Question

becca is just starting a two-day, fully-funded vacation. First thing this morning, she is given $2000. First thing tomorrow morning, she is given $1000. This is all the money that becca has access to. becca has no access to credit and cannot borrow money. She can, however, save her money overnight in a savings account that pays 15% interest per day. She will spend all of her money while on vacation.

(a) Plot and label becca’s endowment (the bundle she starts off with) in the space of consumption today (C1) and consumption tomorrow (C2). Put C1 on the horizontal axis.

Answer 1

Since no commodity is mentioned, let us assume a composite commodity whose price is $1.

C1 consumption today, C2 is consumption tomorrow

M1- income today is $2000, M2- income tomorrow is $1000.

Since Becca cannot borrow she cannot consume more than $2000 worth of composite commodity today. If Becca does not save anything today than she consumes 2000 units of C1 today with her income of $2000 and 1000 units of C2 with her income of $1000 tomorrow.

So B = (C1,C2)= (2000,1000). This is her endowment as she comes in the market with this amount.

If Becca saves entire $2000 today and consumes all the amount tomorrow then she consumes C1= 0 today and C2 = 1000 + 2000 + 15% of 2000 tomorrow i.e. C2 = 3300. So A = (C1,C2) = (0,3300)

Plotting the two combinations and joining them, we get the different possible combinations of C1 and C2 for Becca for different amount of saving. Combination B correspond to zero saving. Combination A corresponding to saving all the amount received today for consumption tomorrow. Combinations on line AB give different combination of C1 and C2 for different amount of saving.