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