Question

Originally, Olivia planned her life assuming she could borrow or save at r1 (interest rate). Now Olivia is told that she can save money at an interest rate of r2 and borrow at an interest rate of r3, where r3>r1>r2. Draw Olivia's budget constraint. What can you conclude about Olivia's new consumption bundle, as compared to the one she anticipated originally?

Answer 1

The consumer lifetime budget constraint for endowment income (y1, y2) is given as

The consumer anticipating a single interest rate r2 will have a straight line budget line given as AB in the figure below. The slope of the line is -(1+r2) and E is the endowment or non-borrowing/ non-lending point where C1=y1 and C2=y2. If the consumer hs equilibrium to the right of this point E, she is a borrower and if the equilibrium is at the left of E she is a lender or saver.

However, in reality, the interest rate for borrowing rises to r3. The rise in interest rate increases the absolute value of the sloe of the budget line from (1+r2) to (1+r3). Then the budget line segment EB becomes steeper to EB' in reality. On the other hand, for saver the interest rate falls to r1, then the slope of the line falls to (1+r1) or the curve segment EA becomes flattered to EA' in reality. Then the actual budget line is A'EB' which lies inside the anticipated budget line AB. This also decreases the budget set of the consumer by the areas AEA' and BEB'. Hence, in reality, the consumption of the consumer falls as compared to the one she anticipated before.