The marginal productive output of workers in a small manufacturing firm is given by MP = 8L-L^2+20 where L is the number of workers hired by the firm. Rewrite the equation above as a first order differential equation and find the general solution for the total productive output function P(L).

ddaeeric 2020-12-25 Answered
The marginal productive output of workers in a small manufacturing firm is given by MP=8LL2+20 where L is the number of workers hired by the firm. Rewrite the equation above as a first order differential equation and find the general solution for the total productive output function P(L).
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Willie
Answered 2020-12-26 Author has 95 answers

Given that marginal productive output of workers in a small manufacturing firm is given by MP=8LL2+20
Since marginal productive output of workers in a small manufacturing firm is given by MP=8LL2+20 that is dP/dL=8LL2+20
Find the general solution for the total productive output function P(L)
P=(8LL2+20)dL
=[(8L2)/2L3/3+20L]
=4L2L3/3+20L+c
Thus, the general solution for the total productive output function
P=4L2L3/3+20L

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