EF 5402: Economic Growth and Development (Due: 28/04/21)
Assignment
Instructor: Zhesheng QIU Name: , ID:
Homework Policy:
• Upload your homework in pdf to Canvas.
• You can discuss in groups, but need to submit your own answer.
• The solution will hopefully be released after the due date.
Problem 1: Basic Facts (10 points)
Provide a figure that highlights a cross-country pattern related to economic growth. Make sure you clearly
include the axis, variable legend, data source, and provide some brief explanation on the pattern.
Problem 2: Solow Model (10 points)
Consider a Solow model in discrete time with A(t) = L(t) = 1 and the following production function
F (K) =
⇢
0 if K 2 (0,K)p
K K if K 2 [K,+1).
Other parts of the model including the capital depreciation rate and saving rate s are still constant parameters.
(a) Prove that for 8(, s) 2 (0, 1)2, there exists K > 0 s.t. the model has two steady-state equilibria. (2 points)
(b) When there are two steady-state equilibria, find the range of K(0) s.t. K(t) converges monotonically to at
least one of the steady-states. (4 points)
(c) Given parameters {,K}, find the range of parameter s, s.t. the economy always fails to grow. (4 points)
Problem 3: Ramsay Model (15 points)
Consider the following functions forms as an extension of the Ramsay model in our slides
F (K(t), N(t), A(t)) = K(t)↵(A(t)N(t))1↵, ↵ 2 (0, 1), A˙(t)
A(t)
= g > 0, u(c(t)) = ln c(t).
(a) Write down the three first order conditions derived from the current-value Hamiltonian of the detrended
social planner’s problem. (6 points)
(b) Solve the steady state saving rate and prove that it is increasing in g. (4 points)
(c) Compare the saving rates of U.S. and China via the potentially di↵erent values of parameters. Use common
sense to compare the parameters. (5 points)
1

Too
a
– Assignment 2
Problem 4: Endogenous Growth (20 points)
Consider a representative household with no population growth choosing {C(t),K(t)}+10 to maximizeZ +1
0
exp(⇢t) (C(t) )
1✓
1 ✓ dt, (⇢, ✓, ) 2 R
3
>0,
subject to initial condition K(0) = K0 and capital law of motion
K˙(t) = AK(t) C(t), AK0 2 R>0.
(a) Write down the expression of current-value Hamiltonian eH(C,K, µ). (1 points)
(b) Write down the three first order conditions derived directly from the current-value Hamiltonian. (3 points)
(c)Write down the equation describing how consumption growth rate depends on consumption level. (2 points)
(d) Solve for C(t) as an expression of C(0). (2 points)
(e) Conjecture that K(t) = 0+ 1C(t) with unknown parameters. Solve for K(t) in terms of C(0). (3 points)
(f) Find the solution of C(t) and K(t) in terms of K0. (3 points)
(g) Prove that the saving rate s(t) is strictly increasing in time t and has a limit as t! +1. (1 points)
(h) Find the range of ⇢ that satisfies transversality condition. (1 points)
(i) Let ✓ = 1. Suppose a developed economy has reached a roughly stable saving rate 20% and per capita GDP
growth rate 2%. What are the values of parameter A and ⇢? (2 points)
(j) Let K0 = 1. Find the range of s.t. the growth rate of per capita GDP g(t) < 1% for 1000 years. (2 points)
Problem 5: Endogenous Innovation (20 points)
Problem 6: Finance Development (15 points)
Problem 7: Industry Policies (10 points)
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