Question

1. Explain the rule for determining the optimal resource use for a single resource or input and determine the optimal amount of labor, given that each output sells at $2 and labor is $26 per unit.

Labor	Output	MP	MRP	MRC
0	0	***	***	***
1	22
2	38
3	52
4	62
5	70

2. 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	MPL	MPL /PL	Capital	MPK	MPK /PK
1	24		1	40
2	16		2	30
3	12		3	28
4	8		4	10
5	4		5	5

3.If the price of output sells for $0.80 each, determine the profit maximizing quantities of labor and capital that should be used, assuming the price of labor is $4 and the price of capital is $8. If labor and capital are the only inputs, compute the profit of this firm.

Labor	MPL	MRPL	MRPL/PL	Capital	MPK	MRPK	MRPK/PK
1	24			1	40
2	16			2	30
3	12			3	28
4	8			4	10
5	4			5	5

Answer 1

Question 1

In case of single resource or input, the optimal amount of resource or input is that amount corresponding to which marginal revenue product of input or resource equals the marginal resource cost of input or resource.

If there is no explicit amount corresponding to which marginal revenue product equals the marginal resource cost the firm will employ the amount of input or resource upto which marginal revenue product exceeds the marginal resource cost.

Marginal revenue product is calculated as follows -

MRP = MP * Price of output

Marginal resource cost is calculated as follows -

MRC = Price of resource

Following is the complete table -

Labor	Output	MP	MRP	MRC
0	0	-	-	-
1	22	22	44	26
2	38	16	32	26
3	52	14	28	26
4	62	10	20	26
5	70	8	16	26

The above table shows that the marginal revenue product exceeds the marginal resource cost up to employment of 3 workers.

So,

The optimal amount of labor is 3 workers.