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Consider a firm with a production function F(l, k) = l^{\frac{3}{4}} k^{\frac{1}{4}} , who faces input prices w = 2 and v = 54.
a) Find the long run cost total cost when q=540.
b) Find the short run cost total cost when q=540 and k is fixed at 16.
c) Find the long run cost total cost and short run total cost when when q=810. For the short run, keep the same k as described in (b)
d) Explain from the results of (a-c) why you know the y where C(q) = SC(q) is less than 540, more than 810, or something in between.
e) Specifically calculate the value of q where C(q) = SC(q)
f) Graph the long run and short run total cost functions together on 1 graph. Put any calculations from (a-c) in the picture and make sure the picture is consistent with everything you’ve found.
At some levels of output Acme's average total costs are less than Generic's, but at some levels of output Generic's average costs are less than Acme's.
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