Consider the following consumption-saving problem. The consumer maximizes max U (c, c') = log(c) + Blog(c')...

 

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Consider the following consumption-saving problem. The consumer maximizes max U (c, c') = log(c) + Blog(c') {c,c'} subject to the lifetime budget constraint and the borrowing constraint c+ c' 1+r y + y' 1 + r c≤ y This last constraint says savings cannot be negative in the first period. Equivalently, this is saying consumers cannot borrow in the first period. (a) (2pts) Draw the budget constraint. (b) (2pts) Assuming the constraint does not bind, what is the Euler equation? (c) (4pts) Using the Euler equation, lifetime budget constraint, and borrowing constraint, solve for the period t consumption function. Clearly state under what circumstances the borrowing constraint binds. = (d) (2pts) Suppose y 3, y'= 10, B = 0.95, and r = 0.1. Show the borrowing constraint binds. Compute the optimal consumption in the present and the future. Consider the following consumption-saving problem. The consumer maximizes max U (c, c') = log(c) + Blog(c') {c,c'} subject to the lifetime budget constraint and the borrowing constraint c+ c' 1+r y + y' 1 + r c≤ y This last constraint says savings cannot be negative in the first period. Equivalently, this is saying consumers cannot borrow in the first period. (a) (2pts) Draw the budget constraint. (b) (2pts) Assuming the constraint does not bind, what is the Euler equation? (c) (4pts) Using the Euler equation, lifetime budget constraint, and borrowing constraint, solve for the period t consumption function. Clearly state under what circumstances the borrowing constraint binds. = (d) (2pts) Suppose y 3, y'= 10, B = 0.95, and r = 0.1. Show the borrowing constraint binds. Compute the optimal consumption in the present and the future.