bv_cvxbook_extra_exercises

p the gravitational potential i energy of mass i is

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Unformatted text preview: for equal distribution of wealth) and 1 − 1/n (when one individual holds all wealth). (a) Show that G is a quasiconvex function on x ∈ Rn \ {0}. + (b) Gini coeﬃcient and marriage. Suppose that individuals i and j get married (i = j ) and therefore pool wealth. This means that xi and xj are both replaced with (xi + xj )/2. What can you say about the change in Gini coeﬃcient caused by this marriage? 13.13 Internal rate of return for cash streams with a single initial investment. We use the notation of example 3.34 in the textbook. Let x ∈ Rn+1 be a cash ﬂow over n periods, with x indexed from 0 to n, where the index denotes period number. We assume that x0 &lt; 0, xj ≥ 0 for j = 1, . . . , n, and x0 + · · · + xn &gt; 0. This means that there is an initial positive investment; thereafter, only payments are made, with the total of the payments exceeding the initial investment. (In the more general setting of example 3.34, we allow additional investments to be made after the initial investment.) 112 (a) Show that IRR(x)...
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