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How mathematics explains economic choices, limited resources, and the value of loosening a constraint.

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From Mathematics for Economists: The Hidden Price in Every Constraint

With the production function Q = K^0.5 L^0.5, what happens to output if both capital and labor double?

  1. Output rises by half
  2. Output doubles
  3. Output quadruples
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Answer: Output doubles

The exponents sum to 1, so the function has constant returns to scale: scaling all inputs by 2 scales output by 2.

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