Assume Kodak's production function for digital cameras is given by Q = 100(L [sup:1mwqevii]0.7K0.3), where L and K are the number of workers and machines employed in a month, respectively, and Q is the monthly output. Moreover, assume the monthly wage per worker is $3,000 and the monthly rental rate per machine is $2,000. Moreover, assume the monthly wage per worker is $3,000 and the monthly rental rate per machine is $2,000.
Note: Given the production function, the marginal product functions are MPL = 70(L–0.3K0.3) and MPK = 30(L 0.7K –0.7).
a. If Kodak needs to supply 60,000 units of cameras per month, how many workers and machines should it optimally employ?
L = # of workers Monthly wage is $3000
K = # of machines Monthly rental rate/machine is $2000
Q is monthly output
Q = 100(L0.7K0.3)
Wk is wage per worker
Mrr is monthly rental rate
Marginal Product (MP) functions are MPL = 70(L -0.3K[/sup:1mwqevii]0.3) & MPk = 30(L[sup:1mwqevii]0.7K-0.7)
Kodak needs to minimize its total cost of producing the 60,000 cameras according to its production function and input prices. It needs to develop of labor-to-capital ration so that:
MPk /MPl = Wk/Wl
(30L[/sup:1mwqevii]0.7Ks[sup:1mwqevii][/sup:1mwqevii] –0.7)/ (70L[sup:1mwqevii][/sup:1mwqevii]–0.3K[sup:1mwqevii][/sup:1mwqevii]0.3) = 2000/3000 - Someone told me this but I don’t know how they got it. Can you break this down so I can understand it?
Lost here as don’t know how to get this down to next steps to figure out how many employees they need to employ.
b. What are the total cost and average cost of producing the quantity given in (a)?
Note: Given the production function, the marginal product functions are MPL = 70(L–0.3K0.3) and MPK = 30(L 0.7K –0.7).
a. If Kodak needs to supply 60,000 units of cameras per month, how many workers and machines should it optimally employ?
L = # of workers Monthly wage is $3000
K = # of machines Monthly rental rate/machine is $2000
Q is monthly output
Q = 100(L0.7K0.3)
Wk is wage per worker
Mrr is monthly rental rate
Marginal Product (MP) functions are MPL = 70(L -0.3K[/sup:1mwqevii]0.3) & MPk = 30(L[sup:1mwqevii]0.7K-0.7)
Kodak needs to minimize its total cost of producing the 60,000 cameras according to its production function and input prices. It needs to develop of labor-to-capital ration so that:
MPk /MPl = Wk/Wl
(30L[/sup:1mwqevii]0.7Ks[sup:1mwqevii][/sup:1mwqevii] –0.7)/ (70L[sup:1mwqevii][/sup:1mwqevii]–0.3K[sup:1mwqevii][/sup:1mwqevii]0.3) = 2000/3000 - Someone told me this but I don’t know how they got it. Can you break this down so I can understand it?
Lost here as don’t know how to get this down to next steps to figure out how many employees they need to employ.
b. What are the total cost and average cost of producing the quantity given in (a)?