# two period consumption problem

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

my attempt:

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: $$C_2^A=(25,000-C_1^A)(1+0/100)+15,000$$

or, $$C_2^A=40,000-C_1^A$$

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!!

• The fact that the budget line is under the x-axis shows you that you have made some mistake. (In this case a sign error.) Please redo your calculations. Or if you are absolutely definitely super sure about them, you can edit them into the question. – Giskard Jun 8 '19 at 15:20
• err, i can't spot any calculation error, i've edited the question and added the calculations. – Chd Jun 8 '19 at 15:58
• After you substitute $Y_1^A$ into $(Y_1^A - C_1^A)$, you should get $(25,000 - C_1^A)$. (You have made a sign error.) – Giskard Jun 8 '19 at 17:31
• Actually I did that since he is borrowing in that case and thus consumption is expected to be greater than income. – Chd Jun 8 '19 at 18:04
• $25,000 - C_1^A$ will indeed be negative. That does not mean you can change the signs as you see fit. In your narrative the equation might be something like $C_2^A = 15,000 - (C_1^A-25,000)(1+200/100)$, which shows that future consumption is decreased by interest due on the loan. This however is not equivalent to your equation. – Giskard Jun 8 '19 at 19:07