Question

Marvin’s Milk Farm produces milk and sells it in a perfectly competitive market at $3 per bottle. The following table shows Marvin's weekly total and marginal product schedules, using labor and capital. Assume that labor and capital may be used independently; that is, one is not needed for the other factor to be productive. Therefore, the total amount of milk that Marvin's produces is obtained by adding together the amount of milk produced by labor and the amount of milk produced by capital. The table also shows total revenue and marginal revenue products (MRPMRP) of labor and capital. Finally, assume that Marvin's Milk Farm is a factor price taker in the labor and capital markets. Labor costs $36 per week, and capital costs $48 per week.

Labor	Total Product	Marginal Physical Product	Total Revenue	MRP of Labor
(Number of workers)	(Bottles)	(Bottles)	(Dollars)	(Dollars)
0	0
1	23	23	69	69
2	41	18	123	54
3	53	12	159	36
4	61	8	183	24

Capital	Total Product	Marginal Physical Product	Total Revenue	MRP of Capital
	(Bottles)	(Bottles)	(Dollars)	(Dollars)
0	0
1	21	21	63	63
2	37	16	111	48
3	49	12	147	36
4	55	6	165	18

If Marvin’s Milk Farm wants to produce 90 bottles of milk per week, the least-cost combination of labor and capital is   of labor and   of capital.

The profit-maximizing combination of resources is   of labor and   of capital.

The profit-maximizing combination contains   the least-cost combination to produce 90 bottles of milk.

Answer 1

If Marvin’s Milk Farm wants to produce 90 bottles of milk per week, the least-cost combination of labor and capital is 3 units of labor and 2 units of capital.
(Least cost combination is that where MPP of labor/Labor cost = MPP of capital/Capital cost.
At L = 3, MPP of labor/Labor cost = 12/36 = 0.33
At K = 2, MPP of capital/Capital cost = 16/48 = 0.33
So, this combination minimizes cost and total output produced = 53 + 37 = 90)

The profit-maximizing combination of resources is  3 units of labor and 2 units of capital.
(Profit maximizing combination is that where MRP of labor = labor cost and MRP of capital = Capital cost.
At L = 3, MRP of labor = Labor cost = 36 and at K = 2, MRP of capital = Capital cost = 48)

The profit-maximizing combination contains the same amount of labor and capital as the least-cost combination to produce 90 bottles of milk.