Question: Both estimates are correct and the both coefficients are statistically significant. I am having trouble answering part b and c. Any help is appreciated! I've
Both estimates are correct and the both coefficients are statistically significant. I am having trouble answering part b and c. Any help is appreciated! I've also included the excel spreadsheet info, but I don't believe that is necessary since I've already got my estimates.
Excel Data:
| Output | Capital | Labor |
| 3563 | 374 | 213 |
| 4554 | 360 | 285 |
| 3658 | 379 | 213 |
| 4107 | 361 | 231 |
| 3639 | 438 | 204 |
| 2610 | 368 | 216 |
| 5497 | 432 | 244 |
| 4219 | 400 | 245 |
| 4400 | 420 | 231 |
| 3812 | 455 | 255 |
| 4817 | 370 | 270 |
| 3762 | 384 | 206 |
| 5579 | 492 | 262 |
| 5834 | 374 | 235 |
| 5365 | 426 | 264 |
| 5153 | 437 | 271 |
| 4843 | 436 | 218 |
| 4752 | 474 | 274 |
| 5492 | 490 | 283 |
| 4654 | 404 | 310 |
| 5256 | 451 | 262 |
| 2960 | 382 | 235 |
| 7416 | 498 | 302 |
| 4727 | 391 | 233 |
| 6702 | 461 | 275 |
| 5059 | 377 | 231 |
| 4914 | 459 | 298 |
| 8769 | 448 | 295 |
| 3313 | 412 | 210 |
| 5164 | 445 | 235 |
| 4925 | 487 | 212 |
| 4781 | 447 | 228 |
| 5716 | 381 | 272 |
| 6983 | 394 | 261 |
| 5723 | 446 | 279 |
| 5441 | 359 | 207 |
| 3446 | 353 | 289 |
| 3588 | 401 | 218 |
| 5196 | 354 | 255 |
| 5171 | 380 | 284 |
| 4661 | 482 | 210 |
| 4967 | 485 | 284 |
| 4122 | 397 | 309 |
| 4603 | 438 | 267 |
| 4538 | 399 | 219 |
| 4615 | 393 | 248 |
| 4877 | 401 | 241 |
| 6627 | 413 | 267 |
| 4035 | 359 | 248 |
| 4445 | 424 | 234 |
| 6224 | 443 | 294 |
| 5384 | 460 | 279 |
| 5406 | 416 | 266 |
| 5104 | 422 | 307 |
| 4990 | 370 | 203 |
| 4478 | 493 | 237 |
| 4917 | 365 | 302 |
| 4735 | 457 | 252 |
| 2877 | 432 | 236 |
| 4898 | 425 | 274 |
| 8642 | 483 | 232 |
| 5758 | 438 | 281 |
| 4139 | 405 | 202 |
| 3559 | 479 | 217 |
| 3492 | 438 | 244 |
| 5089 | 397 | 216 |
| 5177 | 384 | 229 |
| 5886 | 395 | 296 |
| 5874 | 397 | 297 |
| 3760 | 448 | 243 |
| 5728 | 373 | 305 |
| 5684 | 482 | 247 |
| 2825 | 436 | 252 |
| 5709 | 411 | 226 |
| 5325 | 389 | 306 |
| 5325 | 494 | 252 |
| 3566 | 416 | 291 |
| 4158 | 413 | 263 |
| 4226 | 431 | 244 |
| 5652 | 424 | 284 |
| 4737 | 399 | 204 |
| 4401 | 369 | 280 |
| 6437 | 466 | 281 |
| 4362 | 382 | 288 |
| 5779 | 376 | 283 |
| 4684 | 371 | 248 |
| 5201 | 499 | 201 |
| 3508 | 362 | 289 |
| 4858 | 356 | 221 |
| 4084 | 387 | 237 |
| 5197 | 499 | 270 |
| 5052 | 464 | 262 |
| 6069 | 469 | 304 |
| 5492 | 354 | 290 |
| 3609 | 420 | 258 |
| 5378 | 460 | 239 |
| 4863 | 416 | 222 |
| 6067 | 398 | 273 |
| 5279 | 419 | 286 |
| 5037 | 424 | 206 |
| 6067 | 430 | 286 |
| 4222 | 449 | 309 |
| 4967 | 481 | 206 |
| 5745 | 385 | 276 |
| 5552 | 479 | 284 |
| 5324 | 387 | 291 |
| 4997 | 356 | 310 |
| 5908 | 470 | 302 |
| 6020 | 373 | 220 |
| 4860 | 433 | 218 |
| 6891 | 463 | 292 |
| 4874 | 483 | 235 |
| 4941 | 394 | 293 |
