Both are important for productivity The Production Function The production function is a graph or equation showing the relation between outputs and inputs
o Y=A F (L, K, H, N) o F( ) is a function that shows how inputs are combined to produce output o “A” is the level of technology “A” multiplies the function F( ), so improvements in technology (increases in “A”) allow for more output (Y) to be produced from any given combo of inputs The production function has the property constant returns to scale: changing all inputs causes output to change by that percentage Doubling all inputs (multiplying each by 2) causes output to double o 2Y=A F (2L, 2K, 2H, 2N) Increasing all inputs 10% (multiplying each by 1.1) causes output to increase by 10% o 1.1Y=A F (1.1L, 1.1K, 1.1H, 1.1N) If we multiply the input by 1/L, then output is multiplied by 1/L o Y/L=A F(1,K/L, H/L, N/L) This equation shows that productivity (output per worker) depends on: o The level of technology (A) o Physical capital per worker o Human capital per worker o Natural resources per worker Saving and Investment We can boost productivity by increasing K, which requires investment Since resources are scarce, producing more capital requires producing fewer consumption goods Reducing consumption=increasing saving. This extra saving funds the production of investment goods Hence, a tradeoff between current and future consumption Diminishing Returns and the Catch-Up Effect The govt can implement policies that raise saving and investment. Then K will rise, causing productivity and living standards to rise But this faster growth is temporary, due to diminishing returns to capital: as K rises, the extra output from an additional unit of K falls The Production and Function of Diminishing Returns If workers have little K, giving them more increases their productivity a lot If workers already have a lot of K, giving them more increases productivity fairly little Capital per worker=K/L The catch-up effect: the property whereby poor countries tend to grow more rapidly than rich ones Catch up effect examples 1960-1990: US and S Korea devoted a similar share of GDP to investment, so you might assume they might have similar growth performance But growth was >6% in Korea and only 2% in US
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