LO 6, 7 Adapt the two-sided search model to include government activity as follows. Suppose that the government can operate irms, subject to the same constraints as private irms. In particular, the government must incur a cost k to post a vacancy. Supposing that the government operates G irms, then the number of matches in the economy as a whole is M = em(Q, A + G), where A is the number of private irms that choose to post vacancies. Assume that the government pays the same wages as do private sector irms. Determine the efects of G on the unemployment rate, the vacancy rate, the labor force, the number of private irms, the total number of irms (private and government-run), aggregate output, and labor market tightness. Explain your results.