Final answer:
In an Overlapping Generations model, the representative agent's problem is to maximize utility by choosing present and future consumption levels.
Step-by-step explanation:
In an Overlapping Generations model, the representative agent's problem is to choose present and future consumption levels to maximize overall utility. In this case, the agent's utility function is in log form. The agent discounts future consumption at a rate of θ where 0<θ<1. The agent consumes c and saves s in the first period of life from income y, which earns interest at rate r. In the second period, the agent consumes from savings plus interest earned but must also pay a fixed flat tax. The goal is to find the combination of consumption and savings that maximizes the agent's utility.
To solve the problem, we need to set up the agent's intertemporal budget constraint and solve for the optimal solution. The budget constraint represents the different combinations of present and future consumption that the agent can afford. The slope of the budget constraint is determined by the interest rate r. The utility-maximizing choice will depend on the specific values of r, θ, y, c, and the tax rate.
Given that the agent's utility is in log form, the agent's problem can be solved using calculus. By maximizing the agent's utility function subject to the intertemporal budget constraint, we can find the optimal combination of present and future consumption that maximizes the agent's overall utility.