Unit 5: Production, Growth, and the Solow Model
Why a small gap in growth rates compounds into a completely different country in one lifetime, and the Solow picture of capital and technology behind it.
8 topics · 32 questions
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Growth Rates and the Rule of 70
- How it worksHow does compounding a small annual growth rate over decades produce most of the difference between rich and poor countries?
- Worked exampleFind how many years it takes an economy growing at 3.5 percent a year to double in size, using the rule of 70.
- Common mistakeWhy isn't a growth rate difference of two percentage points a small deal over the span of a human lifetime?
- Going furtherWhat happens to the doubling time when a country's growth rate is cut in half?
Your turn1 of 2
Find how many years it takes an economy growing at 4.63 percent a year to double in size, using the rule of 70.The Sources of Economic Growth: Capital, Labor, and Technology
- How it worksHow do physical capital, human capital, and technology each raise the amount one worker can produce?
- Worked exampleFind labor productivity when real GDP is 22 trillion dollars and 160 million people are employed.
- Going furtherWhat happens to output per worker when capital keeps piling up but technology stands completely still?
- Ties togetherHow does productivity growth push both a country's production frontier and its long-run supply curve outward together?
Your turn1 of 2
Find labor productivity when real GDP is 25 trillion dollars and 162 million people are employed.The Production Function and Diminishing Returns to Capital
- How it worksHow does a production function with diminishing returns bend flatter as more capital piles onto the same workers?
- Worked exampleFind the extra output from one more unit of capital per worker when output per worker is the square root of capital, moving from 4 to 9.
- Common mistakeWhy doesn't diminishing returns to capital mean that adding more capital ever makes output fall?
- Going furtherWhat happens to the payoff from one more unit of capital in a country that already has an enormous capital stock?
Your turn1 of 2
Find the extra output from one more unit of capital per worker when output per worker is the square root of capital per worker, moving from 7 to 22.Capital Deepening and the Solow Diagram
- How it worksWalk me through the Solow diagram: a saving curve adding capital and a depreciation line taking it away, both measured per worker.
- Common mistakeWhy isn't capital deepening able to raise a country's growth rate forever, even with a very high saving rate?
- Going furtherWhat happens on the Solow diagram when a country's saving rate rises to a permanently higher level?
- Ties togetherHow does the Solow diagram's saving curve connect back to the same national saving that funds the loanable funds market?
Your turn1 of 2
If a country's saving rate is 0.289 and output per worker is 39470 dollars, how many dollars per worker does the country invest?The Solow Steady State
- How it worksHow does capital per worker settle at the exact point where new investment just replaces the capital that depreciated?
- Worked exampleFind the steady-state capital per worker when investment per worker is 0.3 times the square root of capital per worker and the depreciation rate is 0.06.
- Common mistakeWhy doesn't reaching a Solow steady state mean an economy's total output has stopped growing?
- Going furtherWhat happens to the steady state when a country's population starts growing faster, spreading the same capital more thinly?
Your turn1 of 2
Find the steady-state capital per worker when investment per worker is 0.409 times the square root of capital per worker and the depreciation rate is 0.0789.Convergence: Whether Poor Countries Catch Up
- How it worksHow does diminishing returns to capital make the very first machines in a poor country far more productive than the millionth machine in a rich one?
- Going furtherWhat happens to convergence when a poor country lacks the institutions and education needed to use new capital well?
- Common mistakeWhy doesn't the Solow model predict that every poor country will automatically catch up to every rich one?
- Ties togetherHow does conditional convergence connect a country's own steady state to how fast it actually grows toward it?
Your turn1 of 2
A poor country's output per worker follows the square root of capital per worker. As its capital per worker rises from 3 to 14, how much does output per worker rise?Why Technology Is the Only Source of Permanent Growth
- How it worksHow does new technology shift the entire Solow diagram upward instead of just sliding an economy along it?
- Common mistakeWhy isn't piling up more capital the long-run engine of growth that continuous technological progress is?
- Going furtherWhat happens to a country's steady state, and then to its growth path, the moment a new technology arrives?
- Ties togetherHow does a steady stream of new technology turn a series of one-time jumps into what looks like smooth, permanent growth?
Your turn1 of 2
A country adopts a wave of new technology, raising the amount of output it can produce from any given amount of capital per worker. How does this show up on the Solow diagram, compared to simply raising the saving rate?Public Policy and Long-Run Growth
- How it worksWalk me through how investment in infrastructure, education, and secure property rights each raise a country's long-run output.
- Going furtherWhat happens to potential output when a policy change raises the fraction of adults who work or look for work?
- Common mistakeWhy isn't every dollar of government spending an investment in a country's future growth?
- Ties togetherHow do growth-friendly policies push a country's production frontier and its long-run aggregate supply curve outward together?
Your turn1 of 2
Investment in infrastructure raises a country's potential output by 15 percent over a decade. If potential output starts at 22 trillion dollars, what is potential output after this increase?