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?
3 2
Q = AL + BL ????????
a) What is the average production
function? 2
ANSWER: AP = Q/L = AL + BL
-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'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'.
I apologize for the confusion. It appears that there might be a mistake in the given production function. Let me explain the concept and provide a general framework for analyzing the production function.
In economics, a production function represents the relationship between inputs (such as labor and capital) and output. It is usually expressed as:
Q = f(L, K)
Where Q is the quantity of output, L represents labor input, K represents capital input, and f is a generic function that captures the relationship between these inputs.
To determine the specific form of the production function, you need additional information or data. In your case, the given production function is:
Q = -0.015625K^3 L^2 + 10K^2 L^2
However, this form does not align with typical production function equations, and it does not seem reasonable to have negative values for K and L. It is possible that the given equation has been miswritten. Please double-check the equation or provide additional information to clarify.
Regarding labor hours, it is not explicitly mentioned in the given information. Typically, labor hours refer to the number of hours worked by each worker. Without the specific labor hours, it is difficult to calculate average and marginal product functions accurately.
To better understand the production function and answer your questions, it is necessary to have the correct equation or relevant information. Please provide any additional details, and I will be happy to assist you further.
It seems that there might be some confusion in the given production function equation. The equation you provided, Q = -0.015625K L + 10K L, does not seem to conform to a typical production function format.
In a standard production function, the equation is usually of the form Q = f(K, L), where Q represents the quantity of output, K represents the quantity of capital (such as the number of sheet-metal presses in this case), and L represents the quantity of labor (such as the number of labor-hours per day of sheet-metal workers).
To identify the correct total production function for Dimex, we need to have the correct equation in the format Q = f(K, L). Once we have the correct equation, we can calculate the average production function and the marginal product function.
Regarding the calculation of labor hours, you mentioned that there are 8 workers operating 8 sheet-metal presses. If each worker operates one press, it implies that the number of labor-hours would be the same as the number of workers (in this case, 8 labor-hours).
Once you have the correct production function, you can proceed to calculate the average production function (AP = Q/L) and the marginal product function (MP = ∆Q/∆L) by taking the derivative of the production function with respect to labor (L).
For the question about the marginal product function falling beyond a certain level of employment, you can calculate this by determining the level where the marginal product of labor starts to decrease. In this case, you can find this level by solving for L where MP = 0.
Finally, for the question about employing 50 workers, you can substitute the value of L (50) into the production function and calculate the total product (Q), average product (AP = Q/L), and marginal product (MP = ∆Q/∆L) accordingly.
I apologize for not being able to provide detailed answers due to the incorrect initial production function equation. If you provide the correct equation, I will be able to assist you further in solving the problem.