The Standard Two-Period Consumption/Saving Model
Order ID 53563633773 Type Essay Writer Level Masters Style APA Sources/References 4 Perfect Number of Pages to Order 5-10 Pages Description/Paper Instructions
Consider the standard two-period consumption/saving model discussed in class. The households problem is to choose current and future consumption (???? and ????+1) to maximize its lifetime utility, taken as given the current and future income (???? and ????+1), and the real interest rate
max
subject to
where ?? is the parameter to discount future utility.
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a. Derive the Euler equation for this problem and provide some economic intuition for this important equation.
b. Combine the Euler equation from (a) with the intertemporal budget constraint to get a consumption function, that is, an expression for ???? as a function of parameters and exogenous variables. Whats the marginal propensity to consume?
c. Assume that the household is initially borrowing and analyze a reduction in the real interest rate (????) in a graph representing future consumption (????+1) on the vertical axis and current consumption (????) on the horizontal. Identify in your graph the substitution and income effects. Intuitively explain both effects.
d. After the reduction in the real interest rate, will the current consumption (????) be greater or lower than before? Explain.
2) In the basic two-period model, we consider that the household can save or borrow at the same real interest rate. Consider now that households face different real interest rates for borrowing (????) and for saving (????), where ???? > ????. The difference between the borrowing and saving rates (???? ? ????) is known as the interest rate spread.
a. What is the households budget constraint in the case in which it consumes less than its income in period one? Answer in the form of an equation.
b. What is the households budget constraint in the case in which it consumes more than its income in period one? Answer in the form of an equation.
c. On a single graph, representing future consumption (????+1) on the vertical axis and current consumption (????) on the horizontal,show the two budget constraints from parts (a) and (b). Shade the area that represents the combination of first-period and second-period consumption the household can choose.
d. Now add to your graph the households indifference curves. Show three possible outcomes in three different figures: one in which the household saves, one in which it borrows, and one in which the household neither saves nor borrows.
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