See the data below. As the General Manager of hotel resorts, you seek to understand the relationship
Question:
See the data below. As the General Manager of hotel resorts, you seek to understand the relationship between 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 following 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 profit-maximizing number of labour hours.
a. Estimate the following production function: Q = αLβ, where α and β are the coefficients. First, log-linearise the production function and then estimate the log-linear regression equation. Copy and paste your regression results from your excel file, and write down your estimated function in this form: Q = αLβ.
b.Using the function in (a), derive the marginal product of labour (MPL) and plot it against L in Excel. Copy and paste your plot into your assignment.
c. Does this production function exhibit diminishing marginal returns to labour? Explain. Hint: How does MPL depend on L?
d. 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 profits?
e. Find the profit-maximizing number of labour hours mathematically.
| Q | L |
| 338 | 5215 |
| 361 | 6623 |
| 382 | 6859 |
| 406 | 7948 |
| 308 | 4560 |
| 324 | 5081 |
| 311 | 5383 |
| 311 | 4410 |
| 301 | 4294 |
| 296 | 3913 |
| 321 | 6116 |
| 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 |
Expert Answer:
Given that ShortTerm Profit Maximization 16 points Look at the numbers As the General Manager of a h... View the full answer
