Dynamic Consumption Decisions

Individuals often face decisions about how to trade off more consumption today at the cost of additional debt and less consumption in the future, and how best to plan for consumption with various contingencies when the future is uncertain. Among other applications, this provides a formal model of how to best choose a mixture of financial assets—i.e., portfolios. Consequently, this subsection tests intertemporal consumption choices, optimal portfolio choice—which involves selecting a mix of assets that maximizes expected utility given the risks and returns associated with each asset. Understanding portfolio choice helps explain how consumers manage risk and make investment decisions, which is vital for financial planning and economic stability.

Elements

1. Arbitrage

   Deciding whether a price gap between two locations is an arbitrage opportunity after transport costs, and its profit.

2. Intertemporal Consumption Smoothing

   Computing the optimal consumption path over several periods for a CRRA consumer with savings at a fixed interest rate.

3. Price of Risk with Mean-Variance Utility

   Computing a mean-variance investor's optimal share in a risky asset, or how that share changes with the price of risk.

4. State-Contingent Consumption

   Allocating a budget across two goods before knowing which of two price states will occur.

5. Exponential Discounting

   Computing the present value of future payments under exponential discounting at a stated interest rate or discount factor.

6. Optimal Portfolio Choice with Bid-Ask Spreads

   Choosing the mean-variance optimal share of savings in a risky fund whose round-trip bid-ask spread is deducted from its return, or the best of four funds.