Credit Market Equilibrium
Given parameters {β, N, y1, y2}, a competitive equilibrium consists of an allocation {c*1, c*2, b*1} and an interest rate R* such that:
- {c*1, c*2, b*1} maximize the household’s utility given R*.
- Markets clear:
- Bonds: ∑i=1N b*i,1 | = Nb*1 = 0
- Consumption goods: Nc*1 = Ny1, Nc*2 = Ny2
Overlapping Generations (OLG) Model
Given parameters {N, β, δ, α, s1, {At}t=1∞}, an equilibrium consists of sequences of prices {wt, rt}t=1∞, quantities {cy,t, co,t+1, st+1}t=1∞ for the household, and allocations {Kt, Lt}t=1∞ for the firm such that:
- Given {wt, rt}t=1∞, households make optimal decisions for each generation t ≥ 1, i.e., {cy,t, co,t+1, st+1} satisfy equations (10), (11), and (12).
- The initial old generation maximizes
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