A firm operates with the production function Q = 2.5K 0.4 L0.5. Assume the price of labor and capital are $10 and $20 and the firm decides to spend only
$6,300 on variable production costs (i.e. net of fixed cost).
(a) Use the method of Lagrange Multiplier and determine the firm's level of output.
(b) Calculate the Lagrange multiplier λ.
(c) Assume that the firm increases its expenditure on variable inputs by $63 (1 %) to $6,363. Show that the level of output increases by
λ ∗ 63.