Adapt the two-sided search 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 labour force, the number of private firms, the total number of firms (private and government-run), aggregate output, and labour market tightness. Explain your results.