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Credit Market Interest Rate Differences
Private Borrow Rate > Private Lender Rate = Public Borrow/Lend Rate
Good Borrowers (Never Default)
a
Bad Borrowers (Always Default)
1 - a
Bank Loan Profit Average
π = aL(1+r2) - L(1+r1) = L[a(1+r2) – (1+r1)]
Loan Rate Formula (zero profits)
r2 = (1 + r1)/a - 1
Default Premium
r2 - r1 = x
Collateralized Consumer Lifetime Budget Constraint
c + c’/(1 + r) = y - t + (y’ - t’ + pH) / (1 + r) = we
Collateral Constraint (1)
-s(1 + r) =< pH
Collateral Constraint (2)
c =< y - t + (pH)/(1 + r)
Population Growth
N’ = (1 + n)N
Pay-as-you-go Benefits Constraint
n > r
Government Balance Budget
Nb = N’t
Pay-as-you-go Tax to Benefits Relationship
t = b/(1 + n)