ECO362H1 Study Guide - Midterm Guide: Balanced-Growth Equilibrium, Border Gateway Protocol, Capital Accumulation
ECO 362: Midterm Exam
Instructor: Stephen Ayerst
June 15, 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 is given by At+1 = (1 + g)At. The population is given by Nt+1 = (1 + n)Ntin
period t. 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. The savings
rate in both countries is equal and given by si=sj= 0.1. The initial productivities are
Ai= 2 and Aj= 1. The population growth rates are ni= 0 and nj= 0.10. 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
3and g= 0.02. (to help with the calculations
use the approximation that ng ≈0.) (8 points)
(e) Consider now that economies iand jremove restrictions on the transfer of technologies
and workers. Technology transfer to country jimproves (initial) productivity to Aj= 2 and
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 is given by at+1 = (1 + g)at. The population is given by nt+1 = (1 + n)nt in period t. the capital depreciates at a rate . 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.
