The inverse market demand curve for a final good is \(P=50-Q\) and the wage rate is \(w=20\). Each unit of output requires half a unit of labor, \(L\), and no other factor, \(Q=2 L\). If factor and output markets are competitive, what are the equilibria in both factor and output markets? How does your answer change if the factor market is competitive but the output market is a monopoly?