Let's use the Euler equation two ways. First, to find out the optimal consumption path, taking the interest rate as a given and then to find out the equilibrium interest rate that will eliminate demand for saving and investment, taking the consumption path as a given. Both times, the utility function will be the same. U = In(c₂) + 0.9 ln(c+₁) t+1 So the future counts 90% as much as the present. In Part 1, income each period is 100, and the interest rate is 20%. In Part 2, consumption in each period is 100 -- in other words, income each period is 100, but income isn't

Let's use the Euler equation two ways. First, to find out the optimal consumption path, taking the interest rate as a given and then to find out the equilibrium interest rate that will eliminate demand for saving and investment, taking the consumption path as a given. Both times, the utility function will be the same. U = In(c₂) + 0.9 ln(c+₁) t+1 So the future counts 90% as much as the present. In Part 1, income each period is 100, and the interest rate is 20%. In Part 2, consumption in each period is 100 -- in other words, income each period is 100, but income isn't

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Let's use the Euler equation two ways. First, to find out the optimal
consumption path, taking the interest rate as a given and then to find out the
equilibrium interest rate that will eliminate demand for saving and
investment, taking the consumption path as a given. Both times, the utility
function will be the same.
U =
In(c) + 0.9 ln(c₁+₁)
t+1
So the future counts 90% as much as the present. In Part 1, income each
period is 100, and the interest rate is 20%. In Part 2, consumption in each
period is 100 -- in other words, income each period is 100, but income isn't
storable (it's “manna”), so you have to consume it or lose it. Answer the
following questions:
Part A: What is optimal consumption each period? In period t of this
two-period world, will this person be borrowing or saving or neither?
Part B: What is the equilibrium interest rate between these two periods? If the
equilibrium interest rate were lower than that level, would that create a
surplus or a shortage, in Econ 101 terms?

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Hello! please can you solve question B? Thanks