INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;  Charles van Marrewijk, 2006; 1 X = 10 X = 14 Constant returns to scale 7 21 Suppose 5 labor.

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INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;  Charles van Marrewijk, 2006; 1 X = 10 X = 14 Constant returns to scale 7 21 Suppose 5 labor and 15 capital can produce 10 X This is the isoquant associated with point A Suppose we increase K and L by 40% A 15 5 Under constant returns to scale a proportional increase in inputs leads to a proportional increase in output K from 15 to 21 and L from 5 to 7 Then output also increases by 40% from X = 10 to X = 14 B Thus, the isoquant at point B is X = 14 L K 0

INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;  Charles van Marrewijk, 2006; 2 X = 10 X = 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 B A’ B’ 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 L K 0 A radial Constant returns to scale

INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;  Charles van Marrewijk, 2006; 3 X = A 15 5 X = 14 L K 0 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 B Thus, the slope of the isoquant at point A is the same as at point B 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

INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;  Charles van Marrewijk, 2006; 4 X = A 15 5 X = 14 L K 0 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. B You only have to multiply the input mix times the output ratio (we frequently use the isoquant X = 1) 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.