If the demand function faced by a firm is:
Q = 90 – 2P
TC = 2 + 57Q – 8Q2 + Q3
Determine the level of output at which the firm maximizes the profit.
Determine the best level of output for the above question by the MR and MC approach.
TPL=10L+5L2+L3TP_L = 10L + 5L^2 + L^3TPL=10L+5L2+L3
MPL=dTPLdL=10+10L+3L2MP_L=\frac {dTP_L} {dL} =10+10L+3L^2MPL=dLdTPL=10+10L+3L2
APL=TPLL=10+5L+L2AP_L=\frac {TP_L} {L} =10+5L+L^2APL=LTPL=10+5L+L2
When L=5;
TPL=10(5)+5(5)2+(5)3TP_L=10(5) + 5(5)^2 + (5)^3TPL=10(5)+5(5)2+(5)3
TPL=50+125+125TP_L=50+125+125TPL=50+125+125
TPL=300TP_L=300TPL=300
MPL=10+10(5)+3(5)2MP_L=10+10(5)+3(5)^2MPL=10+10(5)+3(5)2
MPL=10+50+75MP_L=10+50+75MPL=10+50+75
MPL=135MP_L=135MPL=135
APL=10+5(5)+(5)2AP_L=10+5(5)+(5)^2APL=10+5(5)+(5)2
APL=60AP_L=60APL=60
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