You would like to analyze data on a manufacturing firm's output, capital, and labor. You would like to estimate the firm's production function.

a. Try to write down this firm's production function in at least two forms and estimate parameters. (Hint: Linear, or Cobb-Douglas). Which one is your favorite?

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? (Use your Cobb-Douglas function estimation in this question).

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? (Use your Cobb-Douglas function estimation in this question)

1 Output Capital Labor 2 3563 374 213 W 4554 360 285 3658 379 213 4107 361 231 3639 438 204 2610 368 216 8 5497 432 244 9 4219 400 245 10 4400 420 231 11 3812 455 255 12 4817 370 270 13 3762 384 206 14 5579 492 262 15 5834 374 235 16 5365 426 264 17 5153 437 271 18 4843 436 218 19 4752 474 274 20 5492 490 283 21 4654 404 310 22 5256 451 262 23 2960 382 235 24 7416 498 302 25 4727 391 233 26 6702 461 275 27 5059 377 231 28 4914 459 298 29 8769 448 295 30 3313 412 210 31 5164 445 235 32 4925 487 212 33 4781 447 228 34 5716 381 272 35 6983 394 261 36 5723 446 279 37 5441 359 207 38 3446 353 289 39 3588 401 218 40 5196 354 255 41 5171 380 284 42 4661 482 210 43 4967 485 284 44 4122 397 309\f89 3508 362 289 90 4858 356 221 91 4084 387 237 92 5197 499 270 93 5052 464 262 94 6069 469 304 95 5492 354 290 96 3609 420 258 97 5378 460 239 98 4863 416 222 99 6067 398 273 100 5279 419 286 101 5037 424 206 102 6067 430 286 103 4222 449 309 104 4967 481 206 105 5745 385 276 106 5552 479 284 107 5324 387 291 108 4997 356 310 109 5908 470 302 110 6020 373 220 111 4860 433 218 112 6891 463 292 113 4874 483 235 114 4941 394 293 115 4255 380 258 116 5564 495 268 117 8218 410 303 118 3825 357 263 119 5508 431 249 120 3001 391 211 121 4709 361 283 122 4547 471 205 123 3364 486 227 124 6610 453 266 125 5345 440 310 126 4167 363 211 127 4040 350 310 128 5265 488 254 129 5307 449 271 130 4033 387 244 131 7577 387 249\f175 4334 452 283 176 5363 467 268 177 5328 384 292 178 5115 354 261 179 6509 453 264 180 5037 455 212 181 4587 387 295 182 4801 472 227 183 4862 376 261 184 3375 397 251 185 6037 461 281 186 5910 375 295 187 4485 467 256 188 5417 408 260 189 3558 458 232 190 3573 352 247 191 4758 469 277 192 5950 373 207 193 6012 442 292 194 4960 403 272 195 5794 449 209 196 5805 403 291 197 4443 377 227 198 4367 362 217 199 4659 352 275 200 3944 438 289 201 4596 470 289 202 4775 385 225 203 7635 462 243 204 8054 483 201