Consider a continuous-time economy with a representative agent with timeadditive subsistence HARA utility, that is the objective
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Consider a continuous-time economy with a representative agent with timeadditive subsistence HARA utility, that is the objective of the agent is to maximize E
T 0
e
−δt 1 1 − γ
(ct − c¯)
1−γ dt
, where c¯ ≥ 0 is the subsistence consumption level. Assume that aggregate consumption c =
(ct) evolves as dct = μct dt + σ
ct(ct − c¯) dzt, where z = (zt) is a (one-dimensional) standard Brownian motion. Find the equilibrium short-term interest rate r f
t and the market price of risk λt, expressed in terms of ct and the parameters introduced above. How do r f
t and λt depend on the consumption level? Are r f
t and λt higher or lower or unchanged relative to the standard case in which c¯ = 0?
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