Solow Exercise
Edward C. Prescott
Variable 
Meaning / Value 
C_{t}_{ } 
Aggregate consumption 
c_{t} 
Individual consumption 
N_{t} 
Population 
K_{t} 
Aggregate capital stock 
w_{t} 
Rental price of a worker for a year 
r_{t} 
Rental price of a unit of capital for a year 
X_{t} 
Aggregate investment 
R_{t} 
Total capital rents 
W_{t} 
Total wages 
Ownership
A person owns his labor services. Individuals also own capital
and rent it to firms. The initial capital stock is
K_{0} = 1970
Production technology
Y_{t} =
K_{t} ^{1/3} [(1.02)^{t}
N_{t}]^{2/3}
Capital accumulates according to the following equation.
K_{t+1} =
0.95 K_{t} + X_{t}
Preferences
People prefer more consumption to less and save at the rate s = 0.20.
Population Dynamics
N_{t} = (1.01)^{t }N_{0}
Furthermore, the initial population size is
N_{0} = 1000
A date t allocation for this economy is a vector (c_{t}, k_{t},
n_{t}) for households and a vector (C_{t}, K_{t},
N_{t}) for the business sector. Let c_{0} be the numeraire (so its price is 1.0 by definition). Let
w_{t} be the real wage and r_{t} be the real rental price of capital.
QUESTIONS
Report only the answers to the questions asked and report these answers
clearly and concisely. Points will be subtracted for superflous reporting and
points added for well presented answers.
 Report a set of functions that determine the aggregate
quantities (C_{t }, X_{t }, Y_{t }) and prices
w_{t } and r_{t } given K_{t } and N_{t }.
Calculate these numbers for t = 0,1,...10 (we recommend you use excel).
 Report the time series for this economy's national
income and product accounts for t = 0,1,2,3,4, and 5.

Report the constant growth rate paths of aggregate
(K_{t}* , N_{t}* , C_{t}*, X_{t}*
, Y_{t}*) and prices (r_{t}*, w_{t}*).

What is K_{0}/K_{0}*?
What is K_{10}/K_{10}*?
In percentage terms, what fraction of the gap between the value of the capital
stock and its constant growth path value has been reduced in 10 years?