Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 30L / b / Solution

The time-zero indifference price is the unique $\pi (Y)$ satisfyingThe left side is continuous and strictly decreasing in the cash amount by part (a), and its limiting values bracket $u(0)$; existence follows by the intermediate-value theorem and uniqueness by strict monotonicity.