1CHAPTER 3CHAPTER 3 National IncomeNational IncomeTopic 3:National Income:Where it Comes From and Where it Goes (chapter 3) revised 9/21/09IntroductionIntroduction In the last lecture we defined and measured some key macroeconomic variables. Now we start building theories about what determines these key variables. In the next couple lectures we will build up theories that we think hold in the long run, when______________________.  Called ___________________ theory.The Neoclassical modelThe Neoclassical modelIs a general equilibrium model:  Involves multiple _____. each with own supply and demand ____ in each market adjusts to make quantity demanded equal quantity supplied.2Neoclassical modelNeoclassical modelThe macroeconomy involves three types of markets:1.2.needed to produce goods and services3.Are also three types of agents in an economy:1. Households2. Firms3. GovernmentFinancial MarketGoods MarketLabor MarketHouseholds GovernmentFirmssavingborrowing borrowingconsumptiongovernmentspendinginvestmentproductionworkhiringThree Markets Three Markets –– Three agentsThree agentsNeoclassical modelNeoclassical modelAgents interact in markets, where they may be demander in one market and supplier in another 1) Goods market: Supply:Demand: by households for consumption, government spending, and other firms demand them for investment3Neoclassical modelNeoclassical model2) Labor market (factors of production) Supply:Demand:3) Financial marketSupply:Demand: firms borrow funds for investment; government borrows funds to finance expenditures.Neoclassical modelNeoclassical model We will develop a set of equations to charac-terize supply and demand in these markets Then use algebra to solve these equations together, and see how they interact to establish a general equilibrium.  Start with production…Part 1: Supply in goods market: Part 1: Supply in goods market: ProductionProductionSupply in the goods market depends on a production function:denoted Y= F (K,L)Where K=L=4The production functionThe production function shows how much output (Y) the economy can produce fromKunits of capital and Lunits of labor.  reflects the economy’s level of technology.  Generally, we will assume it exhibits constant returns to scale.Returns to scaleReturns to scaleInitially Y1= F (K1,L1) Scale all inputs by the same factor z:K2 = zK1 and L2 = zL1 for z>1(If z= 1.25, then all inputs increase by 25%)What happens to output, Y2= F (K2,L2) ?  If ______ returns to scale, Y2= zY1 If ______ returns to scale, Y2> zY1 If ______ returns to scale, Y2< zY1Exercise: Exercise: determine returns to scaledetermine returns to scaleDetermine whether each the following production function has constant, increasing, or decreasing returns to scale:= +2 15( , )F K L K L5Assumptions of the modelAssumptions of the model1. Technology is fixed.2. The economy’s supplies of capital and labor are fixed at and = =K K L LDetermining GDPDetermining GDPOutput is determined by the fixed factor supplies and the fixed state of technology:So we have a simple initial theory of supply in the goods market:,=( )Y F K LPart 2: Equilibrium in the factors marketPart 2: Equilibrium in the factors market Equilibrium is where factor supply equals factor demand. Recall: Supply of factors is fixed. Demand for factors comes from firms.6Demand in factors marketDemand in factors marketAnalyze the decision of a typical firm. • It buys labor in the labor market, where _____________.• It rents capital in the factors market, __________.• It uses labor and capital to produce the good, which it sells in the goods market, at price P.Demand in factors marketDemand in factors marketAssume the market is competitive: Each firm is small relative to the market, so its actions do not affect the market prices.It takes ____________________________________________________________________Demand in factors marketDemand in factors marketIt then chooses the optimal quantity of Labor and capital to maximize its profit.How write profit:Profit= revenue -labor costs -capital costs=7Demand in the factors marketDemand in the factors market Increasing hiring of L will have two effects:1) Benefit:2) Cost: To see how much output rises, we need the marginal product of labor (MPL)Marginal product of labor (Marginal product of labor (MPLMPL))An approximate definition (used in text) :The extra output the firm can produce using one additional labor (holding other inputs fixed):MPL= F(K,L +1) –F(K,L)YoutputThe MPL and the production functionThe MPL and the production functionLlaborF K L( , )1MPL1MPL1MPLAs more labor is added:Slope…8Diminishing marginal returnsDiminishing marginal returns As a factor input is increased, its marginal product falls (other things equal).  Intuition:↑Lwhile holding Kfixed⇒ fewer machines per worker ⇒ lower productivityMPL with calculusMPL with calculusWe can give a more precise definition of MPL:where ∆ is ‘delta’ and represents change Earlier definition assumed that ∆L=1.F(K, L +1) –F(K, L) We can consider smaller change in labor.MPL as a derivativeMPL as a derivativeAs we take the limit for small change in L:Which is the definition of the (partial) derivative of the production function with respect to L, treating Kas a constant.This shows the slope of the production function at any particular point, which is what we want.∆ →+ ∆ −=∆0LF K L L F K LMPLL( , ) ( , )lim=Lf K L( , )9The MPL and the production functionThe MPL and the production functionLlaborYoutputF K L( , )∆LMPL is slope of the production function (rise over run)F(K, L +∆L) –F(K, L))fL:F(L):L:Derivative as marginal productDerivative as marginal product= = =122 3 3) ( )Y F L L LYL∂= =∂LYfL640.756941199 3Return to firm problem: hiring LReturn to firm problem: hiring LFirm chooses Lto maximize its profit.How will increasing Lchange profit?∆ profit = ∆ revenue - ∆ cost= ______________If this is: > 0 should ________< 0 should ________= 0 ______________10Firm problem continuedFirm problem continuedSo the firm’s demand for labor is determined by the condition:___________Hires more and more L, until MPL falls enough to satisfy the condition.Also may be written:________, where W/Pis the ‘real wage’Real wageReal wageThink about units:W= ______P= _______W/P= ($/hour) / ($/good) = _________The amount of purchasing power,