A consumer makes decision to consume in this year and next year. This year she has an income of M1 = $ 1.5 million and next year her income will be M2 = $ 2.75 million. Interest rate is 10%. Her intertemporal preferences are represented by function U(c1, c2) = c1*c2, whose intertemporal marginal rate of substitution is IMRS = c2/c1. a) Find and graph Budget Constraint b) Find and graph optimal consumption basket and indicate whether the consumer SAVES or BORROWS in the FIRST YEAR. c) Indicate whether following statement is true or false: "Any increase in interest rate will cause a decrease in consumer's welfare" Justify.
Course: Introduction to
Topic: Intertemporal Consumption Decisions
A consumer makes decision to consume in this year and next year. This year she has an income of M1 = $ 1.5 million and next year her income will be M2 = $ 2.75 million. Interest rate is 10%. Her intertemporal preferences are represented by function U(c1, c2) = c1*c2, whose intertemporal marginal rate of substitution is IMRS = c2/c1.
a) Find and graph Budget Constraint
b) Find and graph optimal consumption basket and indicate whether the consumer SAVES or BORROWS in the FIRST YEAR.
c) Indicate whether following statement is true or false: "Any increase in interest rate will cause a decrease in consumer's welfare" Justify.
d) If next year's income is maintained, how much would this year's income have to be for consumer to neither save nor borrow money at 10% interest rate?
e) How much would interest rate have to be for consumer to consume exactly her initial endowment (M1 = $ 1.5 million and M2 = $ 2.75 million) in each period? Identify ALL interest rates for which consumer is borrowing in FIRST YEAR.
Here we are given the intertemporal consumption problem. Here consumer decides the consumption in both the periods such that he is able to maximized his utility following the budget constraint (as consumer is earning limiting income in both the periods).
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