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Jacob is a naïve present-biased agent with β = 0.8, δ = 0.95, and u(x) = x. Jacob is in Year 12 (at t = 0) and deciding which course to study at university. He is deciding between physics, which is hard but will deliver a rewarding career, or basket weaving, which is a fun course but has worse career prospects. Jacob can only choose the career for which he studies. The options deliver the following costs and benefits: Studying physics: cost of 5 in each of t = 1, t = 2, and t = 3. Studying basket weaving: no cost. Physics career: benefit of 20 at t = 4. Basket weaving career: benefit of 2 at t = 4. Task: Draw a plot illustrating the discounted utility at each time from t = 0 to t = 4 of the physics career at t = 4. Describe the plot and its main features. (Note: you are plotting only the career benefit, not the costs.)

Explore the decision-making process of a present-biased agent, Jacob, as he chooses between studying physics and basket weaving. This problem illustrates concepts of discounted utility, present bias, and decision theory using a case of long-term versus short-term rewards.

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