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X = 10

K. B. 21. 15. A. X = 14. X = 10. L. 0. 5. 7. Constant returns to scale. Suppose 5 labor and 15 capital can produce 10 X. This is the isoquant associated with point A. Under constant returns to scale a proportional increase in inputs leads to a proportional increase in output.

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X = 10

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  1. K B 21 15 A X = 14 X = 10 L 0 5 7 Constant returns to scale Suppose 5 labor and 15 capital can produce 10 X This is the isoquant associated with point A Under constant returns to scale a proportional increase in inputs leads to a proportional increase in output Suppose we increase K and L by 40% K from 15 to 21 and L from 5 to 7 Then output also increases by 40% from X = 10 to X = 14 Thus, the isoquant at point B is X = 14

  2. K But if A’ is another point on the X=10 isoquant we can use the same procedure to conclude that B’ must be also on the X=14 isoquant B’ 44 B A’ 40 110 A 100 X = 14 X = 10 L 0 Constant returns to scale Increasing the inputs at A with 40% is equivalent to increasing the length of a line from the origin through A with 40% This procedure can be repeated for any arbitrary point on the X=10 isoquant; here are a few The X = 14 isoquant is a blow-up radial

  3. K B 21 A 15 X = 14 X = 10 L 0 5 7 Constant returns to scale Under constant returns to scale the isoquants are radial blow-ups of each other, which implies that drawing 1 isoquant gives information on all others For example, that if cost is minized at point A for X = 10, then it is also minimized at the 40% radial blow-up of A (B) for X = 14 Thus, the slope of the isoquant at point A is the same as at point B

  4. K B 21 A 15 X = 14 X = 10 L 0 5 7 Constant returns to scale Since the isoquants are radial blow-ups of one another and the slope at point A is the same as the slope at point B cost minimization is simpler. If we know the cost minimizing input mix for one isoquant and any ratio of w/r, we also know it for any other production level. You only have to multiply the input mix times the output ratio (we frequently use the isoquant X = 1)

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