Solow Exercise

Edward C. Prescott

Variable Meaning / Value
Ct  Aggregate consumption
ct Individual consumption
Nt  Population 
Kt  Aggregate capital stock 
wt  Rental price of a worker for a year 
rt Rental price of a unit of capital for a year 
Xt Aggregate investment
Rt Total capital rents
Wt Total wages

Ownership

A person owns his labor services. Individuals also own capital and rent it to firms. The initial capital stock is

K0 = 1970

Production technology

Yt = Kt 1/3 [(1.02)t Nt]2/3

Capital accumulates according to the following equation.

Kt+1 = 0.95 Kt + Xt

Preferences People prefer more consumption to less and save at the rate s = 0.20.

Population Dynamics

Nt = (1.01)t N0

Furthermore, the initial population size is

N0 = 1000

A date t allocation for this economy is a vector (ct, kt, nt) for households and a vector (Ct, Kt, Nt) for the business sector. Let c0 be the numeraire (so its price is 1.0 by definition). Let wt be the real wage and rt 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.
  1. Report a set of functions that determine the aggregate quantities (Ct , Xt , Yt ) and prices wt and rt given Kt and Nt . Calculate these numbers for t = 0,1,...10 (we recommend you use excel).

  2. Report the time series for this economy's national income and product accounts for t = 0,1,2,3,4, and 5.

  3. Report the constant growth rate paths of aggregate (Kt* , Nt* , Ct*, Xt* , Yt*) and prices (rt*, wt*).

  4. What is K0/K0*? What is K10/K10*? 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?