Pozdravljeni. Težave imam s sledečo nalogo, in sicer predvsem z dokazovanjem prvega dela. Drugi del naloge sem še nekako rešil. Prilagam izvirno besedilo naloge in prevedeno besedilo naloge.
Izvirno besedilo:
Let \($(a_1, a_2, ..., a_q)$\) represent cash-flows over \($q$\) years. A man decides to
discount cash-flows and compare alternatives according to
\($v(a_1, a_2, ..., a_q) = \sum_{i=1}^q \rho^{i-1} a_i, (\rho > 0)$\). Show that:
\($$
(\alpha, a_1, a_2, ..., a_{q-1}) \succeq (\alpha, b_1, b_2, ..., a_{q-1})
$$\)
\($$
(a_1, a_2, ..., a_{q-1}, \alpha) \succeq (b_1, b_2, ..., a_{q-1}, \alpha)
$$\)
The decision maker is indifferent between the following five-year cash-flows.
Find the discount factor that represents his preferences.
\((5, 3, 5, 7, 10) $\sim$ (4, 3, 9, 7, 6)\)
Prevod:
Naj \($(a_1, a_2, ..., a_q)$\) predstavlja denarni tok za obdobje \($q$\) let. Nekdo se odloči diskontirati
denarni tok in primerjati alternative po formuli
\($v(a_1, a_2, ..., a_q) = \sum_{i=1}^q \rho^{i-1} a_i, (\rho > 0)$\). Pokaži, da velja:
\($$
(\alpha, a_1, a_2, ..., a_{q-1}) \succeq (\alpha, b_1, b_2, ..., a_{q-1})
$$\)
\($$
(a_1, a_2, ..., a_{q-1}, \alpha) \succeq (b_1, b_2, ..., a_{q-1}, \alpha)
$$\)
Sprejemalec odločitve je indiferenten med naslednjima petletnima denarnima tokovoma.
Poišči diskontni faktor, ki predstavlja njegove preference.
\((5, 3, 5, 7, 10) $\sim$ (4, 3, 9, 7, 6)\)