Consider a general Cobb-Douglas production function q = ALaKb
where A, a and b are positive constants.
Using this production function, derive the short-run cost function for a fixed capital stock, K0, wage rate w, and capital rental rate r.
ANSWER
The production function is
q = ALaKb
Rearrange to get
La = (q/AKb)
L = (q/AKb)1/a
Substitute into the costs
C(q) = wL + rK = w(q/AK0b)1/a + rK0
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