Task 3
Consider the following Cobb-Douglas production function: q=AL^aK^b. Use the Lagrangian method to derive the cost minimizing capital-labor ratio, K/L (Hint: See Solved Problem 7.4).
B. Derive the optimal quantities of labor (L) and capital (K) as a function of the output q and factor prices (w and r). (Hint: To do so, utilize your result from part (a) in the third first-order condition of your cost minimization problem.)
Davis # 4
Task 4
A. Use your results from Task 3 to derive the long-run cost function of the firm as a function of output level q (Hint: See Solved Problem 7.6).
B. After you derived the general expression for the long-run cost function, substitute the parameter values A=1.5, a=0.5, b=0.5, w=20, r=10 to obtain C as a function of q only. Illustrate this relationship in a suitable diagram.
PLS EXPLAIN STEP BY STEP TASK 3 AND 4. THX IN ADVANCE.
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