Final answer:
In the Keynesian model scenario, if the economy purchases $3 million and firms produce $2.5 million, inventories will decrease by $0.5 million to a new level of $0.7 million, reflecting an adjustment to match purchases with available goods.
Step-by-step explanation:
The student's question is focused on the Keynesian model, specifically on the impact of purchasing and production levels on inventories in an economy. In the scenario described, firms are holding an optimum inventory level of $1.2 million before the transactions occur. If the economy purchases $3 million worth of goods while firms produce $2.5 million, there will be a discrepancy since purchases exceed production. To address the purchases, firms will need to deplete their inventories by the difference between purchases and production, i.e., $3 million - $2.5 million = $0.5 million. Therefore, the new inventory level will be $1.2 million - $0.5 million = $0.7 million. This adjustment reflects firms' expectations of selling their output and maintains an equilibrium between aggregate expenditure and national income as demonstrated in Keynesian Cross Diagrams like Figure D7 or B7.