Question

a.   Which functional form (linear, quadratic, cubic) is most suitable to your data? Construct a scatter diagram but be sure to just do the dots, don’t include the lines that connect them. Then, play around with the trendline feature and include what you consider to be the best trendline.

b.   Using OLS, estimate the firm’s short-run production function. Comment on the strength of the regression results.

c.   Calculate the Q, AP, and MP for L = 8 workers.

d.   At 8 workers, is SMC rising or falling, and how do you know?

Q	L	L^2	L^3
74	1	1	1
264	2	4	8
515	3	9	27
714	4	16	64
1,049	5	25	125
1,319	6	36	216
1,445	7	49	343
1,642	9	81	729
1,539	10	100	1000
1,208	11	121	1331

Answer 1

a. The production function is quadratic in form.

b. Y = -24.211L2 + 436.3L - 483.48

if L = 1, then Y = -71.39

The R square of the OLS model is 0.95 that is 95 percent. Hence the model is perfect as R square is close to 100 percent.

c. Q = -24.211*64 + 436.3*8 - 483.48 = 1461.42

AP = TP/L = -24.211*64 - (483.48/8) = -1609.94

MP = 2(-24.211*8) + 436.3 = 48.92

d. Falling because AP is decreasing.