A firm’s total profit is given by: F(K,L)= 10KL - L^2 -460K -2K^2 . What values...
A firm’s total profit is given by: F(K,L)= 10KL - L^2 -460K -2K^2 . What values of K and L will maximize firm’s profits? Show your work
Homework Answers
Profit function is maximized when its partial derivatives are set equal to 0
This implies we have to find F'(K) = 0 and F'(L) = 0
10L - 460 - 4K = 0 or 2.5L - K = 115
and
10K - 2L = 0 or L = 5K
Use L = 5K in the first equation to get
2.5*5K - K = 115
11.5K = 115
K = 115/11.5 = 10
Hence, K = 10 and L = 5*10 = 50
Profit maximizing values are K* = 10 and L* = 50
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