Question

Dear Economic Analyst,

I need your expertise in determining how many workers to hire and how much feed to purchase. The current price of labor is $60 per day, and feed costs $75 per ton. Below is my marginal physical product of both labor and feed.

First, my current budget is unknown. Can you tell me the order in which I should purchase labor and feed? This order will provide priority when deciding on my level of inputs.

Secondly, although my budget is not completely known, I am guessing I will have around $480 to spend. If this amount becomes my true budget, what combination of labor and feed should I choose?

In your report, please give me all the data you are using for your analysis in a simple table. Clearly state how you are reaching your recommended decision.

Thank you in advance,

Donna Pigtail

Owner, Fat Pigs Inc.

X1 (labor)	MPP1	X2 (feed)	MPP2
0		0
	210		278
1		1
	186		255
2		2
	162		240
3		3
	144		218
4		4
	120		188
5		5
	102		173
6		6

Answer 1

PX1 = $60 per day

PX2 =$75 per day

The budget is: 60L + 75F = 480

It shall be noted that that level of X1 and X2 would be deployed, for which the MPP1/X1 = MPP2/X2

That is , the marginal physical product of labour per unit of labor is equal to marginal product of feed per unit of labor.

X1 (labor)	MPP1	X2 (feed)	MPP2	MPP1/X1	MPP2/X2
0		0
	210		278	3.5	3.706667
1		1
	186		255	3.1	3.4
2		2
	162		240	2.7	3.2
3		3
	144		218	2.4	2.906667
4		4
	120		188	2	2.506667
5		5
	102		173	1.7	2.306667
6		6

It shall be noted that MPP1/X1 is not equal to MPP2/X2 for given units of X1 and X2.

Thus, various combination of X1 and X2 should be discovered for which the budget is 480

It is X1 = 3 and X2 = 4 for which the Buget required is 480

MPP1/X1 at X1 = 3 is 2.7

MPP2/X2 at X2 = 4 is 2.90667

The firm should use 3 units of Labor and 4 units of Feed