Profit Max Perfect Subs?

[J]

How does one go about doing this? From the Critical Thinking worksheet.

Obviously you don't use the first order condition because the marginal product of an input is just going to be a constant so you can't solve for either variable. 

We're given F(L,K) = 2L + 5K and I know by comparing "bang for buck" MPl/w and MP2/r, that we will choose all L. 

P = 3 w= 3 r =10

MPl = 2

MPk = 5

MPl/w = 2/3

MPk/r = 5/10 = 1/2

MPl/w > MPk/r

So we choose all L... Now what? How much L can we afford? 

[Taylor Stoltzfus]

Hey J,

Normally for profit max we have something with DRTS, which allows us to use P*MPL=w or P*MPK=r. P*MPL is the marginal revenue from one more worker, and w is the marginal cost. This condition works with DRTS because P*MPL (MR) is decreasing. Once it is equal to MC, we stop hiring. 

However, when we have CRTS, P*MPL=w is no longer a condition we can use. instead we compare P*MPL and w to see if labor will make us an infinite negative or positive profit. Notice in this problem P*MPL = 6 and w = 3. Since we have CRTS every additional worker we hire will bring in 3 dollars of profit. Try the math if you want to see it for yourself. If there are no further restrictions, we would want an infinite amount of Labor. However the professor tends to avoid infinite answers, so I would expect further restrictions on a problem like this. 

If you want to see more realistic examples, check out the profit max practice problems, I think I have 2 substitutes on there.

Let me know if you have questions!