ECON1102 Study Guide - Final Guide: Compound Annual Growth Rate, Budget Constraint, Capital Accumulation
Economic Growth
• Economic growth - growth in total (national) real economic output.
• We calculate growth using simple arithmetic of proportionate change in y between period t and t + 1:
(yt+1 - yt)/yt
Financial Compounding
• Financial compounding - a process whereby the value of an investment increases exponentially over
time due to compound interest.
• Compound interest - interest is paid on both principal and the interest being earned on that principal as
it is accumulating.
• This process means that relatively low annual growth rates can lead to big changes over time.
Annual Compound Growth Rates
• Because of compounding, one cannot use the simple arithmetic formula we used earlier.
• Instead we use the Compound Annual Growth Rate (CAGR) formula - this rate provides a much accurate
measure of annualised growth over long periods.
• CAGR = (Ending value/Beginning Value)(1/no. of years) - 1
• ^ Dot eed to do calculatios.
The Economic "Problem" of Growth
• The modern economic paradigm of the last 300 years or so is built to grow and people have come,
overall, to expect regular increases in economic output and income.
• If there is no growth, stagnation occurs and this leads to what feels like a permanent recession.
• In the 1990s, Japan was the second richest country in the world.
• Japanese GDP has remained stagnant for 20 years now while other countries have grown.
• This means that Japanese living standards are stuck in absolute terms and falling in relative terms.
Constrained Optimisation
• Solow did not invent growth theory. In fact, there were models similar to his, particularly the Harrod-
Domar model, which posited economic growth in terms of constrained optimisation.
• This is a type of problem whereby an 'objective function' (i.e. a functional relationship posited for a
particular goals) is maximised subject to posited constraints, eg: utility maximisation with a budget
constraint.
Maximising Growth
• One could posit the problem of maximising GDP growth subject to particular resource constraints.
• We could say Y = f(K,L).
• Subject to K̅ ,̅L, where the 'bars' above the inputs indicate some fixed amount.
Growth Theory pre-Solow-Swan
• This is basically how Harrod and Domar posited the growth problem. Their time-frame was the long-run:
they were trying to model the economy's 'growth path', given constraints, over many years.
• The technical problem with their model was that it was extremely sensitive to small changes in variable
values and would expand or contract 'explosively'.
The Solow-Swan 'Neoclassical' Growth Model
1. Production: The Solow-Swan growth model starts with a national production function put into a particular
form referred to as 'Cobb-Douglas':
2. Resource Constraint: It then adds an explicit constraint in which output can be used for either
consumption or investment: Ct + It = Yt
3. Capital Accumulation: We also add a description of the evolution of capital stock (and in so doing make
it 'endogenous':
o Depreciation - what the equation above says is that capital accumulation at time t+1 consists of
investment in time t, plus new investment at time t minus the change in existing capital stock due
to depreciation. Thus, we have net investment which equals investment less depreciation.
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