16_ProductionSets

# 16_ProductionSets - “Today’s material is very boring...

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Unformatted text preview: “Today’s material is very boring. And that’s a good thing.” –J eremy Petranka ECON 410 Production Functions 2 Class 16 - Production Functions 3 Class 16 - Production Functions 4 Class 16 - Production Functions 5 Class 16 - Production Functions Convexity A production set displays Convexity if, whenever (x1,y1) and (x2,y2) are elements of the set, then [ax1 + (1-a)x2, ay1 + (1-a)y2] is also part of the set where 0<=a<=1. Intuitively, convexity implies that a balanced production plan is at least as efficient as an unbalanced production plan. Group-Clicker Question (P): Which of the following production sets does NOT display the Convexity Property [whenever (x1,y1) and (x2,y2) are elements of the set, then [ax1 + (1-a)x2, ay1 + (1-a)y2] is also part of the set where 0<=a<=1]? 1. A 2. B 3. C A B C 7 Class 16 - Production Functions Decreasing Returns to Scale (global) A production set displays Decreasing Returns to S cale if, whenever (x1,y1) is an element of the set, then (ax1,ay1) is also part of the set where a[0,1). Intuitively, decreasing returns to scale means you can scale down your operations. Group-Clicker Question (P): Which of the following production sets displays Decreasing Returns to Scale [whenever (x1,y1) is an element of the set, then (ax1,ay1) is also part of the set where a[0,1)]? 1. A 2. B 3. C A B C 9 Class 16 - Production Functions Increasing Returns to Scale (global) A production set displays Increasing Returns to S cale if, whenever (x1,y1) is an element of the set, then (ax1,ay1) is also part of the set where a>1. Intuitively, increasing returns to scale means you can scale up your operations. Group-Clicker Question (P): Which of the following production sets displays Increasing Returns to Scale [whenever (x1,y1) is an element of the set, then (ax1,ay1) is also part of the set where a>1 1. A 2. B 3. C A B C 11 Class 16 - Production Functions Constant Returns to Scale (global) A production set displays Constant Returns to S cale if, whenever (x1,y1) is an element of the set, then (ax1,ay1) is also part of the set where a>0. Intuitively, constant returns to scale means you can scale your operations up or down. Group-Clicker Question (P): Which of the following production sets displays Constant Returns to Scale [whenever (x1,y1) is an element of the set, then (ax1,ay1) is also part of the set where a>0 1. A 2. B 3. C A B C 13 Class 16 - Production Functions Returns to Scale (weak) Returns to Scale (increasing, decreasing, or constant) can exist in ranges. For instance, you might be able to scale up or down by a certain percentage. 14 Class 16 - Production Functions x y 15 Class 16 - Production Functions 16 Class 16 - Production Functions Assumptions on Firms Given its current resources, a firm 1. Will maximize profits....
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16_ProductionSets - “Today’s material is very boring...

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