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# ch08 - Chapter Eight Costs Curves Chapter Eight 1 Chapter...

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1 Costs Curves Chapter Eight Chapter Eight

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2 Chapter Eight Overview 1. Introduction: HiSense 1. Long Run Cost Functions Shifts Long run average and marginal cost functions Economies of scale Deadweight loss – "A Perfectly Competitive Market Without Intervention Maximizes Total Surplus" 1. Short Run Cost Functions 1. The Relationship Between Long Run and Short Run Cost Functions Chapter Eight
3 Chapter Eight Long Run Cost Functions Definition: The long run total cost function relates minimized total cost to output, Q, to the factor prices (w and r). TC(Q,w,r) = wL*(Q,w,r) + rK*(Q,w,r) Where: L* and K* are the long run input demand functions

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4 Chapter Eight What is the long run total cost function for production function Q = 50L 1/2 K 1/2 ? L*(Q,w,r) = (Q/50)(r/w) 1/2 K*(Q,w,r) = (Q/50)(w/r) 1/2 TC(Q,w,r) = w[(Q/50)(r/w) 1/2 ]+r[(Q/50)(w/r) 1/2 ] = (Q/50)(wr) 1/2 + (Q/50)(wr) 1/2 = (Q/25)(wr) 1/2 What is the graph of the total cost curve when w = 25 and r = 100? TC(Q) = 2Q Long Run Cost Functions
5 Q (units per year) TC (\$ per year) TC(Q) = 2Q \$4M. Chapter Eight A Total Cost Curve

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6 1 M. \$2M. Chapter Eight TC (\$ per year) Q (units per year) TC(Q) = 2Q A Total Cost Curve
7 1 M. 2 M. \$2M. \$4M. Chapter Eight A Total Cost Curve TC (\$ per year) Q (units per year) TC(Q) = 2Q

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8 Chapter Eight Long Run Total Cost Curve Definition: The long run total cost curve shows minimized total cost as output varies, holding input prices constant. Graphically, what does the total cost curve look like if Q varies and w and r are fixed?
9 Chapter Eight Long Run Total Cost Curve

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10 Chapter Eight Long Run Total Cost Curve
11 Chapter Eight Long Run Total Cost Curve

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12 Q (units per year) L (labor services per year) K TC (\$/yr) 0 0 L 0 L 1 K 0 K 1 Q 0 Q 1 TC = TC 1 TC = TC 0 Chapter Eight Long Run Total Cost Curve
13 Q (units per year) L (labor services per year) K TC (\$/yr) 0 0 LR Total Cost Curve Q 0 TC 0 =wL 0 +rK 0 L 0 L 1 K 0 K 1 Q 0 Q 1 TC = TC 1 TC = TC 0 Chapter Eight Long Run Total Cost Curve

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14 Q (units per year) L (labor services per year) K TC (\$/yr) 0 0 LR Total Cost Curve Q 0 Q 1 TC 0 =wL 0 +rK 0 L 0 L 1 K 0 K 1 Q 0 Q 1 TC = TC 1 TC = TC 0 TC 1 =wL 1 +rK 1 Chapter Eight Long Run Total Cost Curve
15 Chapter Eight Long Run Total Cost Curve Graphically, how does the total cost curve shift if wages rise but the price of capital remains fixed?

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16 L K 0 TC 0 /r Chapter Eight A Change in Input Prices
17 L 0 -w 0 /r TC 0 /r TC 1 /r -w 1 /r Chapter Eight K A Change in Input Prices

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18 L 0 A B -w 0 /r TC 0 /r -w 1 /r Chapter Eight TC 1 /r K A Change in Input Prices
19 L Q 0 0 A -w 0 /r TC 0 /r -w 1 /r Chapter Eight B TC 1 /r K A Change in Input Prices

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20 Q (units/yr) TC (\$/yr) TC(Q) post Chapter Eight A Shift in the Total Cost Curve
21 Q (units/yr) TC(Q) ante TC(Q) post Chapter Eight TC (\$/yr) A Shift in the Total Cost Curve

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22 Q (units/yr) TC(Q) ante TC(Q) post TC 0 Chapter Eight TC (\$/yr) A Shift in the Total Cost Curve
23 Q (units/yr) TC(Q) ante TC(Q) post Q 0 TC 1 TC 0 Chapter Eight TC (\$/yr) A Shift in the Total Cost Curve

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24 Chapter Eight How does the total cost curve shift if all input prices rise (the same amount)? For example, suppose that all input prices double: Input Price Changes
25 L (labor services/yr) K (capital services/yr) 0 A Chapter Eight All Input Price Changes

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26 0 -w/r Chapter Eight K (capital services/yr) All Input Price Changes L (labor services/yr)
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ch08 - Chapter Eight Costs Curves Chapter Eight 1 Chapter...

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