ECO362H1 Study Guide - Midterm Guide: Balanced-Growth Equilibrium, Border Gateway Protocol, Capital Accumulation
ECO 362: Midterm Exam
Instructor: Stephen Ayerst
June 6, 2017
Duration: 110 minutes
Instructions: This is a closed-book exam with 120 total points. Non-programmable calcu-
lators are allowed. Read the entire question before answering. Clearly state any additional
assumptions you consider necessary. Be concise in your answers. Good luck.
Question 1 (40 Points)
Consider the Solow model with exogenous technical progress where the production func-
tion is given by Yt=Kα
t(AtNt)1−αwith α∈(0,1). The capital accumulation equation is
Kt+1 = (1 −δ)Kt+sYtwhere sis the investment rate, which is a constant fraction of GDP.
Productivity growth is given by At+1 = (1 + g)At. The population is constant and equal to
Nt= 1 in all periods. The capital depreciates at a rate δ. Answer the following questions:
(a) Derive the normalized capital accumulation equation - recall normalized capital is kt=
Kt
AtNt. The equation should not include ytor Yt.(8 points)
(b) Solve for the balanced growth path (BGP) normalized capital k∗and normalized output
y∗.(8 points)
(c) What is the growth rate of output-per-capita on the BGP? What is the growth rate of
aggregate output on the BGP? (8 points)
(d) Consider two countries iand jthat are both on the Balanced Growth Path. In country
i, the savings rate is si= 0.4and productivity Ai= 2. In country j, the savings rate is
sj= 0.1and productivity is Aj= 1. What is the relative output-per-capita Yi/Ni
Yj/Nj? Assume
that other parameters have standard values and are equal in both countries: δ= 0.08,α=1
3
and g= 0.02.(8 points)
(e) Consider now that technology is transfered from country ito country j, such that Aj= 2.
Explain the transition of country jto the new BGP. Graph yand Y /N in both countries
1
Document Summary
Instructions: this is a closed-book exam with 120 total points. Clearly state any additional assumptions you consider necessary. Consider the solow model with exogenous technical progress where the production func- t (atnt)1 with (0, 1). The capital accumulation equation is tion is given by yt = k . Kt+1 = (1 )kt + syt where s is the investment rate, which is a constant fraction of gdp. Productivity growth is given by at+1 = (1 + g)at. Answer the following questions: (a) derive the normalized capital accumulation equation - recall normalized capital is kt = The equation should not include yt or yt. (8 points) What is the growth rate of aggregate output on the bgp? (8 points) (d) consider two countries i and j that are both on the balanced growth path. In country i, the savings rate is si = 0. 4 and productivity ai = 2.
