05 Jun Question Last Name: _________________First Name: ________________ Student ID: ______________ ARE/ECN 115A
Question
Last Name: _________________First Name: ________________ Student ID: ______________
ARE/ECN 115A
Summer Session 1, 2015
PROBLEM SET 2: GROWTH MODELS
(Due: Thursday, July 9 in sections)
In this problem set we become familiar with the mechanics and the implications of the HarrodDomar and Solow growth models. You will be asked to present several graphs. Please title your
graphs and make sure you clearly label the axes of each graph.
11. Harrod-Domar Growth Model
Now lets walk through the mechanics of the H-D model for an imaginary country, which well
call South. Lets assume the following parameter values for South:
The incremental capital-output ratio, (v = 1.5);
Capital depreciates at a rate of 4% per year (d = 0.04);
The population grows at 3% per year (n = 0.03);
The savings rate is 15% (s = 0.15).
For South, in the initial year (t=0) the capital stock equals 300 and the population is 1
A2. Continuing under the assumption that the economy evolves according to the Harrod-Domar
model, fill in Table 2 below.
Note: Do not use the H-D growth equations yet. Instead, first completely fill in columns A to G
using the production function from the H-D model and the equation for capital accumulation,
then calculate the growth rates using the definition of growth rate: g(t) = [Y(t+1)-Y(t)]/Y(t)
Table 1. Evolution of a Harrod-Domar Economy
(A)
(B)
(C)
(D)
(E)
(F)
(G)
(H)
(I)
Year
t
Population
L(t)
Total
Capital
Stock
K(t)
Per Capita
Capital
Stock
k(t)
Total
Income
Y(t)
Per Capita
Income
y(t)
Total
Savings
S(t)
Growth
Rate of
Total
Income
g(t)
Growth Rate
of Per Capita
Income
NA
NA
0
1.00
300.00
g*(t)
300.00
1
2
B3. Use the Harrod-Domar growth equations to find the growth rate of aggregate income, g, and
the growth rate of per-capita income, g* for South. Recall that the equation for the growth rate of
per-capita income is an approximation.
1
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