Consider an economy, where there is a single consumption good and two states of nature {a,b}. There are two consumers, A and B, with preferences and (random) endowments as follows: Agent A: u (¤Â(a),ïÂ(b)) = logxÂ(ª) + logïÂ(b), (¤Â(a), ¤Â(b)) = (1,2) ● Agent B: uß (¤Â(a), xß(b)) = logxß(a) + logxß(b), (eß(a), eß(b)) = (3, 1) (i) In order to hedge against risk individuals can trade two securities with returns · (¹), (9), where the top payoff refers to state a and the bottom to state 6. How many units of the asset r₁ will be held by individual A at equilibrium? denominated in units of the commodity: r₁ = and r2 =

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Consider an economy, where there is a single consumption good and two states of
nature {a, b}. There are two consumers, A and B, with preferences and (random)
endowments as follows:
E logt A (a) + logzA(6), (ел(а), ед()) — (1, 2)
• Agent A: ua (xA(a), xA(b))
. Agent B: ив (лв (а), тв ()) — 1oga в (а) + loga в (), (ев(а), ев ()) — (3, 1)
(i) In order to hedge against risk individuals can trade two securities with returns
()-
denominated in units of the commodity: ri =
and r2
where the
top payoff refers to state a and the bottom to state b. How many units of the asset
ri will be held by individual A at equilibrium?
Transcribed Image Text:Consider an economy, where there is a single consumption good and two states of nature {a, b}. There are two consumers, A and B, with preferences and (random) endowments as follows: E logt A (a) + logzA(6), (ел(а), ед()) — (1, 2) • Agent A: ua (xA(a), xA(b)) . Agent B: ив (лв (а), тв ()) — 1oga в (а) + loga в (), (ев(а), ев ()) — (3, 1) (i) In order to hedge against risk individuals can trade two securities with returns ()- denominated in units of the commodity: ri = and r2 where the top payoff refers to state a and the bottom to state b. How many units of the asset ri will be held by individual A at equilibrium?
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