Question 1 For a borrower constrained only by a lifetime budget constraint, theory predicts that a higher real interest rate r 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 sy-t+pH/(1+r) is binding. How does the set of feasible consumption plans (c, c') change with a higher real interest rate r (for given pH)? Does the binding collateral constraint necessarily make the response of current consump- tion c larger or smaller than it would be if there was no binding collateral constraint (and the same amount was borrowed initially, for comparability)? Explain your answer. [6 marks]