This document contains the solution to a problem set question on advanced macroeconomics. The summary is:
1. The optimal investment strategy is a linear combination of an agent's private signal and the public signal of aggregate investment. The weights depend on complementarities, signal precisions, and their interaction.
2. Heterogeneity and volatility of investment both depend on these same factors and their effects. Higher complementarities reduce information aggregation while more precise private signals enhance it.
3. Social welfare depends on heterogeneity and volatility in a specific linear way, allowing its dependence on the key parameters to be analyzed through their effects on heterogeneity and volatility. More precise private information unambiguously improves welfare unlike in some models.