108	10	10/8 = 1.25
5	60 + 4 = 64	4	4/4 = 1	5	108 + 5 = 113	5	5/8 = 0.625

Since there are 138 units,

TPL + TPK = 138

TPL of 2 labor is 40 and TPK of 3 capital is 98; combining these two (40 + 98 =) 138 units.

Minimum cost = 40 × $4 + 98 × 8

= 160 + 784

= $944 (Answer)

Rahul Sunny answered 1 year ago

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