Answer to Question #267652 in Microeconomics for Jane

Question #267652

Q = - 50 + 10 L – 0.02 L2

1) Find out MP

2) Find out AP

3) At what level of labor input does the AP curve reach its maximum? What is the MP at this input level?


1
Expert's answer
2021-11-21T17:08:54-0500

Answer:

1.). MP ="\\frac{\\partial Q} {\\partial L}"


Q = -50 + 10L – 0.02L2

MP = "\\frac{\\partial Q} {\\partial L}" = -0.04L + 10

MP = -0.04L + 10

 

2.). AP = "\\frac{Q}{L}"

AP = -50 + 10L – 0.02L2 "\\div" L = "-\\frac{50}{L} -10 + 0.02L"


AP = "-\\frac{50}{L} -10 + 0.02L"

 

3.). At maximum: AP = MP

"-\\frac{50}{L} -10 + 0.02L" = -0.04L + 10

"-\\frac{50}{L} + 0.02L +0.04L" = 10 + 10

"-\\frac{50}{L} + 0.06L" = 20


L = 335.81

AP curve reaches its maximum when labor = 335.81

 

MP = -0.04L + 10 = (-0.04 "\\times" 335.81) + 10 = -13.43 + 10 = -3.43

MP = -3.43



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