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Consider the production function Q=10L-.5L^2+24K-K^2 for L and K in the range 0 to 10 units. Does this production function exhibit diminishing returns to each input? Does it exhibit decreasing returns to scale? Explain.

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This solution assesses returns to scale.

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Q=10L-0.5L^2+24K-K^2
Let us do the analysis first for L.
Marginal Product of Labor MPL = dQ/dL=10-0.5*2L=10-L
MPL is a decreasing function in L. As the value of L increases, the MPL decreases. Thus while the first unit of labor produces 9 ...

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