141029W first summarized and advance-posted on FB Summarized from Greg Mankiw’s Principles of Economics PART 9 The Real Economy in the Long Run Chapter 25 of 36 – Production and Growth section 7 … completed first summary edit of this new section today, will re-edit and re-post in sequence later … Economists use a production function equation to describe the relationship between • the quantity of inputs used in production • the quantity of output from production Abbreviations used in the following • Y means quantity of output • L quantity of labor • K quantity of physical capital • H quantity of human capital • N quantity of natural resources • ϝ( ) means function that shows how the inputs are combined to produce output • x means any positive number • A is a variable that reflects the available production technology So, we can write Y = A ϝ (L, K, H, N) or output = technology times function of (quantity of labor, quantity of physical capital, quantity of human capital, quantity of natural resources) Note if technology level is now 1 and then becomes 2, output doubles if L, K, H, N are held constant • as technology improves A rises • the economy produces more output from any combination of inputs Many production functions have a property of constant returns to scale • if a production function has constant returns to scale • doubling all inputs causes the amount of output to also double We write a production function has constant returns to scale, if • for any positive number x xY = A ϝ (xL, xK, xH, xN) A doubling of all inputs would be represented in this equation by x = 2 • the right side shows all the inputs doubling • the left side shows output doubling Production functions with constant returns to scale have an interesting and useful implication • to see this implication set x = 1/L • then the equation becomes: Y/L = A ϝ(1, K/L, H/L, N/L) or quantity of output per quantity of labor = level of technology times function of quantity of labor / quantity of labor (1), quantity of physical capital / quantity of labor, quantity of human capital / quantity of labor, quantity of natural resources / quantity of labor Y/L (quantity of output per quantity of labor) is output per worker, a measure of productivity This equation says labor productivity depends on • physical capital per worker (K/L) • human capital per worker (H/L) • natural resources per worker (N/L) Productivity also depends on the state of technology, as reflected by the variable A. This production function equation • Y = A ϝ (L, K, H, N) • is a mathematical summary of the determinants of productivity • technology, labor, physical capital, human capital, natural resources … many production functions have property of constant returns to scale 多く の 生産機能 は 収穫 一定 の スケール のプロパティ を 持ってる おおく の せいさん きのう は しゅうかく いってい の スケール のプロパティ を もってる ōku no seisan kinō wa shūkaku ittei no sukēru no puropatei o motteru スケール … sukēru … scale 生産機能 … せいさん きのう … production function
Posted on: Wed, 29 Oct 2014 11:05:55 +0000