Peerless Manufacturing is a profit-maximizing firm and, operating at capacity, it can produce 50 units of output per production period using any one of the following techniques of production. The market price of land, labor, capital are $5, $4, $6, respectively. And the profit associated with T1 is $124.
TECHNIQUE |
T1 |
T2 |
T3 |
T4 |
LAND |
8 |
8 |
8 |
8 |
LABOR |
16 |
18 |
20 |
22 |
CAPITAL |
12 |
8 |
6 |
3 |
(1)
Cost of T1 = 5 x 8 + 4 x 16 + 6 x 12 = 40 + 64 + 72 = 176
Revenue (TR) = Cost + Profit = 176 + 124 = 300
Since TR = P x Q,
P = TR / Q = 300 / 50 = $6
(2)
Cost of T2 = 5 x 8 + 4 x 18 + 6 x 8 = 40 + 72 + 48 = 160
TR = 6 x 50 = 300
Profit of T1 = TR - Cost = 300 - 160 = $140
(3)
With T3, Revenue = 6 x 50 = $300
(4)
Cost of T4 = 5 x 8 + 4 x 22 + 6 x 3 = 40 + 88 + 18 = 146
TR = 6 x 50 = 300
Profit of T4 = TR - Cost = 300 - 146 = $154
(5)
Cost of T3 = 5 x 8 + 4 x 20 + 6 x 6 = 40 + 80 + 36 = 156
So, total cost is minimized (= 146) ith T4.
(6)
Profit is maximized when Cost is minimized.
Cost of T1 = 5 x 8 + 5 x 16 + 6 x 12 = 40 + 80 + 72 = 192
Cost of T2 = 5 x 8 + 5 x 18 + 6 x 8 = 40 + 90 + 48 = 178
Cost of T3 = 5 x 8 + 5 x 20 + 6 x 6 = 40 + 100 + 36 = 176
Cost of T4 = 5 x 8 + 5 x 22 + 6 x 3 = 40 + 110 + 18 = 168
Profit is maximized (cost is minimized) with T4.
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