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# Answer to Question #63160 in Microeconomics for Seán

Question #63160
Firm produce output according to C.D technology Y=F(K,L)=AK^α L^(1-α). Derive short run profit maximising input demand, output supply and profit functions with this technology, ignoring firm's shutdown condition.
1
2016-11-08T14:59:10-0500
the marginal products for the Cobb–Douglas production function are: MPL = (1 – α)Y/L. MPK = αY/K. Competitive profit-maximizing firms hire labor until its marginal product equals the real wage, and hire capital until its marginal product equals the real rental rate. Using these facts and the above marginal products for the Cobb–Douglas production function, we find: W/P = MPL = (1 – α)Y/L. R/P = MPK = αY/K. Rewriting this: (W/P)L = MPL × L = (1 – α)Y. (R/P)K = MPK × K = αY. Note that the terms (W/P)L and (R/P)K are the wage bill and total return to capital, respectively.

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Assignment Expert
10.11.16, 17:55

Dear Seán, You're welcome. We are glad to be helpful. If you liked our service please press like-button beside answer field. Thank you!

Assignment Expert
10.11.16, 17:55

Dear Seán, You're welcome. We are glad to be helpful. If you liked our service please press like-button beside answer field. Thank you!

Assignment Expert
10.11.16, 17:55

Dear Seán, You're welcome. We are glad to be helpful. If you liked our service please press like-button beside answer field. Thank you!

Seán
08.11.16, 22:47

Great answer! Many thanks, does this include the profit function and both input supply and output demand? Also, should ID and OS be the same thing in this function? I forgot to mention that K is fixed as it in the short term. Many thanks again!