# Econ: Economics and Steady State

Spring 2014: Jenkins

Assignment #2

Due: Wednesday, May 7, 2014

Instructions: You may work with your colleagues, but you must submit your own assignment to receive credit. The assignment is due at the beginning of the class on the the due date for the assignment. Late assignments must be submitted to your TA within 24 hours of the due date/time to be eligible for half credit. You may make arrangements with your TA to submit your assignment early if necessary.

1. The Solow model and the steady state. Under the assumption of a constant labor supply and constant TFP, the Solow model is formulated as:

Y

C

Y

K

=

=

=

=

AK α L1−α

(1 − s)Y

C +I +G

I + (1 − δ)K

(1)

(2)

(3)

(4)

where K > 0 is given.

(a) Rewrite the model in terms of per worker quantities. As usual, use lowercase letters to denote variables that are in per worker terms.

(b) Suppose that δ = 0.06, s = 0.15, α = 0.35, and A = 100. If k = 2,000, then ﬁnd y, c, i, and k .

(c) Construct the Solow diagram that illustrates y, c, i, k, and k from your previous answer.

(d) Derive an algebraic expression for the steady state levels of capital per worker k ∗ and output per worker y ∗ .

(e) Find numerical values for k ∗ , y ∗ , c∗ , and i∗ .

2. Solow Diagram and Transition Paths. Assume that initially an economy is saving at a rate that exceeds its golden rule saving rate and that the economy is in a steady state equilibrium. Suppose that the economy reduces its saving rate towards the golden rule saving rate.

(a) Construct a Solow diagram that shows the eﬀects on the steady state values of capital, output, and investment per eﬀective worker.

(b) Does steady state consumption rise or fall? How do you know? 1

(c) Construct a transition path diagram that shows the eﬀect of the reduction in the saving rate on capital per eﬀective worker. You may do this by hand or you may use a computer.

(d) Construct a transition path diagram that...

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