Adapt the DMP model to include government activity as follows. Suppose that the government can operate firms, subject to the same constraints as private firms. In particular, the government must incur a cost k to post a vacancy. Supposing that the government operates G firms, then the number of matches in the economy as a whole is M = em(Q, A + G), where A is the number of private firms that choose to post vacancies. Assume that the government pays the same wages as do private sector firms. Determine the effects of G on the unemployment rate, the vacancy rate, the labor force, the number of private firms, the total number of firms (private and government-run), aggregate output, and labor market tightness. Explain your results.