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Rebecca is just starting a two-day, fully-funded vacation. First thing this morning, she is given $1000. First thing tomorrow morning, she is given $500. This is all the money that Rebecca has access to. Rebecca has no access to credit and cannot borrow money. She can, however, save her money overnight in a savings account that pays 10% interest per day. She will spend all of her money while on vacation.
(a) Plot and label Rebecca’s endowment (the bundle she starts off with) in the space of consumption today (C1) and consumption tomorrow (C2). Put C1on the horizontal axis.
(b) On a new set of axes, plot and label the point indicating the maximum amount of consumption that Rebecca can get today. Plot and label the maximum amount of consumption that Rebecca can get tomorrow. Use these points, along with the endowment from(a), to draw Rebecca’s budget line and label its slope.
(c) Suppose that Rebecca’s preferences are given by the following utility function:
U (C1, C2) = C1+ 2C2
What is Rebecca’s marginal rate of substitution given these preferences? How does this marginalrateofsubstitutionchangeasshegetsmoreC1?Explainintwosentencesorless.
(d) Suppose that Rebecca’s preferences are instead given by the following utility function:
U(C1, C2) = C10.5C20.5
What is Rebecca’s marginal rate of substitution given these preferences? How does this marginal rate of substitution change as she gets moreC1?Explain in two sentences or less.