A firm estimates its long-run production function to be $Q = - 0.0075 K ^ { 3 } L ^ { 3 } + 12 K ^ { 2 } L ^ { 2 }$ Suppose the firm employs 12 units of capital.The product curve(s)in the short-run are A)TP = -12.96 L³ + 1,728L². B)AP = -12.96 L³ + 1,728L². C)MP = -38.88 L² + 3,456L. D)both a and b E)both a and c

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Given the production function $Q = - 0.0075 K ^ { 3 } L ^ { 3 } + 12 K ^ { 2 } L ^ { 2 }$ and $K = 12$, we substitute $K$ into the equation to find the short-run production function. This results in the Total Product (TP) curve. The Marginal Product (MP) curve is derived by taking the derivative of the TP curve with respect to $L$. Choices A and C correctly represent the TP and MP curves, respectively, after substituting $K = 12$ and differentiating.

A Firm Estimates Its Long-Run Production Function to Be Q=−0.0075K3L3+12K2L2Q = - 0.0075 K ^ { 3 } L ^ { 3 } + 12 K ^ { 2 } L ^ { 2 }Q=−0.0075K3L3+12K2L2

A Firm Estimates Its Long-Run Production Function to Be $Q = - 0.0075 K ^ { 3 } L ^ { 3 } + 12 K ^ { 2 } L ^ { 2 }$