The 7. Mercantile Metalworks, Inc. manufactures wire carts for grocery stores. p

ID: 1166287 • Letter: T

Question

The 7. Mercantile Metalworks, Inc. manufactures wire carts for grocery stores. 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 $140 per day in wages and benefits Using E-views (a computer regression package) to estimate short-run cubic production function, we obtained the results in the table below: 0 AL +BL Dependent Variable:Q Method: Least Squares Date: 12/02/16 Time: 16:05 Sample: 1 22 Included observations: 22 Q = A.LCUB + B.LSQ Coefficient Std. Error t Statistic Prob. 0.036843 0.013958 2.639548 0.0157 2.532560 0.532178 4.758856 0.0001 R squared S.E. of regrossion Sum squared resid 3953962. Log likelihood Durbin Watson stat 2.368164 0.612286 Mean depondent var 1090.227 Adjusted R-squared0.592900 S.D. dependent var 696.8685 444.6326 Akaike info criterion 15.11888 15.21807 164.3077 Hannan-Quinn criter. 15.14225 Schwarz criterion a. What are the estimated total, average, and marginal product functions from your regression results? i. Total Product ii. Average Product iii. Marginal Product b. At what level of labor usage does average product reach its maximum value? In a day, how many carts per worker are assembled when e. What is short-run marginal cost when average product is maximized? d. Beyond what level of labor employment does the law of diminishing average product is maximized? returns set in? Beyond what level of output?

Explanation / Answer

700

58.71

11.74

22.56

1400

216.41

21.64

39.60

2100

445.48

29.70

51.11

2800

718.28

35.91

57.10

3500

1007.18

40.29

57.57

4200

1284.54

42.82

52.50

4900

1522.74

43.51

41.92

5600

1694.14

42.35

25.80

6300

1771.12

39.36

4.17

7000

1726.03

34.52

-22.99

7700

1531.24

27.84

-55.68

8400

1159.13

19.32

-93.89

9100

582.06

8.95

-137.63

9800

-227.61

-3.25

-186.89

i.(-0.036843*L^3)+(2.53256*L^2)
ii. (-0.036843*L^2)+(2.53256*L)
iii.3*-0.036843*L^2+2*2.53256*L =5.06512L-0.1105L^2

b. Maximum average product is reached when L = 35 and AP = 43.51

c. SMC = 41.92

d. Diminishing returns set in when L = 30

700