Sharjah Mercantile Metalworks, LLC. manufactures wire carts for grocery stores. The production manager at Mercantile wishes to estimate an empirical production function for the assembly of carts using the following time-series data for the last 22 days of assembly operations. L is the daily number of assembly workers employed, and Q is the number of carts assembled (completely) for that day. Mercantile pays its assembly workers AED160 per day in wages and benefits.

1. Use a computer regression package, such as the excel Solver or Excel, to estimate the following short-run cubic production function:

Q=AL3+BL2

2. What are the estimated total, average, and marginal product functions from your regression results in Part a?

3. Beyond what level of labor employment does the law of diminishing returns set in? Beyond what level of output?

Day Number of workers L 1 2 3 4 5 6 7 8 9 10 11 15 21 24 32 36 38 18 18 41 36 44 Number of carts assembled Q 75 897 1,280 1,251 1,315 2,837 590 129 1,572 2,005 1,024 12 13 14 15 16 17 18 19 20 21 22 40 21 27 20 15 36 14 24 25 32 21 2,165 1,534 835 906 102 1,424 111 868 916 1,341 806 Day Number of workers L 1 2 3 4 5 6 7 8 9 10 11 15 21 24 32 36 38 18 18 41 36 44 Number of carts assembled Q 75 897 1,280 1,251 1,315 2,837 590 129 1,572 2,005 1,024 12 13 14 15 16 17 18 19 20 21 22 40 21 27 20 15 36 14 24 25 32 21 2,165 1,534 835 906 102 1,424 111 868 916 1,341 806