03 Jun Question The output (Q) of a production process is a funct
Question
The output (Q) of a production process is a function of two inputs (L and K) and
is given by the following relationship:
Q = 0.50LK 0.10L2 0.05K2
The per-unit prices of inputs L and K are $20 and $25, respectively. The firm is
interested in maximizing output subject to a cost constraint of $500.
a. Formulate the Lagrangian function:
LQ = Q (CLL + CKK C)
b. Take the partial derivatives of LQ with respect to L, K, and , and set them
equal to zero.
c. Solve the set of simultaneous equations in Part (b) for the optimal values of
L, K, and .
d. Based on your answers to Part (c), how many units of L and K should be
used by the firm? What is the total output of this combination?
e. Give an economic interpretation of the value determined in Part (c ).
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