Professor K.D. Hoover, Econ 210D Topic4 Spring Econ 210D Intermediate Macroeconomics Spring 2015 Professor Kevin D. Hoover Topic 4 Long-term Economic Growth

Professor K.D. Hoover, Econ 210D Topic4 Spring Illustrative Growth Questions Why does GDP rise over time? Why is GDP and GDP per capita higher in some countries than others How is GDP affected by increases in population from immigration or from population growth? How are GDP and labor related: how much does unemployment fall in the slump?

Professor K.D. Hoover, Econ 210D Topic4 Spring Aggregate Supply and Demand Y = C + I + G + NX Production = Expenditure Aggregate Supply = Aggregate Demand

Professor K.D. Hoover, Econ 210D Topic4 Spring

5 Production Function – 1 y = f(k, l) o y = output o k = capital service input o l = labor service input

Professor K.D. Hoover, Econ 210D Topic4 Spring The Production Function – 2

Professor K.D. Hoover, Econ 210D Topic4 Spring Properties of Production Functions – 1 the production function : y = f ( k, l ) no free lunch : y = f (0, l ) = 0; y = f ( k, 0) = 0 effort pays : dy/dk = f k ( k, l ) > 0; dy/dl = f l ( k, l ) > 0

Professor K.D. Hoover, Econ 210D Topic4 Spring Properties of Production Functions – 2 diminishing returns to a factor of production : o d 2 y / dk 2 = f kk ( k, l ) < 0 o d 2 y / dl 2 = f ll ( k, l ) < 0 an increase in one factor raises the productivity of the other : d 2 y / dkdl = f kl ( k, l ) > 0;

Professor K.D. Hoover, Econ 210D Topic4 Spring Choosing the Technological Mix Profits = Revenue – Cost Add labor until marginal unit (  l ) leads to more costs ( w  l ) than revenues ( p  y) Add capital until marginal unit (  k ) leads to more costs ( k ) than revenues ( p  y) Profit maximization: Marginal Cost = Marginal Revenue

Professor K.D. Hoover, Econ 210D Topic4 Spring Rules of Profit Maximization Add labor until: o marginal product of labor (mpl) = real wage o mpl =  y/  l = w/p Add capital until: o marginal product of capital (mpk) = (implicit) real rental rate o mpk =  y/  k = /p

Professor K.D. Hoover, Econ 210D Topic4 Spring

Professor K.D. Hoover, Econ 210D Topic4 Spring Aggregate Production Function Y = F ( L, K ) Cobb-Douglas Production Function: Y = AL  K 1- 

Professor K.D. Hoover, Econ 210D Topic4 Spring Creators of the Cobb-Douglas Production Function Paul H. Douglas ( ) o labor economist o later U.S. Senator from Illinois Charles W. Cobb o mathematician, Amherst College Created production function in 1928

Professor K.D. Hoover, Econ 210D Topic4 Spring Properties of the Cobb-Douglas Production Function Y = AL  K 1-  mpL =  mpK = (1-  Diminishing returns to capital and labor Constant returns to scale Labor share in GDP =  Capital share in GDP = 1– 

Professor K.D. Hoover, Econ 210D Topic4 Spring Why is the Cobb-Douglas a Good Production Function? – 1

Professor K.D. Hoover, Econ 210D Topic4 Spring

Professor K.D. Hoover, Econ 210D Topic4 Spring U.S. Aggregate Production Function, 2008

Professor K.D. Hoover, Econ 210D Topic4 Spring Concepts of Productivity Labor productivity :  = Y/L Capital productivity :  = Y/K Total-factor productivity:

Professor K.D. Hoover, Econ 210D Topic4 Spring Short-run Production Function - Labor

Professor K.D. Hoover, Econ 210D Topic4 Spring Short-run Production Function - Capital

Professor K.D. Hoover, Econ 210D Topic4 Spring Measures of Capacity - Labor LF = labor force EMP = employment rate = L / LF U = unemployment rate =

Professor K.D. Hoover, Econ 210D Topic4 Spring Measures of Capacity - Capital CU = capacity utilization rate =

Professor K.D. Hoover, Econ 210D Topic4 Spring Potential Output potential output scaled output

Professor K.D. Hoover, Econ 210D Topic4 Spring

Professor K.D. Hoover, Econ 210D Topic4 Spring Growth Over Time U.S. GNP per capita: o 1790: $500 o 2000: $40,000 o Increase: 80 times Chad GDP per capita, 2000: $500

Professor K.D. Hoover, Econ 210D Topic4 Spring The Power of Growth Rates $1 at 1.5%/year for 2000 years = $8.5 billion o < less than U.S. GDP $1 at 2.0%/year for 2000 years = $158,614 trillion o 2,638 times world GDP 2.91%/year = best U.S. 30-year average growth ( ): at that rate = $171,600 per capita o 6 times actual U.S. per capita income 1990

