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pM. Calculate the consumer's optimal investment decision IM at t = 0, the price of the bond pM, and the optimal consumption in the two states CM, cM. Compare the mutual fund and bond market allocations: are c and cM bigger or smaller than cand c², respectively?

pM. Calculate the consumer's optimal investment decision IM at t = 0, the price of the bond pM, and the optimal consumption in the two states CM, cM. Compare the mutual fund and bond market allocations: are c and cM bigger or smaller than cand c², respectively?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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The following question is based on the model of Diamond and Dybvig (1983). There are three dates t = 0, 1, 2 and a continuum of consumers with measure one, each endowed with one unit of wealth. A fraction a of consumers is impatient, i.e. they derive utility u (c1) from consuming only at t = 1, and 1 – a are patient and derive utility u (c2) from consuming only at t = 2. The utility function is u(c) = 1 – (1/c). At t = 0 consumers don't know their type, i.e. it is unknown whether the consumer wishes to consume at date t = 1 or t = 2. At t =1 all consumers observe their own type, but cannot observe others' types (i.e. type is private information). Consumers can store their wealth across periods, with one unit stored today yielding one unit tomorrow. Alternatively, wealth can be invested in a long term technology at date t 0, which yields 0 at t = 1, but R > 1 at t = 2. %3D
Transcribed Image Text:The following question is based on the model of Diamond and Dybvig (1983). There are three dates t = 0, 1, 2 and a continuum of consumers with measure one, each endowed with one unit of wealth. A fraction a of consumers is impatient, i.e. they derive utility u (c1) from consuming only at t = 1, and 1 – a are patient and derive utility u (c2) from consuming only at t = 2. The utility function is u(c) = 1 – (1/c). At t = 0 consumers don't know their type, i.e. it is unknown whether the consumer wishes to consume at date t = 1 or t = 2. At t =1 all consumers observe their own type, but cannot observe others' types (i.e. type is private information). Consumers can store their wealth across periods, with one unit stored today yielding one unit tomorrow. Alternatively, wealth can be invested in a long term technology at date t 0, which yields 0 at t = 1, but R > 1 at t = 2. %3D
Now suppose there is no financial intermediary to handle liquidity shocks. However, at t = 1 a market for bonds opens up and agents can trade their wealth at t = 1 for wealth at t = 2. Each bond pays 1 at t = 2 and its price is pM. Calculate the consumer's optimal investment decision IM at t = 0, the price of the bond pM, and the optimal consumption in the two states cM, cM. Compare the mutual fund and bond market allocations: are c4 and c bigger or smaller than cf and c, respectively?
Transcribed Image Text:Now suppose there is no financial intermediary to handle liquidity shocks. However, at t = 1 a market for bonds opens up and agents can trade their wealth at t = 1 for wealth at t = 2. Each bond pays 1 at t = 2 and its price is pM. Calculate the consumer's optimal investment decision IM at t = 0, the price of the bond pM, and the optimal consumption in the two states cM, cM. Compare the mutual fund and bond market allocations: are c4 and c bigger or smaller than cf and c, respectively?
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