Monday, September 14, 2009

Farm Decisions

An economy consisting of farms has the unusual production function for each farm as described in the table below. Apparently with an even number of workers, they play cribbage.

Number of Workers Marginal Product
1 20
2 15
3 19
4 14
5 18
6 13
7 17
etc. etc.

If you had 10 farms and 40 workers, how would you allocate them among the farms? How much total output would your farms produce? Explain.

Congratulations to Qi Wu for being the first to come up with a correct answer to this week's question. Read her answer (spread over two comments) in the comments section.

By the way, thanks to the late George Stigler for the above question.


Molly said...

I will arrange 5 workers to each 5 farms and 3 workers to rest 5 farms. The total output of my farms produce will be 185. Because, 5*(18+19) = 185.

Qi Wu

Greg Delemeester said...

Molly: Some of your numbers are correct, and some of them are incorrect. Thus, I'm still waiting for a complete correct answer to this question.

Molly said...

Dr. Greg Delemeester,
This is Qi Wu, thanks for giving me another chance. I am wodering about the total output. I guess the total output is 700. Because:
(54+86)*5 = 700.

Have a good evening!
Qi Wu

Cody Meglio said...

Molly is correct in terms of the allocation of workers. Five farms should each get 5 workers and the other 5 farms should each get 3 workers. Total production would equal the marginal product of each worker at each farm. For farms with 5 workers, total production should be (20+15+19+14+18) = 86. For farms with 3 workers, total production should be (20+15+19) = 54. Since there are 5 farms of each, total output would equal (86 * 5) + (54 * 5) = 430 + 270 = 700.

Cody Meglio
ECON 375 & 371