Chapter 3Slide 2Outline of modelFactors of productionThe production function: Y = F(K,L)Returns to scale: a reviewReturns to scale: Example 1Returns to scale: Example 2Returns to scale: Example 3NOW YOU TRY Returns to scaleANSWERS Returns to scale, part (a)ANSWERS Returns to scale, part (b)AssumptionsDetermining GDPThe distribution of national incomeNotationHow factor prices are determinedDemand for laborMarginal product of labor (MPL )NOW YOU TRY Compute & graph MPLANSWERS Compute & graph MPLMPL and the production functionDiminishing marginal returnsNOW YOU TRY Identifying Diminishing ReturnsANSWERS Identifying Diminishing ReturnsNOW YOU TRY MPL and labor demandANSWERS MPL and labor demandMPL and the demand for laborThe equilibrium real wageDetermining the rental rateThe equilibrium real rental rateThe Neoclassical Theory of DistributionHow income is distributed to L and KSlide 34The Cobb-Douglas Production FunctionThe Cobb-Douglas Production FunctionLabor productivity and wagesOutline of modelDemand for goods and servicesConsumption, CThe consumption functionInvestment, IThe investment functionGovernment spending, GThe market for goods & servicesThe loanable funds marketDemand for funds: InvestmentLoanable funds demand curveSupply of funds: SavingTypes of savingNotation:  = change in a variableNOW YOU TRY Calculate the change in savingNOW YOU TRY AnswersBudget surpluses and deficitsU.S. Federal Government Surplus/Deficit, 1940–2016U.S. Federal Government Debt, 1940–2016Loanable funds supply curveLoanable funds market equilibriumThe special role of rDigression: Mastering modelsMastering the loanable funds modelCASE STUDY: The Reagan deficitsCASE STUDY: The Reagan deficitsAre the data consistent with these results?NOW YOU TRY The effects of saving incentivesMastering the loanable funds model, continuedAn increase in investment demandSaving and the interest rateAn increase in investment demand when saving depends on rCHAPTER SUMMARYCHAPTER SUMMARYCHAPTER SUMMARY1CHAPTER 3 National IncomeNational Income: Where It Comes From and Where It GoesChapter 32CHAPTER 3 National Incomewhat determines the economy’s total output/incomehow the prices of the factors of production are determinedhow total income is distributedwhat determines the demand for goods and serviceshow equilibrium in the goods market is achieved23CHAPTER 3 National IncomeOutline of modelA closed economy, market-clearing modelSupply sidefactor markets (supply, demand, price)determination of output/incomeDemand sidedeterminants of C, I, and GEquilibriumgoods marketloanable funds market4CHAPTER 3 National IncomeFactors of productionK = capital: tools, machines, and structures used in productionL = labor: the physical and mental efforts of workers5CHAPTER 3 National IncomeThe production function: Y = F(K,L)shows how much output (Y ) the economy can produce fromK units of capital and L units of labor reflects the economy’s level of technology exhibits constant returns to scale6CHAPTER 3 National IncomeReturns to scale: a reviewInitially Y1 = F (K1 , L1 ) Scale all inputs by the same factor z: K2 = zK1 and L2 = zL1 (e.g., if z = 1.2, then all inputs are increased by 20%)What happens to output, Y2 = F (K2, L2 )? If constant returns to scale, Y2 = zY1 If increasing returns to scale, Y2 > zY1 If decreasing returns to scale, Y2 < zY17CHAPTER 3 National IncomeReturns to scale: Example 1( , )F K L KL=( , ) ( )( )F zK zL zK zL=z KL=2z KL=2z KL=( , )z F K L=constant returns to scale for any z > 08CHAPTER 3 National IncomeReturns to scale: Example 2( , )F K L K L= +( , )F zK zL zK zL= +z K z L= +( , )z F K L=decreasing returns to scale for any z > 1( )z K L= +9CHAPTER 3 National IncomeReturns to scale: Example 3( , )F K L K L= +2 2( , ) ( ) ( )F zK zL zK zL= +2 2( , )z F K L=2increasing returns to scale for any z > 1( )z K L= +2 2 210CHAPTER 1 The Science of MacroeconomicsNOW YOU TRYReturns to scaleDetermine whether each of these production functions has constant, decreasing, or increasing returns to scale:(a)(b)10( , )F K L K L= +11CHAPTER 1 The Science of MacroeconomicsANSWERSReturns to scale, part (a)1112CHAPTER 3 National IncomeANSWERSReturns to scale, part (b)1213CHAPTER 3 National IncomeAssumptions1. Technology is fixed.2. The economy’s supplies of capital and labor are fixed at and K K L L= =14CHAPTER 3 National IncomeDetermining GDPOutput is determined by the fixed factor supplies and the fixed state of technology:,= ( )Y F K L15CHAPTER 3 National IncomeThe distribution of national incomedetermined by factor prices, the prices per unit firms pay for the factors of production wage = price of Lrental rate = price of K16CHAPTER 3 National IncomeNotation W = nominal wage R = nominal rental rate P = price of output W /P = real wage (measured in units of output) R /P = real rental rate W = nominal wage R = nominal rental rate P = price of output W /P = real wage (measured in units of output) R /P = real rental rate17CHAPTER 3 National IncomeHow factor prices are determinedFactor prices determined by supply and demand in factor markets. Recall: Supply of each factor is fixed.What about demand?18CHAPTER 3 National IncomeDemand for laborAssume markets are competitive: each firm takes W, R, and P as given.Basic idea:A firm hires each unit of labor if the cost does not exceed the benefit.cost = real wagebenefit = marginal product of labor19CHAPTER 3 National IncomeMarginal product of labor (MPL )definition:The extra output the firm can produce using an additional unit of labor (holding other inputs fixed):MPL = F (K, L +1) – F (K, L)20CHAPTER 1 The Science of MacroeconomicsNOW YOU TRYCompute & graph MPLa. Determine MPL at each value of L.b. Graph the production function.c. Graph the MPL curve with MPL on the vertical axis and L on the horizontal axis.20L Y MPL0 0 n.a.1 10 ?2 19 ?3 27 84 34 ?5 40 ?6 45 ?7 49 ?8 52 ?9 54 ?10 55 ?21CHAPTER 1 The Science of MacroeconomicsANSWERSCompute & graph MPL2122CHAPTER 3 National IncomeYoutputMPL and the production function LlaborF K L( , )1MPL1MPL1MPLAs more labor is added, MPL As more labor is added, MPL Slope of the production function equals MPL23CHAPTER 3 National IncomeDiminishing marginal returnsAs an input is increased, its marginal product falls (other things equal). Intuition:Suppose L while