Suppose a certain contractor wants to maximize profit from building one bridge. The
contractor uses both labor and capital, and efficient combinations of Labor and capital
that are sufficient to make a bridge is by the function 0.75L1/2 K 1/2. If the prices of labor
(w) and capital (r) are $ 6 and $ 16 respectively
A) Find the least cost combination of L and K?
B) Find the minimum cost?
Solution:
A.). The least cost combination of L and K is where:
MRTS =
Q = 0.75L1/2 K 1/2
MPL =
MPK =
MRTS =
MRTS =
K = 0.375L
The least cost combination of L and K is where: K = 0.375L where the contractor uses 0.375 as much capital as labor.
B.). The minimum cost:
C = wL + rK
C = 6L + 16K
K = 0.375L
C = 6L + 16(0.375L)
C = 6L + 6L
C = 12L
The minimum cost: C = 12L
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