Suppose a price-taking profit-maximising firm produces output in the short run using only labour as a variable factor. Output (Q) and labour input (L) are related by the equation: Q = La Where a a positive constant, the price of output is given and denoted by p, and the wage is given and denoted by w. The firm seeks to maximise profits, given by pQ - WL. Show that the first order condition for a profit maximum may be written as: apLa-1= W and hence show that in this case the firm's demand for labour is given by L = op W Further, by examining the second-order conditions explain carefully the requirement that 0