Professor K.D. Hoover, Econ 210D Topic4 Spring Divergence of Growth Experience

Professor K.D. Hoover, Econ 210D Topic4 Spring Production Functions: 1948 & : Y = AL  K 1-  = 4.60 L 0.69 K : Y = AL  K 1-  = 9.63 L 0.69 K 0.31

Professor K.D. Hoover, Econ 210D Topic4 Spring Production Functions: Counterfactual Interpretation – 1

Professor K.D. Hoover, Econ 210D Topic4 Spring Production Functions: Counterfactual Interpretation – 2

Professor K.D. Hoover, Econ 210D Topic4 Spring Thought Experiment – 1 What would GDP be in 1948 if ceteris paribus 1998 labor were available:

Professor K.D. Hoover, Econ 210D Topic4 Spring Thought Experiment – 2 What would GDP be in 1948 if ceteris paribus 2008 capital were available: homework problem

Professor K.D. Hoover, Econ 210D Topic4 Spring Thought Experiment – 3 What would GDP be in 1948 if ceteris paribus 1998 labor were available: o difference = $13,312 – $6.360 = $6,952 bil. (effect of  A )

Professor K.D. Hoover, Econ 210D Topic4 Spring Algebra of Growth Rates if z = xy  if z = x/y  if z = xy  if z = x 1/y  or if 

Professor K.D. Hoover, Econ 210D Topic4 Spring Growth Accounting – 1 Y = AL  K 1- 

Professor K.D. Hoover, Econ 210D Topic4 Spring Growth Accounting – 2 Percentage of Growth Attributable to: Labor: Capital: Total Factor Productivity:

Professor K.D. Hoover, Econ 210D Topic4 Spring Sources of U.S. Growth

Professor K.D. Hoover, Econ 210D Topic4 Spring The Growth Process: Rising Total Factor Productivity Product Innovation Process Innovation Research and Development

Professor K.D. Hoover, Econ 210D Topic4 Spring Product Innovation – 1

Professor K.D. Hoover, Econ 210D Topic4 Spring Product Innovation – 2

Professor K.D. Hoover, Econ 210D Topic4 Spring Product Innovation – 3: recorded music

Professor K.D. Hoover, Econ 210D Topic4 Spring Product Innovation – 4: recorded music

Professor K.D. Hoover, Econ 210D Topic4 Spring Product Innovation – 4: recorded music ?

Professor K.D. Hoover, Econ 210D Topic4 Spring Process Innovation - 1

Professor K.D. Hoover, Econ 210D Topic4 Spring Process Innovation - 2

Professor K.D. Hoover, Econ 210D Topic4 Spring Research and Development -1

Professor K.D. Hoover, Econ 210D Topic4 Spring Research and Development -2

Professor K.D. Hoover, Econ 210D Topic4 Spring Research and Development -3

Professor K.D. Hoover, Econ 210D Topic4 Spring The Growth Process: Labor Law of motion for labor: L t = (1 + n ) L t -1 Solution: L t = L 0 (1 + n ) t o n = growth rate of labor

Professor K.D. Hoover, Econ 210D Topic4 Spring The Growth Process: Capital – 1 Law of motion: K t = K t- 1 + I t -1 – depreciation t- 1 o I t = gross investment o I t – depreciation t = net investment  K t = K t – K t- 1 = I t -1 – depreciation t- 1 = net investment t- 1

Professor K.D. Hoover, Econ 210D Topic4 Spring The Growth Process: Capital – 2  K t = net investment t- 1

Professor K.D. Hoover, Econ 210D Topic4 Spring Balanced and Unbalanced Growth capital widening = more workers with same K / L capital deepening = more capital per worker ( K / L  ) balanced growth = all inputs and outputs grow at same rate – i.e., capital widening, no capital deepening unbalanced growth = inputs and output grow at different rates – capital widening and deepening

Professor K.D. Hoover, Econ 210D Topic4 Spring Balanced Growth

Professor K.D. Hoover, Econ 210D Topic4 Spring Unbalanced Growth

Professor K.D. Hoover, Econ 210D Topic4 Spring Technical Progress Recall: labor-augmenting technical progress = as if more workers ( ) capital-augmenting technical progress = as if more capital ( )

Professor K.D. Hoover, Econ 210D Topic4 Spring Balanced Growth with Technical Progress Replace with Balanced growth condition with technical progress: =

Professor K.D. Hoover, Econ 210D Topic4 Spring Balanced Growth for the U.S. and Therefore, = = speed limit for the economy

Professor K.D. Hoover, Econ 210D Topic4 Spring END of Topic 4 Next Topic: 5. Labor and Unemployment