(a) A firm has production function q(k,l) = k1/3l 2/3, where k denotes the capital used and l denotes the labour employed. Suppose that each unit of capital costs v dollars and each unit of labour costs w dollars, so that the capital and labour costs are vk + wl. Use the Lagrange multiplier method to determine the values of k and l that minimise the cost of producing Q units of the firm's good. Find the corresponding minimised value, C, of this cost and the value, , of the Lagrange multiplier corresponding to the optimising values of k and l. Show that = @C @Q.