10. (20 points) Regression Problem: TSU, Inc. produces teddy bears. The production manager at Mercantile wishes to estimate an empirical production function for the bear production using the following time-series data for the last 22 days of operations. L is the daily number of workers employed, and Q is the number of teddy bears completed for that day. TSUpays its assembly workers $150 per day in wages and benefits. I Excel datafile attached. Take screenshot of your estimations and add it to your PDF document. Q=AL + BL a. Do the parameter estimates have the appropriate algebraic signs? Re-write the production function with the parameters A and B that you obtained in the regression. b. Are the parameters statistically significant at the 1 percent level of statistical significance? How well did the empirical model do in explaining the variation in the number of bears produced each day? c. d. What are the estimated total, average, and marginal product functions from your regression results? e. At what level of labor usage does average product reach its maximum value? In a day, how many bears per worker are assembled when average product is maximized? What is average variable cost when average product is maximized? What is short-run marginal cost when average product is maximized? Beyond what level of labor employment does the law of diminishing returns set in? Beyond what level of output? Number of workers. f. g. Day 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 A L 0 1.5 2.1 2.4 3.2 3.6 3.8 1.8 1.8 4.1 3.6 4.4 4 2.1 2.7 2 1.5 3.6 1.4 24 2.5 3.2 2.1 Number of carts assembled Q 0 7.5 89.7 128 125.1 131.5 283.7 59 12.9 157.2 200.5 102.4 216.5 153.4 83.5 90.6 10.2 1424 11.1 86.8 91.6 134.1 80.6 10. (20 points) Regression Problem: TSU, Inc. produces teddy bears. The production manager at Mercantile wishes to estimate an empirical production function for the bear production using the following time-series data for the last 22 days of operations. L is the daily number of workers employed, and Q is the number of teddy bears completed for that day. TSUpays its assembly workers $150 per day in wages and benefits. I Excel datafile attached. Take screenshot of your estimations and add it to your PDF document. Q=AL + BL a. Do the parameter estimates have the appropriate algebraic signs? Re-write the production function with the parameters A and B that you obtained in the regression. b. Are the parameters statistically significant at the 1 percent level of statistical significance? How well did the empirical model do in explaining the variation in the number of bears produced each day? c. d. What are the estimated total, average, and marginal product functions from your regression results? e. At what level of labor usage does average product reach its maximum value? In a day, how many bears per worker are assembled when average product is maximized? What is average variable cost when average product is maximized? What is short-run marginal cost when average product is maximized? Beyond what level of labor employment does the law of diminishing returns set in? Beyond what level of output? Number of workers. f. g. Day 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 A L 0 1.5 2.1 2.4 3.2 3.6 3.8 1.8 1.8 4.1 3.6 4.4 4 2.1 2.7 2 1.5 3.6 1.4 24 2.5 3.2 2.1 Number of carts assembled Q 0 7.5 89.7 128 125.1 131.5 283.7 59 12.9 157.2 200.5 102.4 216.5 153.4 83.5 90.6 10.2 1424 11.1 86.8 91.6 134.1 80.6
