(All Steps) Consider the production function: Q=L^1 / 4 K^3 / 4 Does this production show increasing, decreasing, or constant returns to scale? Show your


Question: Consider the production function:

\[Q=L^{1 / 4} K^{3 / 4}\]
  1. Does this production show increasing, decreasing, or constant returns to scale? Show your work. (3 points)
  2. Derive an expression for the marginal product of labor. ( 2 points)
  3. Show mathematically whether the marginal product of labor is increasing, decreasing, or constant, as the labor input is increased. (3 points)
  4. Derive the average product of labor. Explain whether the average product of labor is increasing, decreasing, or constant, as the labor input is increased. (2 points $)$
  5. Derive the expression for the slope of the isoquant. Is the isoquant convex? Briefly explain why or why not. (3 points)

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