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A factory hires workers at a wage of w=4 and capital at a rental...

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A factory hires workers at a wage of w=4 and capital at a rental...

A factory hires workers at a wage of w=4 and capital at a rental rate of r=3. The factory currently has 
four units of capital (K=4). Output (Q) is determined by the production function: 
Q = 0.25L^2K^3


(d) In the long run, if the firm wishes to continue producing Q=65,536, how much labor and capital 
will it employ? What is the cost of 65,536 in the long run?


explain the solution.    why there are   2K/3L =4/3 ?



Screen Shot 2022-10-25 at 6.33.36 PM.png

Image transcription text

(d) In the LR, the firm will choose L and K where: W MRTS = r 2K Previous Page 3L 3 :. K = 2L Using the production function to solve: 0.2512 (2L) 3 = 65536 0.251223 13 = 65536 215 = 65536 15 = 32768 L = 8 Therefore L=8 and K=16. The cost is: CLR (65536) = 4(8) + 3(16) = 80...


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