# Demo: Life Cycle Consumption with Assets

For the best results, we recommend using Firefox for this interactive case study.
To solve the Life Cycle Consumption with Assets Problem:

• Enter a planning horizon (max=15), a discount factor, and an interest rate.
• Enter a minimum asset level.
• Select a utility function.
• Click "Submit" to solve the problem using the NEOS Server.
• Wait for the results to show up in the solution section at the bottom. The solution section will display the
objective value, the optimal amount to consume in each period, and the corresponding asset value for each period.

Read the examples to learn how to set an appropriate minimum asset level.

Back to Life Cycle Consumption with Assets case study.

### Input Parameters

Planning Horizon (T)
Discount Factor
Interest Rate
Minimum Asset Level
Utility Function
Wage Function w(p,T)
Solver

### Solution

Objective Value
Consumption  Assets Period 1
Period 2
Period 3
Period 4
Period 5
Period 6
Period 7
Period 8
Period 9
Period 10
Period 11
Period 12
Period 13
Period 14
Period 15

### Examples

1. No Borrowing Allowed ($a_{min} = 0$): If we run the applet for a 15 period problem with the exponential utility function, the default wage function, the default values of 0.96 for beta and 0.10 for the interest rate, and a minimum asset value of 0 (no borrowing) using KNITRO, we obtain a solution in which consumption increases over the planning horizon, starting at 0.93 in period 1, increasing at a higher rate through period 4 (to 2.71), and then increasing at a slower rate to a peak of 3.31 in period 15. The assets have zero accumulation until period 4, then a steady increase to period 12 followed by a steady decrease to period 15.
2. Borrowing Allowed ($a_{min} < 0$): If we run the applet again with the same inputs except we set the minimum asset value to -5 (borrowing allowed) using KNITRO, we obtain a solution in which consumption increases at the same rate over the planning period, starting at 2.24 in period 1 and peaking at 2.99 in period 15. In this scenario, the consumer can consume more in the earlier periods because he can borrow. The assets decrease from 0 in period 1 to -2.35 in period 4, then have a steady increase to period 13 followed by a decrease to period 15.