If Marvin’s Milk Farm wants to produce 75 bottles of milk per week, the least-co
ID: 1223450 • Letter: I
Question
If Marvin’s Milk Farm wants to produce 75 bottles of milk per week, the least-cost combination of labor and capital is(1unit,2unit,3unit,4unit) of labor and (1 unit , 2 unit, 3 unit, 4 unit) of capital.
The profit-maximizing combination of resources is( 1 unit, 2 unit, 3 unit, 4 unit) of labor and (1 unit, 2 unit, 3 unit ,4 unit) of capital.
The profit-maximizing combination contains( fewer units of labor and capital than, the same amounts of labor and captial as, more units of labor and capital than) the least-cost combination to produce 75 bottles of milk.
Labor Total Product Marginal Product Total Revenue MRP of Labor (Number of workers) (Bottles) (Bottles) (Dollars) (Dollars) 0 0 1 24 24 96 96 2 42 18 168 72 3 54 12 216 48 4 62 8 248 32Explanation / Answer
Question
Marvin’s Milk Farm produces milk and sells it in a price-taker market at $4 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 in order for the other to be productive. Therefore, the total amount of milk that Marvin's produces is obtained by adding the amount of milk produced by labor to the amount produced by capital. The table also shows the total revenue and marginal revenue product ( ) of labor and capital. Finally, assume that Marvin's Milk Farm purchases labor and capital in price-taker markets. Labor costs $48 per week, and capital costs $84 per week.
Labor
Total Product
Marginal Product
Total Revenue
MRP of Labor
(Number of workers)
(Bottles)
(Bottles)
(Dollars)
(Dollars)
0
0
1
24
24
96
96
2
42
18
168
72
3
54
12
216
48
4
62
8
248
32
Capital
Total Product
Marginal Product
Total Revenue
MRP of Labor
(Bottles)
(Bottles)
(Dollars)
(Dollars)
0
0
1
21
21
84
84
2
39
18
156
72
3
51
12
204
48
4
57
6
228
24
If Marvin’s Milk Farm wants to produce 75 bottles of milk per week, the least-cost combination of labor and capital is(1unit,2unit,3unit,4unit) of labor and (1 unit , 2 unit, 3 unit, 4 unit) of capital.
The profit-maximizing combination of resources is( 1 unit, 2 unit, 3 unit, 4 unit) of labor and (1 unit, 2 unit, 3 unit ,4 unit) of capital.
The profit-maximizing combination contains( fewer units of labor and capital than, the same amounts of labor and captial as, more units of labor and capital than) the least-cost combination to produce 75 bottles of milk.
PART A
To produce 75 bottles per week the possible combinations of Capital and Labor are:
OR
It is known that Labor costs $48 per week, and capital costs $84 per week.
At A the total cost incurred per week is
(1 X 48) + (3X84) = $300
At B the total cost incurred is
(3X48) + (1X84) = $228
Thus, If Marvin’s Milk Farm wants to produce 75 bottles of milk per week, the least-cost combination of labor and capital is combination B or 3 units of labor and 1 unit of capital.
PART B
The profit-maximizing combination of resources is( 1 unit, 2 unit, 3 unit, 4 unit) of labor and (1 unit, 2 unit, 3 unit ,4 unit) of capital.
Now the profit maximizing combination of resources is the combination where:
MRPL/PL = MRPK/PK
(please note that in the question the MRP of capital is incorrectly written as MRP of labor)
So we need to add a column to each of the table above for MRP/P for each factor of production. Lets do it here
MRP of Labor
MRP/PL where P=$48
96
2
72
1.5
48
1
32
0.67
Similarly we have a table for capital
MRP of Capital
MRP/PK where P=$84
84
1
72
0.86
48
0.57
24
0.28
Now we see that where MRP for Labor is 48 the MRP/PL =1(this happens at 3 units of labor)
And when MRP of Capital is 84 the MRP/PK= 1( this happens at 1 units of capital)
Thus, the profit maximizing condition MRPL/PL = MRPK/PK
Is satisfied at 3 units of labor and 1 unit of capital
PART C
The profit-maximizing combination contains _________ than the least-cost combination to produce 75 bottles of milk.
a. fewer units of labor and capital than,
b. the same amounts of labor and captial as(Answer) see the answers in part A and B
c. more units of labor and capital than
Labor
Total Product
Marginal Product
Total Revenue
MRP of Labor
(Number of workers)
(Bottles)
(Bottles)
(Dollars)
(Dollars)
0
0
1
24
24
96
96
2
42
18
168
72
3
54
12
216
48
4
62
8
248
32
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