Question: Borrowers and savers have utility function u (C b 1, C b 2 )= log(C 1 b) +B b log(C b 2 ), u (C

Borrowers and savers have utility function u (C^b_^1,C^b_²)= log(C₁^b)+B_blog(C^b₂), u (C^s_^1,C^s_²)= log(C₁^s)+B_blog(C^s₂). with b < s. The representative borrower is subject to the period-by-period budget constraints:

C₁^b= Y₁^b q K + D₁^b, C₂^b= Y₂^b+ q K ( 1 + r ) D₁^b,

whereD1bis debt,Ytbis income in periodt, 1+ris the gross real interest rate, andKis a durable asset in fixed supply. The borrower is also subject to the following borrowing constraint:

D1bqK. (1) The representative saver is subject to the period-by-period budget constraints:

C₁^s=Y₁^s+D₁^s,

C₂^s=Y₂^s(1+r)D₁^s.

How can I derive the intertemporal budget constraint from this? can you also help me to explain its meaning?

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