Government sets both the wage of a fire fighter and the price of a bench. We have incorporated the purchase of another good by the government. The relationship between how much it pays and how much it gets continues to be inverse. The y-intercepts on all 3 graphs are the points where the government gets only benches and no fire fighters. The x-intercept is the point where the government only employs fire fighters and does not purchase any benches.
Government spending includes the purchase of labor and park benches.
Government accepts market determined prices for both the wage of a fire fighter and the price of a bench. In this case, however, P L also fluctuates due to changing market conditions. Hence Case 3c is similar to Case 2b, where there were infinite possible outcomes. Both Case 3c and 2b are characterized by the absence of exogenous price control by the government, with price and, therefore, quantity determined by the taxpayer. Case 4 introduces different levels of Sn to Case 2a.