# 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 Where do cost curve shapes come from? Eventually Diminishing Marginal Product = Eventually Increasing Marginal Cost L Q K Q \$

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1/4/2008 4 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/
1/4/2008 5 Example LTC(Q,w,r)=Q 4/3 (w 1/2 r 1/2 ) Find LMC LMC= (4/3)Q 1/3 (w 1/2 r 1/2 ) Set P=LMC(Q,w,r) P= (4/3)Q 1/3 (w 1/2 r 1/2 ) Flip it around to get Q*=Q(P,w,r) Q 1/3 = P/[(4/3)Q 1/3 (w 1/2 r 1/2 )] Q = P 3 /[(4/3)Q 1/3 (w 1/2 r 1/2 )] 3

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1/4/2008 6 Where do cost curve shapes come from?  (Marginal product, marginal cost) AP L MP L L Q \$ Q
1/4/2008 7 1. What will this firm do in the short run?  A. Shut Down B. Produce at a Loss C. Make Profit Q P \$

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1/4/2008 8 1. What point shows the firms short-run average total cost  when it produces at optimal Q*?  Q P A B C \$ D E F
1/4/2008 9 1. What point shows the firms short-run average variable cost  when it produces at optimal Q*?  Q P A B C \$ D E F

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1/4/2008 10 Equilibrium Dynamics of  Competitive Markets
1/4/2008 11 Market Supply: N identical Firms We know market supply in SHORT RUN because there is no entry of new firms N firms respond identically to a price change and we can map out quantity supplied. But… Entry complicates the long run P q* P Firm Market P Q Nq*

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1/4/2008 12 Region I: P>LAC min Q*(P,w,r) solves : P=LMC(Q,w,r) Region II : P<LAC min Q*=0 Shut down Recall: Q \$ LMC LAC LAC min I II
1/4/2008 13 If we add SMC curve to this picture, will it be steeper or flatter than LMC? A. Steeper B. Flatter C. Can’t tell Question 1 Q \$ LMC LAC LAC min I II

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1/4/2008 14 What does a supply curve look like in the very short run, when neither L nor K can be changed?
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