Exercise 21.1 A firm has weekly production function q(k, l) = k1/411/2, and the unit weekly costs for capital and labour are v = 20 and w = 10. The firm wishes to produce 200 units a week of its good. Find the minimum cost of doing so.Key terms, notations and formulae . capital, k; labour, I . unit cost of capital, v; unit cost of labour (wage), w . total production costs uk + wl . constrained optimisation, e.g., optimise F(x, y) subject to G(x, y) = 0 . objective function; constraint . Lagrange multiplier, 2 . Lagrangean L(x, y, A) = F(x, y) - AG(x, y) OL OL . solve equations ax dy =0, G=0 . cost function C(q); C(q*) is solution to minimise ok + w/ subject to q(k, !) = q" . efficient small firm with Cobb-Douglas production function q(k, !) = Ak*18 has C(q) = Zq1/(*+#) = Zqf . form of supply curve of the efficient small firm depends on f