The logarithmic scale on the vertical axis allows for the same proportional increase in a variable to be represented by the same distance. Growth: the steady increase in aggregate output over time. Aggregate U.S. output has increased by a factor of 42 since U.S. GDP Since 1890

Translating a country’s GDP into dollars at the current exchange rate of its currency does not work for two reasons:  Exchange rates can vary a lot The country will seem affluent one year, destitute in another year  The lower a country’s output per capita, the lower the prices of food and basic services in that country You don’t need that many dollars to live well in Ecuador The price of a Big Mac is low in Quito because Ecuadoran hamburger flippers aren’t paid much Measuring Standard of Living: Per capita Purchasing Power Parity GDP in “International Dollar Prices”  Each country’s outputs in US prices

3 of 26 Income and Happiness: Stay tuned for Carol Graham Happiness and Income per Person across Countries

The Facts of Growth – The Very Long Run On the scale of human history, the growth of output per capita is a recent phenomenon. Looking across two millennia From the end of the Roman Empire to 1500, no output per capita growth in Europe Small growth in output per capita (0.1%/year and 0.2%/year 1700 to 1820) Modest growth (U.S. = 1.5%) The high-growth of the 1950s and 1960s is unusual Leaders in output/capita change over the centuries: Italy  Netherlands  U.K.  US

Growth in Rich Countries since 1950 The Convergence of Output per Person since 1950 Countries with initially lower levels of output per person have typically grown faster. Turkey, Greece, New Zealand are off of the frontier Growth Rate of GDP per Person since 1950 versus GDP per Person in 1950, OECD Countries

Looking at Growth Across Many Countries There is no clear relation between per person the growth rate of output since 1960 and the level of output per person in Torture the data and you’ll find “conditional convergence,” e.g., conditional on initial educational attainment Growth Rate of GDP per Person since 1960 versus GDP per Person in 1960 (2000 dollars) for 70 Countries

The aggregate production function is the relation between aggregate output and the inputs in production. The Aggregate Production Function Y = aggregate output. K = capital—the sum of all the machines, plants, and office buildings in the economy. N = labor—the number of workers in the economy. The aggregate production function F: how much output is produced for given quantities of capital and labor The aggregate production function depends on the state of technology. The higher the state of technology, the more output for a given inputs of K and N.

Returns to Scale and Returns to Factors Constant returns to scale: if the quantities of capital and labor are doubled— then output will also double. You can replicate what you’re doing well. Or more generally, for any number, Decreasing returns to capital: increases in capital, given labor, lead to smaller and smaller increases in output as the level of capital increases. The same worker using bigger and bigger shovels will dig deeper and faster... but the hole won’t increase in proportion to the increased sizes of shovels. Decreasing returns to labor: increases in labor, given capital, lead to smaller and smaller increases in output as the level of labor increases. More and more workers staffing the same hotel front desk will process increasing numbers of guests...but not in proportion to the increase in workforce.

Output per Worker and Capital per Worker Constant returns to scale implies that we can rewrite the aggregate production function as: The amount of output per worker, Y/N depends on the amount of capital per worker, K/N. As capital per worker increases, so does output per worker. But with decreasing returns to capital, output won’t increase in proportion to the increase in capital.

Output per Worker and Capital per Worker Increases in capital per worker lead to smaller and smaller increases in output per worker.  Increases in output per worker (Y/N) can come from increases in capital per worker (K/N).  Accumulation of capital depends on saving exceeding depreciation.  Or increases in Y/N can come from improvements in technology that shift the production function, F, and lead to more output per worker given capital per worker.  Because of decreasing returns to capital, capital accumulation by itself cannot sustain growth.

An improvement in technology shifts the production function up, leading to an increase in output per worker for a given level of capital per worker. The Effects of an Improvement in the State of Technology  Sustained growth requires sustained technological progress. The economy’s rate of growth of output per person is eventually determined by the economy’s rate of technological progress.

Key Terms  growth  logarithmic scale  standard of living  output per person  purchasing power, purchasing power parity (PPP)  convergence  Malthusian trap  four tigers  emerging economies  aggregate production function  state of technology  constant returns to scale  decreasing returns to capital  decreasing returns to labor  capital accumulation  technological progress  saving rate