Answer
a) Please see the graph. The new price and level of output after the increased investment are $P_{1}$ and $Q_{1}$, respectively. The quantity supplied changes since the price level increased. Also, people might still have misperceptions of the price level, wages might be sticky, or prices might be sticky, any of which would lead to the increased output.
Work Step by Step
b) The new long-run equilibrium price and quantity, respectively, are $P_{2}$ and $Q_{0}$. The aggregate quantity demanded changes between the short run and the long run due to the increased price level. The price level increases as misperceptions disappear, wages change and/or prices change.
c) The investment boom would affect the long run aggregate supply curve. The boom would be due to the increased capital stock derived from today's increased investment. In turn, the increased capital stock would drive higher productivity and output.