# 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.

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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 > 0

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 Quantity Price Supply Demand Equilibrium price

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 F(K,L) Labor in the variable input 1 1 1 MPL

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 labor Units of output MPL

The Firm’s Demand for Labor Demand for labor depends on its price and marginal product In a competitive market: MPL = W/P = the real wage. The labor demand is W = P  MPL

The Firm’s Demand for Capital Demand for capital depends on its price and marginal product In a competitive market: MPK = R/P = the real interest. The capital demand is R = P  MPK

Diminishing Marginal Product of Capital As more capital input is added, holding labor input constant, the output will increase at a decreasing rate. Hence, MPK declines, due to inefficiency, as more capital is added. Units of capital Units of output MPK

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 Firms Households Labor Resources Income Payments Products Saving Labor Market Product Market Government Financial Market Investment Consumption Expenditures Government Purchases Taxes

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 Disposable income, Y - T Consumption, C C = C(Y – T) MPC 1

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 Quantity of investment, I I(r)

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: S p = Y – T – C Public saving: left over government revenue: S g = T – G

Determination of Real Interest Rate Investment, Saving I(r) Real interest rate S Equilibrium interest rate

Increase in Investment Demand I(r) S r1r1 I’(r) r2r2 An increase in investment demand results in a higher interest rate. Real interest rate Investment, Saving

Classical Saving Function Saving is positively related to the real interest rate S = S(r) Quantity of Saving Real interest rate S(r)

Increase in Investment Demand Quantity of Saving Real interest rate S(r) I1I1 I2I2 r1r1 r2r2 I1I1 I2I2

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