For a borrower constrained only by a lifetime budget constraint, theory predicts that a higher real interest rate / leads to reinforcing income and substitution effects on current consumption c and conflicting income and substitution effects on future consumption c'. In practice, borrowing is often limited by the need to pledge collateral for loans (think of home equity withdrawal). Consider the model of limited commitment where the borrower owns housing assets with expected future value pH. Assume the collateral constraint c