| 4255 | 380 | 258 |
| 5564 | 495 | 268 |
| 8218 | 410 | 303 |
| 3825 | 357 | 263 |
| 5508 | 431 | 249 |
| 3001 | 391 | 211 |
| 4709 | 361 | 283 |
| 4547 | 471 | 205 |
| 3364 | 486 | 227 |
| 6610 | 453 | 266 |
| 5345 | 440 | 310 |
| 4167 | 363 | 211 |
| 4040 | 350 | 310 |
| 5265 | 488 | 254 |
| 5307 | 449 | 271 |
| 4033 | 387 | 244 |
| 7577 | 387 | 249 |
| 4229 | 473 | 235 |
| 3896 | 366 | 240 |
| 4959 | 405 | 223 |
| 4624 | 367 | 304 |
| 5793 | 398 | 269 |
| 6634 | 448 | 295 |
| 3950 | 360 | 206 |
| 6634 | 486 | 225 |
| 5629 | 427 | 298 |
| 5406 | 446 | 242 |
| 5209 | 454 | 290 |
| 5536 | 469 | 272 |
| 4885 | 499 | 310 |
| 3959 | 498 | 226 |
| 5414 | 382 | 232 |
| 5634 | 380 | 231 |
| 6682 | 454 | 284 |
| 3935 | 445 | 304 |
| 4936 | 440 | 257 |
| 3855 | 466 | 230 |
| 5417 | 411 | 233 |
| 5318 | 467 | 265 |
| 4173 | 474 | 237 |
| 4200 | 416 | 281 |
| 5726 | 477 | 288 |
| 5009 | 415 | 213 |
| 5914 | 450 | 265 |
| 4771 | 439 | 243 |
| 7434 | 438 | 248 |
| 3903 | 379 | 219 |
| 3656 | 428 | 264 |
| 4219 | 368 | 243 |
| 4241 | 483 | 231 |
| 7098 | 376 | 242 |
| 7518 | 441 | 282 |
| 4456 | 366 | 208 |
| 3615 | 363 | 218 |
| 6359 | 380 | 231 |
| 5295 | 353 | 242 |
| 6205 | 437 | 271 |
| 5667 | 431 | 298 |
| 5760 | 458 | 252 |
| 4506 | 385 | 222 |
| 4334 | 452 | 283 |
| 5363 | 467 | 268 |
| 5328 | 384 | 292 |
| 5115 | 354 | 261 |
| 6509 | 453 | 264 |
| 5037 | 455 | 212 |
| 4587 | 387 | 295 |
| 4801 | 472 | 227 |
| 4862 | 376 | 261 |
| 3375 | 397 | 251 |
| 6037 | 461 | 281 |
| 5910 | 375 | 295 |
| 4485 | 467 | 256 |
| 5417 | 408 | 260 |
| 3558 | 458 | 232 |
| 3573 | 352 | 247 |
| 4758 | 469 | 277 |
| 5950 | 373 | 207 |
| 6012 | 442 | 292 |
| 4960 | 403 | 272 |
| 5794 | 449 | 209 |
| 5805 | 403 | 291 |
| 4443 | 377 | 227 |
| 4367 | 362 | 217 |
| 4659 | 352 | 275 |
| 3944 | 438 | 289 |
| 4596 | 470 | 289 |
| 4775 | 385 | 225 |
| 7635 | 462 | 243 |
| 8054 | 483 | 201 |
As a member of Analysts Incorporated consulting firm, you have carefully collected data on a manufacturing firm's output, capital and labor. The data are in the spreadsheet below. You believe the firm's production function to be Cobb-Douglas, Q=CaLb. a. Use regression analysis to get estimates for the parameters a and b from the Cobb-Douglas production function. Round your answers to the nearest hundredth. Estimate for a: Estimate for b: Are your estimates statistically significant? b. Suppose capital is fixed at 400 and the price of output is $100. If labor costs $95 per unit, how many units of labor should the firm hire to maximize profits? Round your answer to the nearest whole number. c. If labor costs $75 per unit and capital costs $125 per unit, what is the cost-minimizing input mix for producing 4,000 units of output? Round your answers to the nearest whole number. Labor: Capital
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