Looks like the formual dropped the exponents when I posted it, I've fixed that below....does this make any more sense?
I'm not sure I have the formulas correct for this problem and I do not know what the labor hours are....
Dimex Company, a sheet-metal mfg., estimates its long run production function is:
3 3 2 2
Q = -0.015625K L + 10K L
where Q is the number of body panels produced daily. K is the number of sheet-metal presses in the mfg. plant. L is the number of labor-hours per day of sheet-metal workers employed at Dimex Company.. Dimex is currently operating with 8 sheet-metal presses.
a) What is the total production
ntion for Dimex?
Answer: Q = f(L,K) but...I am not sure what "f" is or the labor hours? Also there is no capital could this formual be used instead?
Perhaps the above is wrong and the below formula is correct?
3 2
Q = AL + BL ????????
a) What is the average production
function? 2
ANSWER: AP = Q/L = AL+ BL
2
-0.015625/L = -0.015625xL + 10xL
a) What is the marginal product
function?
ANSWER: MP = change in Q/change in L =
2
3AL + 2BL
Again I'm stumped on the labor, is it 8 hours per day times 8 guys to run 8 presses?
b) Manager at Dimex can expect the
marginal product of additional
workers to fall beyond what level
of employment?
ANSWER: Lm = B/3A
Lm = 10/3(-0.015625)
c) Dimex plans to employ 50 workers. Calculate the total product, average product, and marginal product.
ANSWER: I think this is the same as 1a, a, and a, but where does the 50 workers fit in, that has me preplexed...help!
Thanks,
EY
I still mucho confused as to what your long run production function is. I now understand that the source of the confusion lies in how your mathmatical formula is displayed. To me, it appears the same as last time. What I see is:
3 3 2 2
Q = -0.015625K L + 10K L
Im guessing that the 3s and 2s are exponents. But I wonder how they line up. Further, expressing the formula as:
Q = -0.015625(K^3)(L^3) + 10(K^2)(L^2)
doesnt make sense as it would imply serious and permanent increasing returns to scale. So, I believe the equation must be something else. But what?
Hummm, as I re-examine the equation, my knee-jerk reaction that it has permanent increasing returns to scale may not be true. Let me re-consider. (more later)
2 answers