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.