3. Prot-Maximization in Short Run (16 points) See the data in Comm172_Assignment1_Data_2021.xlsx, the Question 3 sheet. As the General Manager of hotel resorts, you seek to understand the relationship be tween the number of vacation packages provided and hours of labour expended in providing this service. From resort hotels' records (accounting, human resources, and marketing departments), you collected four years of monthly data on the fol lowing variables: the number of vacation packages provided (Q) and the hours of labour expended in providing the service (L). Additionally, you know that the hourly wage is $15, and the price of a vacation package is $700. You want to calculate the protmaximizing number of labour hours. (a) (3 points) Estimate the following production function: Q = aL, where 0: and ,8 are the coeicients. First, loglinearise the production function and then estimate the loglinear regression equation. Copy and paste your regression results from your excel le, and write down your estimated function in this form: Q = aL. (b) (3 points) Using the function in (a), derive the marginal product of labour (M PL) and plot it against L in Excel. Copy and paste your plot into your assignment. (0) (3 points) Does this production function exhibit diminishing marginal returns to labour? Explain. Hint: How does MP1, depend on L? (d) (3 points) You are currently employing L = 5, 215. Is this number optimal? To answer this question, compare the value of the marginal product at L = 5, 215 with the hourly wage. Should the number of labour hours employed be increased, decreased, or kept unchanged in order to maximize prots? \fL 338 5215 361 6623 382 6859 406 7948 308 4560 324 5081 311 5383 311 4410 301 4294 296 3913 321 61 16 550 25411 461 18043 283 3351 377 7038 360 5719 314 4248 314 5036 310 4278 334 5175 306 4343 305 4675 293 3985 527 16359 559 27389 319 5875 375 7021 342 7123 408 10989 357 6626 317 4389 330 5530 288 3586 315 4721 291 4685 487 19869 533 22663 320 4700 297 3723 333 6745 359 7876 329 5181 308 4838 323 6014 276 3424 308 4634 293 3523 428 12484