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?
Solution:
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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