Exercise
Set 9
ECONOMIC GROWTH
I. Objectives
- To understand diminishing
returns to capital
- To analyze sources of
economic growth
II. Data
Consider the aggregate
production function, y = Ak0.6,
where y
is real GDP per worker (or productivity), A
is level of technology, and k
is (physical) capital per worker. The technology level (A)
is also referred to as total
factor productivity
(TFP). When TFP increases, the economy can produce more output
with the same quantity of physical capital, human capital, and labor.
TFP is is considered central to economic
growth. (Note: In the current problem, we ignore human capital,
focusing instead on physical capital.)
Assume
values for A
and k,
and compute the corresponding real GDP per worker.
Click on Gimme
per-capita GDP! to confirm.
III. Questions
In the questions that follow, let A
= 10.
- Sketch the aggregate
production function, with k
on the horizontal axis and y
on the vertical axis.
- From the graph above, we
conclude that as capital per worker increases, ceteris paribus,
output per worker
will increase at [ an increasing
rate | a
constant rate | a decreasing rate ].
- Compute the GDP per worker
for the following values of k:
- k
= 60:
y60
= __________
- k
= 90:
y90
= __________
- k
= 120:
y120
= __________
- Compute the differences:
- y90
- y60
= ______________
- y120
- y90
= ______________
- Consider
your answers in Q. 3 and Q.4. In Q.3 we
increased k
by the same amount (30) from (a) to (b), and then (b) to (c). In Q.4 we
obtained the corresponding increases in output per worker. Do
these calculations reflect diminishing returns to
physical capital?
- Consider an improvement in
technology. This is captured by an increase in the parameter A. Suppose
A
increases to 15.
- Sketch
the new production function on the same graph in Q. 1.
- We
note from the graph
that, at a given value
of k,
the value of y
is now [ greater
| smaller | unchanged ].
Video: Solution to Section
III Questions at
http://www.screencast.com/t/UijKULipln4O