Economics 302 (Sec. 001)( )Intermediate Macroeconomic Theory and Policy(Spring 2011)Theory and Policy (Spring 2011)4/27/2011Instructor: Prof. Menzie ChinnInstructor: Prof. Menzie ChinnUW Madison12‐1 Technological Progress and the Rate of GrowthTechnological Progress and the Production Function•Technological progre ss has many dimensions. It may mean:–Larger quantities of output–Larger quantities of output– Better products– New productsA l it f dt–A larger variety of products•Technological progre ss leads to increases in output for given t f it l d lb2of 30amounts of capital and labor.12‐1 Technological Progress and the Rate of Growth•Let’s denote the state of technology by A and rewrite the difiTechnological Progress and the Production Functionproduction function as:YFKNA=(,,)(+++)(+ ++)A more restrictive but more convenient form isYFKAN=(, )Output depends on both capital and labor (K and N), and on the state of technology (A). “AN” is labor efficiency units.3of 30Th l ilP d h Pd i Fi12‐1 Technological Progress and the Rate of Growth•The relation between output per effective work er and capital per effective work er is:Technological Progress and the Production Functioncapital per eff ective work er is:, 1YKFAN AN⎛⎞=⎜⎟⎝⎠AN AN⎜⎟⎝⎠which we can redefine asYKfAN AN⎛⎞=⎜⎟⎝⎠AN AN⎝⎠In words: Output per effective worker is a function of capital per effective worker4of 30effective worker.Th l ilP d h Pd i Fi12‐1 Technological Progress and the Rate of GrowthTechnological Progress and the Production FunctionFigure 12‐1Output per Ef fective Worker versus Capital per Effective WorkerFigure 12 1Because of decreasing returns to capital, increases in capital per effective worker lead to smaller and smaller increases smaller and smaller increases in output per effective worker.5of 30Iib O d Cil12‐1 Technological Progress and the Rate of Growth•The dynamics of output and capital per worker involve:Interactions between Output and Capital–The relation between output per worker and capital per work er.ISsY==Di idi bhid bANIANsYAN=⎛⎝⎜⎞⎠⎟Dividing both sides by AN, we getANAN⎝⎠YK⎛⎜⎞⎟IK⎛⎜⎞⎟YANfKAN=⎛⎝⎜⎞⎠⎟Given thatIANsfKAN=⎛⎝⎜⎞⎠⎟then,6of 30Iib O d Cil12‐1 Technological Progress and the Rate of GrowthInteractions between Output and CapitalThe dynamics of output and capital per work er involve: The relation between depreciation per worker—equivalently, the investment per worker needed to maintain a constant level of capital per worker—and capital per worker.δKg gKAN+=()cap ta pe oe()δ++ggKANor or equivalentlyKThe amount of investment per effective work er needed to maintain a constant level of capital per effective worker is7of 30()δ++ggKANANIib O d Cil12‐1 Technological Progress and the Rate of Growth•This figure focuses on output, capital, and investment per effective workerrather thanInteractions between Output and Capitaleffective worker, rather than per worker:– Output per effective worker increases with capital per effectivecapital per effective worker, but at a decreasing rate.– The relation between i ff iinvestment per effective worker and capital per effective work er is drawn as the upper curve, li li db h imultiplied by the saving rate, s.– Tech progress is A increasing.8of 30Dif Cil d O12‐1 Technological Progress and the Rate of Growth•In steady state, output (Y) grows at the same rate as effective Dynamics of Capital and Outputlabor (AN); effective labor grows at a rate (gA+gN); therefore, output growth in steady state equals (gA+gN). Capital per eff ective work er also grows at a rate equal to (gA+gN).•The growth rate of output is independent of the saving rate.•Because output, capital, and eff ective labor all grow at the same rate, (gA+gN), the steady state of the economy is also called a state of balanced growth.9of 30Th Eff f h Si R12‐1 Technological Progress and the Rate of GrowthThe Effects of the Saving RateFigure 12‐3The Effects of an Increase in the Saving Rate: IFigure 12 3An increase in the saving rate leads to an increase in the steady-state levels of output per effective worker and capital per effective worker and capital per effective worker.10 of 30Th Eff f h Si R12‐1 Technological Progress and the Rate of GrowthThe Effects of the Saving RateFigure 12‐4The Effects of an Increase in the Saving Rate: II Figure 12 4The increase in the saving rate leads to higher growth until the economy reaches its new, higher balanced growth pathhigher, balanced growth path.11 of 3012‐2 Determinants of Technological Progress•“Technological progress” in modern economies is the result of firms’ research and development (R&D) activities. The outcome of R&D is fundamentallyideasof R&D is fundamentally ideas.•Spending on R&D depends on:The fertility of the research process, or how spending on R&D translates into new ideas and new products, andthi bilit f hlt th ttt hi hthe appropriability of researchresults, or the extent to which firms benefit from the results of their own R&D.12 of 30Th F ili f h RhP12‐2 Determinants of Technological Progress•The determinants of fertility include:The Fertility of the Research ProcessThe interaction between basic research (the search for general principles and results) and applied research (the application of results to specific uses).The country: some countries are more successful at basic research; others are more successful at applied research and development.Time: It takes many years, and often many decades, for the full potential of major discoveries to be realized.13 of 30Th A i bili f RhRl12‐2 Determinants of Technological Progress•If firms cannot appropriate the profits from the development of d h ill i R&D F kThe Appropriability of Research Resultsnew products, they will not engage in R&D. Factors at work include:Th f h h I h ff iThe nature of the research process. Is there a payoff in being first at developing a new product?Ll ttiPt ti fi th t h di dLegal protection. Patents give a firm that has discovered a new product the right to exclude anyone else from the production or use of the new product for a period of time.14 of 30Labor Productivity Growth.06.07Lbdtiit.0506Laborproductivitygrowth, 4 qtr change.03.04.01.0201.00-.0190 92 94 96 98 00 02 04 06 08