ECON100A_16

ECON100A_16 - Review Profit Max 1 Maximize Total Revenue...

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1/4/2008 1 Review Profit Max

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1/4/2008 2 Profit Maximization - Algebraically Maximize Total Revenue minus Total Cost max PQ-LTC(Q,w,r) Q FOC: Q* solves: (P=LMC(Q*,w,r)) Solution function is Q*(P,w,r) Q r)/ w, LTC(Q, P =
1/4/2008 3 Profit Max - Graphically Slope of Total Revenue curve= P Slope of LTC = =LMC When LTC flatter (P > LMC): gap widening so… Distance (profit) not at maximum When LTC steeper (P<LMC): gap narrowing… Distance (profit) not at maximum Profit Max where P=LMC Q \$ Q LTC TR π widening narrowing Q LTC/

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1/4/2008 4 Example F(L,K)=L 1/3 K 1/3 Find LTC. In this case: LTC(Q,w,r)=2Q 3/2 w 1/2 r 1/2 Find LMC LMC= 3Q 1/2 w 1/2 r 1/2 Set P=LMC(Q,w,r) P= 3Q 1/2 w 1/2 r 1/2 Flip it around to get Q*=Q(P,w,r) Q 1/2 = P/[3 w 1/2 r 1/2 ] Q = P 2 /[9 wr]
1/4/2008 5 Region I: P>LAC min Q*(P,w,r) solves : P=LMC(Q,w,r) Region II : P<LAC min Q*=0 Shut down Darkened line is Supply Curve Long Run Supply Curve Q \$ LMC LAC LAC min I II

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ECON100A_16 - Review Profit Max 1 Maximize Total Revenue...

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