posted by Ed .
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
fucntion 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?
Q = AL + BL ????????
a) What is the average production
ANSWER: AP = Q/L = AL + BL
-0.015625/L = -0.015625xL + 10xL
a) What is the marginal product
ANSWER: MP = change in Q/change in L =
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
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!
I'm confused too. I suspect there is something not right with your initial production function.
First some notational explanations.
Q=f(K,L) is an extremely general statement about production; the 'f' stands for 'function'. The statement says that quantity Q is some function of capital K and labor L.
Capital K in your example is the number of presses.
Now heres the part where I'm confused. You say:
Q= -0.015625K L + 10K L
Mathmatically, this would mean:
Q = 9.984375K L
This doesnt make sense to me.
Typically, a production function is of the form Q=aK^x bL^y where a and b are parameter constants and x and y are exponential values less than one. E.g., In a commonly used Cobb Douglas production function, x+y=1.
So, plz double check your initial production function then repost. If your initial equation is correct, then my answer to your questions is 'beats me'.