(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:
\[Q=L^{1 / 4} K^{3 / 4}\]- Does this production show increasing, decreasing, or constant returns to scale? Show your work. (3 points)
- Derive an expression for the marginal product of labor. ( 2 points)
- Show mathematically whether the marginal product of labor is increasing, decreasing, or constant, as the labor input is increased. (3 points)
- 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 $)$
- 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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