Edward C. Prescott - Advanced Undergraduate Macro - Solow Exercise

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

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 N₀

Furthermore, the initial population size is

N₀ = 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 c₀ 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.

1. 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).

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 (K_t* , N_t* , C_t*, X_t* , Y_t*) and prices (r_t*, w_t*). 

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?