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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 + (1a)x2, ay1 + (1a)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. GroupClicker 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 + (1a)x2, ay1 + (1a)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. GroupClicker 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. GroupClicker 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. GroupClicker 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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 Fall '07
 Codrin
 Microeconomics, Monotonic function, Convex function

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