Ms. A earns 25,000 dollars in period 1 and 15,000 dollars in period 2. Mr. B earns 15,000 dollars in period 1 and 30,000 dollars in period 2. they can borrow money at an interest rate of 200% and can lend money at an interest rate of 0%. They both like consumption in period 1 ($C_1$) and consumption in period 2 ($C_2$) and their preferences are such that their chosen consumption bundles will always lie on their budget lines.
a) Write down the equations of their budget constraints and draw their budget lines in the same figure by plotting consumption in period 1 ($C_1$) on x-axis and consumption in period 2 ($C_2$) on Y-axis.
(b)Given the income profile and the market interest rates, Mr.B chooses to borrow 5000 dollars in period 1. Give an example of a consumption profile (i.e, $C_1, C_2$) such that, if Ms.A chooses this profile we know for sure that Ms.A and Mr.B have different preferences for consumption in period 1 ($C_1$) and consumption in period 2 ($C_2$). Give an explanation.
(c)Suppose now that ms.A and Mr.B have the same preferences for $C_1$ and $C_2$ and as in part (b), Mr.B borrows 5000 dollars in period 1.
i. Suppose that ms.A chooses to be a lender in period 1. Find out, with a clear explanation, the maximum amount that she will lend in period 1 consistent with the fact that they have the same preferences for $C_1$ and $C_2$.
ii. Explain whether Mr.B is better off than Ms.A
a) for A:
$C_2^A=(Y_1^A-C_1^A)(1+r) + Y_2^A$
for borrow this becomes: $C_2^A=(C_1^A-25,000)(1+200/100)+15,000$
or, $ C_2^A=3C_1^A-60000$
for lend this becomes: $C_2^A=(25,000-C_1^A)(1+0/100)+15,000$
my idea was to supersede one over the other and draw the kinked budget line but the borrow budget line in this case is totally below the x-axis and similarly for Mr.B. So, my initial plan fails. I'm clueless about (b) and (c). Please shed some light. Thank you in advance!!