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1 macroeconomics fifth edition N Gregory Mankiw PowerPoint Slides by Ron Cronovich CHAPTER SEVEN Economic Growth I macro 2003 Worth Publishers all rights reserved 1 Econ 101 Intermediate Macro Theory Lecture notes Professor Cetorelli UC Davis Fall 2003 Lecture 6 2 Reading so far Chapter 1 pp 1 14 Chapter 2 pp 15 23 bottom section excluded 24 27 bottom section excluded 30 38 Chapter 3 pp 42 69 Exclude FYI boxes p 57 66 Appendix to Chapter 3 pp 71 73 Chapter 7 pp 180 195 2 3 Reading for next class Chapter 7 pp 180 205 Don t forget Homework due in or before class on Friday CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 4 CobbCobb Douglas Production FunctionDouglas Production Function Special type of production function with nice properties 1 LAKLKFY CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 5 Data on U S economy 1960 2000 MPL L Y 3 CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 6 CobbCobb Douglas cont Douglas cont YLY L LMPLIncomeLabor YKY K KMPKIncomeCapital Y L LAK L LAKMPL Y K LAK K LAKMPK 1 1 1 1 1 1 1 1 1 11 111 111 1 LAKLKFY Hence capital and labor income are a constant share of income Consistent with data CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 7 Back to Economic GrowthBack to Economic Growth CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 8 4 CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 9 Income and poverty in the world Income and poverty in the world selected countries 2000selected countries 2000 0 10 20 30 40 50 60 70 80 90 100 0 5 000 10 000 15 000 20 000 Income per capita in dollars of population living on 2 per day or less Madagascar India Bangladesh Nepal Botswana Mexico Chile S Korea Brazil Russian Federation Thailand Peru China Kenya CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 10 The The SolowSolow ModelModel How How SolowSolow model is different from model is different from Chapter 3 s modelChapter 3 s model 1 Kis no longer fixed investment causes it to grow depreciation causes it to shrink 2 Lis no longer fixed population growth causes it to grow 3 The consumption function is simpler CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 11 How Solow model is different from How Solow model is different from Chapter 3 s modelChapter 3 s model 4 No Gor T only to simplify presentation we can still do fiscal policy experiments 5 Cosmetic differences 5 CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 12 The production functionThe production function In aggregate terms Y F K L Define y Y L output per worker k K L capital per worker Assume constant returns to scale zY F zK zL for any z 0 Pick z 1 L Then Y L F K L 1 y F k 1 y f k where f k F k 1 CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 13 The production functionThe production function Output per worker y Capital per worker k f k Note this production function exhibits diminishing MPK Note this production function exhibits diminishing MPK 1 MPK f k 1 f k Please note variables on the axes are not the same as in the graph from CH 3 Here variables are in per capita terms CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 14 The national income identityThe national income identity Y C I remember no G In per worker terms y c i where c C Land i I L 6 CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 15 The consumption functionThe consumption function s the saving rate 0 s 1 the fraction of income that is saved sis an exogenous parameter Note Note s s is the only lowercase variable is the only lowercase variable that is not equal to that is not equal to its uppercase version divided by its uppercase version divided by L L Consumption function c 1 s y per worker CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 16 Back to national income identityBack to national income identity National income identity is y c i Substituting for cits function y 1 s y i Rearranging i sy i e investment equal saving as in Chapter 3 Recalling that y f k i sf k CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 17 Output consumption and investmentOutput consumption and investment Output per worker y Capital per worker k f k sf k k1 y1 i1 c1 7 CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 18 Capital accumulationCapital accumulation Remember the definition of investment spending on new plants equipment etc from firms That is investment increases the capital stock Or i k CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 19 Capital accumulation cont Capital accumulation cont However to be realistic the existing capital stock is also subject to depreciation that is the loss of value over time due to simple wearing out obsolescence etc Example Think of a computer as a piece of capital Could you still use a 486 processor nowadays CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 20 DepreciationDepreciation Depreciation per worker k Capital per worker k k the rate of depreciation the fraction of the capital stock that wears out each period the rate of depreciation the fraction of the capital stock that wears out each period 1 8 CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 21 Capital accumulationCapital accumulation The basic idea Investment makes the capital stock bigger depreciation makes it smaller The basic idea The basic idea Investment makes Investment makes the capital stock bigger the capital stock bigger depreciation makes it smaller depreciation makes it smaller CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 22 Capital accumulationCapital accumulation Change in capital stock investment depreciation k i k Since i sf k this becomes k sf k k CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 23 The equation of motion for The equation of motion for k k the Solow model s central equation Determines behavior of capital over time which in turn determines behavior of all of the other endogenous variables because they all depend on k E g income per person y f k consump per person c 1 s f k k sf k k 9 CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 24 The steady stateThe steady state If investment is just enough to cover depreciation sf k k then capital per worker will remain constant k 0 This constant value denoted k is called the steady state capital stock k sf k k CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 25 The steady stateThe steady state Investment and depreciation Capital per worker k sf k k k CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 26 Moving toward the steady stateMoving toward the steady state Investment and depreciation Capital per worker k sf k k k k sf k k depreciation k k1 investment 10 CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 27 Moving toward the steady stateMoving toward the steady state Investment and depreciation Capital per worker k sf k k k k1 k sf k k k CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 28 Moving toward the steady stateMoving toward the steady state Investment and depreciation Capital per worker k sf k k k k1 k sf k k k k2 CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 29 Moving toward the steady stateMoving toward the steady state Investment and depreciation Capital per worker k sf k k k k sf k k k2 investment depreciation k 11 CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 30 Moving toward the steady stateMoving toward the steady state Investment and depreciation Capital per worker k sf k k k k sf k k k k2 CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 31 Moving toward the steady stateMoving toward the steady state Investment and depreciation Capital per worker k sf k k k k sf k k k2 k k3 CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 32 Moving toward the steady stateMoving toward the steady state Investment and depreciation Capital per worker k sf k k k k sf k k k3 Summary As long as k k investment will exceed depreciation and kwill continue to grow toward k Summary As long as k k investment will exceed depreciation and kwill continue to grow toward k 12 CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 33 Now you try Now you try Draw the Solow model diagram labeling the steady state k On the horizontal axis pick a value greater than k for the economy s initial capital stock Label it k1 Show what happens to kover time Does kmove toward the steady state or away from it CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 34 A numerical exampleA numerical example Production function aggregate 1 21 2 YF K LKLKL 1 2 1 21 2 YKLK LLL 1 2 yf kk To derive the per worker production function divide through by L Then substitute y Y Land k K L to get CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 35 A numerical example A numerical example cont cont Assume s 0 3 0 1 initial value of k 4 0 13 CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 36 A numerical example cont A numerical example cont Assume s 0 3 0 1 and y k1 2 Use the equation of motion k sf k k to solve for the steady state values of k y and c CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 37 Solution to exercise Solution to exercise 0 def of steady statek and 3yk eq n of motion with 0s f kkk 0 3 0 1 using assumed valueskk 3 k k k Solve to get 9k Finally 1 0 732 1cs y CHAPTER 7CHAPTER 7Economic Growth IEconomic Growth I slide 38 Approaching the Steady State Approaching the Steady State A Numerical ExampleA Numerical Example Yearkyci kD Dk 14 0002 0001 4000 6000 4000 200 24 2002 0491 4350 6150 4200 195 34 3952 0961 4670 6290 4400 189 Yearkyci kD Dk 14 0002 0001 4000 60