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      Question

      A production function Q = f(K, L) is homogeneous of

      degree n. Euler's theorem applied to this function states that:
      A nQ = (∂Q/∂K)·K + (∂Q/∂L)·L, implying that under CRS, total output exactly exhausts the total factor payments at competitive factor prices Correct Answer Incorrect Answer
      B nQ = (∂Q/∂K) + (∂Q/∂L), meaning marginal products sum to n times output Correct Answer Incorrect Answer
      C Under CRS, doubling K alone (with L fixed) doubles output, satisfying Euler’s condition Correct Answer Incorrect Answer
      D The degree of homogeneity n equals the sum of output elasticities only when the production function is Cobb-Douglas Correct Answer Incorrect Answer

      Solution

      Euler's Theorem states: nQ = (∂Q/∂K)·K + (∂Q/∂L)·L. Under CRS (n = 1): Q = MP₂ₖ·K + MPₗ·L. In competitive markets, factors earn their marginal products (r = ∂Q/∂K, w = ∂Q/∂L), so Q = r·K + w·L — total output exactly exhausts total factor payments. This is the Product Exhaustion Theorem. Why others are wrong: • (B) — Marginal products must be multiplied by factor quantities, not simply summed. • (C) — Doubling only K with L fixed does NOT double output under CRS; both inputs must scale proportionally. • (D) — n = sum of output elasticities holds for any homogeneous function, not exclusively Cobb-Douglas.

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