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Calculate apl and mpl determine if the production function

A firm's production is given by

q = 5L^2/3 K^1/3

(a) Calculate AP_L and MP_L. Determine if the production function exhibits the law of diminishing marginal returns. Calculate the output (production) elasticity with respect to labor.

(b) Calculate MRTS. Determine if the production function exhibits the law of diminishing MRTS.

(c) Show with appropriate calculations if the production technology exhibits, increasing, decreasing or constant returns to scale.

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