ECON-4330 Advanced Macroeconomics I Professor Nurlan Turdaliev
Homework Assignment 4 Fall 2021
Due: Friday, December 3, 2021, 6pm
Problem 1
Consider the economy with capital studied in class. Assume the endowment vector (y, 0). Suppose
the production function is f(k) =
√
k and u(c1, c2) = ln c1 + ln c2.
a. Suppose there is no money. Find the equilibrium consumption allocation (c∗1, c∗2).
b. Now suppose there is money in this economy. Find the equilibrium consumption allocation
(cˆ1, cˆ2).
c. Let u∗(y) = u(c∗1, c∗2) and uˆ(y) = u(cˆ1, cˆ2). Calculate the values of u∗(y) and uˆ(y) for the
values y = 1, 5, 10. What is larger, u∗(y) or uˆ(y)?
d. Plot u∗(y) and uˆ(y) for values of y ∈ [0, 10] on the same graph using different colours or
thickness. You can use Maple, Excel, or any other software.
Problem 2
Consider the economy with capital and private debt but without money studied in class. Assume
the endowment vectors are (y, 0) for lenders and (0, y) for borrowers. Suppose the production
function is f(k) =
√
k and u(c1, c2) = ln c1 + ln c2.
a. Find the equilibrium gross interest rate r∗. (Remember that r > 0. Note that you may obtain
more than one value of r∗. Hint: use the fact that one of the roots of the equation you will
be solving is r = 1.)
b. Find the value(s) of k∗.
c. Find the values of consumption in both periods for borrowers and lenders?
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