Prove that the production function f(X1, X2, X3) = 29X1aX2bX3c, where a + b + c > 1, has increasing returns to scale.
Multiply all inputs by a fraction z
New Q = 29(zX1)^a (zX2)^b (zX3)^c
= 29 * z^a X1^a z^b X2^b z^c X3^c
= 29 * z^(a + b + c) X1^a X2^b X3^c
= z^(a + b + c) * old Q
Now a + b + c is greater than 1 which means z^(a + b + c) > z
This implies that when all inputs are increased by a given fraction, output is increased by a greater fraction. Hence there are increasing returns to scale
Prove that the production function f(X1, X2, X3) = 29X1aX2bX3c, where a + b + c...
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