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1−q (3) Note that h is by deﬁnition a continuous non-decreasing function. For a value β ≥ 0, consider the following equation in terms of the variable x: qx/(1 − q) = h(β − x) − r. At x = 0, the right-hand side of this equation is h(β) − r = h(β) − h(0) ≥ 0 and the left-hand side is zero. At x = β, the right-hand side is h(0) − r = 0 and the left-hand side is non-negative. Therefore, since the righthand side of the equation is non-increasing in x, the left-hand side is strictly increasing, and both sides are continuous functions of x, this equation has a unique solution in [0, β].