Time inconsistency (hyperbolic discounting). again, this should mirror ai. page overview if necessary. call it that?
\(\sum_{t=T}C^t(1+r)^{-t}=\sum_{t=T}Y_t(1+r_t)^{-t}+W_T\)
\(W_t\) is wealth endowment at time \(T\).
If we have exponential discounting we have:
\(U_T=E[ \sum_{t=T}^\infty (1+\delta )^t U(C_t) ]\)
The first-order conditions give us:
\(u'(x_t)=(1+\delta)(1+r_t)u'(x_{t+1})\)
\(u'(x_t)=(1+\delta)(1+r_t)u'(x_{t+1})+\lambda_{t+1}\)
Hold cash, equity, bonds, mortgages.
Different utility function.
Can wait to purchase. depends on expected prices in future.
production of other commodities. house produces rentable space eg if you own house, you have rentable space each period.
depreciation? 1 for something like rent, maybe 0.01 for long term asset