# US Economy & Growth Theory Questionnaire

### Question Description

Conceptual Questions

1. Find the following information on the current US economy (get the most recent data you can –

this website will probably be helpful: https://fred.stlouisfed.org)

a. The unemployment rate

b. The labor force participation rate

c. The current level of nominal GDP

d. The most recent growth rate of real GDP

e. In

ation (CPI)

f. Government debt as a percentage of GDP

2. Explain Robert Solow’s ndings in his decomposition of growth into labor, capital and technology.

In particular, discuss the role of \Total Factor Productivity” (TFP) in Solow’s ndings. Explain

some ways Solow’s model has been extended to make it more empirically relevant (as discussed

in the slides and the reading: \The growth of growth theory.”

Analytical Questions

1. An economy produces with the production function Y = 10K1=2L1=2. There is no population

growth or technological progress. The depreciation rate is 10% and the saving rate is 60%

a. Show that the production function is constant returns to scale.

b. Show that the function can be written y = 10k1=2 where y = Y

L and k = K

L

c. Assume kt = 3025. Find kt+1, kt+2, and kt+3

d. Now assume kt = 4225. Again nd kt+1, kt+2, and kt+3

that the steady state of capital must fall within.

f. Find the exact steady state capital per worker. Also nd output per worker and consumption

per worker at the steady state.

g. Find the steady state capital per worker that maximizes consumption. What is consumption

at this level?

h. Assume the economy starts in the steady state corresponding to s = 0:6. If it adjusts its

savings to the optimal level (i.e. the level that maximizes consumption in the steady state),

what is consumption per worker immediately after the change in savings (i.e. before capital

changes)? Draw a graph of consumption per worker over time as it adjusts to the new steady

state.

i. Thanos snaps his ngers and half the labor force disappears. Draw a graph of output per

worker and total output over time.

2. An economy produces with the production function Y = F(K;L) = AK1=3L2=3. Population

grows at 2% per year and A grows at 2% per year. The depreciation rate is 5% and the saving

rate is 40%. The economy is in steady state.

a. De ne A~ = A3=2. Show that the production function can be written as y~ = k~1=3 where

~y = Y

A~L

and ~k = K~

AL

. What is the growth rate of A~?

b. What is the growth rate of each of the following in steady state: K~

AL

, Y

A~L

, A~L, Y , Y

L , K

Y ,

C (hint: use the approximation that if X grows at gx and Y grows at gy then XY grows at

gx + gy)

c. At what rate do wages and the capital rental rate grow? (hint: wage=MPL and rental

rate=MPK)

d. Find the steady state value of capital per e ective worker

e. If the economy wants to maximize consumption per e ective worker, should it save more or

less? Find the consumption maximizing saving rate.

f. In 2014, L=1000 and A=9. Find total output in 2014 and 2015 (hint: for 2015 use the

growth rate you derived in part b for total output)

g. The growth rate of population falls to 0. What is the new steady state? Show the change

on a graph with investment and depreciation on the y axis and capital on the x axis (i.e. the

usual steady state graph). Also show the change over time of capital per e ective worker,

capital per worker, and aggregate capital. In your graph, be sure to capture the old steady

state, transition, and new steady state (hint: the slope of the line should be equal to the

growth rate at each point).

h. Another country uses the same production function, has the same level of total capital, but

only has 810 workers. If there is free mobility across countries (so wage rates are equalized),

what can we say about the level of technology (A) in the other country (Which country has

a higher level of technology? You do not need to solve for the actual level, but you can if it

helps)

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