## Growth Accounting

I. Growth Rates [10 points]
The number of slurms in Wormulon is 200 in year 1600, 400 in 1800, and 600 in 1820.
(1) [3 points] Compute the percentage change in slurms over the two periods defined by these
three dates.
(2) [4 points] Compute the average rate of growth in slurms for the period 1600-1800, 1800-1820,
and 1600-1820.
(3) [3 point] Your answer for the growth rate in the period 1600-1820 in question (2) is not equal
to the growth rate in either sub-period. Comment.
II. Total Factory Productivity [25 points; 5 points each]
Total factory productivity (TFP) and factor accumulation are useful concepts that help us better
understand patterns of economic growth. It is especialy important in economic history since
economic growth and its determinants are central issues in the field.
In this section, we will work with an equation of the following form:
∆Y
Y
= a ·
∆K
K
+ b ·
∆L
L
+ c ·
∆T
T
+ R
where the delta symbols denote changes (so that ∆Y /Y describes the percentage change in Y ). Y is
output, K, L, and T are capital, labor, and resource inputs, respectively. R is the growth-accounting
residual or the measure of TFP. a, b, and c are weights.
1
Economics 308
Prof. Artunç
Spring 2018
(1) Your 14 year-old sister is a very intelligent person but knows nothing about economics. Explain
this equation to her.
(2) Why do we need the weights a, b, and c?
Consider the experience of the economy summarized in the following table.
Year Y K L T
1 100 40 80 50
2 200 80 100 60
3 250 120 110 60
(3) Assume a = 0.10, b = 0.70, c = 0.20. Compute R for growth between year 1 and year 2, and
for growth between year 2 and year 3.
(4) Assume a = 0.20, b = 0.70, c = 0.10. Compute R again for growth between year 1 and year 2,
and for growth between year 2 and year 3. Why is your answer different? Explain in economic
terms.
(5) Suppose I gave you data on Y , the weights, and the labor input L. Sketch, in words, a method
for speculating about R without getting it too wrong.