A firm estimates its cubic production function of the form

Q = AL³ + BL²

and obtains the following estimation results:a. What are the estimated total, average, and marginal product functions?b. Are the parameters of the correct sign, and are they significant at the 1 percent level?c. At what level of labor usage is average product at its maximum?Now recall the following formulas derived in Chapter 8: AP = Q/L, AVC = w/AP, and SMC = w/MP. Assume that the wage rate for labor (w) is $200.d. What is output when average product is at its maximum?

e. At the output level for part d, what are average variable cost and marginal cost?f. When the rate of labor usage is 120, what is output? What are AVC and SMC at that output?g. Conceptually, how could you derive the relevant cost curves from this estimate of the production functions?

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DEPENDENT VARIABLE: Q R-SQUARE F-RATIO P-VALUE ONE OBSERVATIONS: 25 0.8457 126.10 0.0001 PARAMETER STANDARD VARIABLE ESTIMATE ERROR T-RATIO P-VALUE L3 -0.002 0.0005 -4.00 0.0005 L2 0.400 0.080 5.00 0.0001