Chapter 3: National Income Production Function Output of goods and services as a function of factor inputs Y = F(K, L) Y = product output K = capital input L = Labor input Constant Returns to Scale When an increase in the quantity of the inputs results in an equal increase in the quantity of the output F(zK, zL) = zY where z > Supply of Products Because we assume that the supplies of capital and labor inputs and the production technology are fixed, the supply of product output is also fixed Y = F(K, L) = Y Input Price Determination Input or factor prices are determined by the supply and demand for them Because we assume the input supply is fixed, its supply line is vertical The factor demand curve is downward sloping The intersection of demand and supply determines the factor price Input Price Determination Price Supply Equilibrium price Demand Quantity Profit Determination Profit = Revenue – Labor Cost – Capital Cost П = PY – WL – RK P = price of output W = price of labor input = wage rate R = price of capital input = interest rate Production Function Output Labor in the variable input MPL F(K,L) MPL MPL Labor Marginal Product of Inputs Additional productivity gained from hiring an extra unit of the labor input MPL and MPK are: MPL = F(K, L+1) – F(K, L) MPK = F(K+1, L) – F(K, L) Diminishing Marginal Product of Labor As more labor input is added, holding capital input constant, the quantity of output will increase at a decreasing rate Hence, MPL declines, due to inefficiency, as more labor is added Units of output MPL Units of labor Determinants of Demand for Products The GDP for a closed economy is total spending by households, firms, and government: Y=C+I+G Consumption = C Investment = I Government purchases = G The Circular Flow on Income and Product Income Payments Labor Market Investment Labor Resources Financial Market Saving Households Firms Government Purchases Government Taxes Products Product Market Consumption Expenditures Consumption Function Consumption is a function of disposable personal income: C = C(Y – T) Y = personal income T = personal income taxes Consumption Function Marginal propensity to consume = additional consumption from an extra dollar of disposable personal income MPC = ΔC / Δ(Y –T) MPC is slope of consumption function Consumption Function Consumption, C C = C(Y – T) MPC Disposable income, Y - T Investment Function Investment is a negative function of the real interest rate I = I(r) Low interest rates encourage borrowing for investment purposes, whereas high interest rates discourage borrowing Investment Function Real interest rate, r I(r) Quantity of investment, I Government Role We assume government purchases of goods and services and resources and personal income taxes are fixed amounts: G=G T=T National Income Identity Y = C + I + G, where C = C(Y –T) I = I(r) G = G and T = T Y = C(Y – T) + I(r) + G Saving Investment Identity Equilibrium in the product market: Y = C(Y – T) + I(r) + G Y - C(Y – T) - G = I(r) S = I(r) Where S is national saving Components of National Saving Private saving: left over household income: Sp = Y – T – C Public saving: left over government revenue: Sg = T – G Determination of Real Interest Rate Real interest rate S Equilibrium interest rate I(r) Investment, Saving Increase in Investment Demand Real interest rate S An increase in investment demand results in a higher interest rate r2 r1 I’(r) I(r) Investment, Saving Classical Saving Function Saving is positively related to the real interest rate S = S(r) Real interest rate S(r) Quantity of Saving Increase in Investment Demand Real interest rate S(r) r2 r1 I1 I1 I2 I2 Quantity of Saving