Chapter 3: National Income

Production Function

Output of goods and services as a function of factor inputs

Y = F(K, L)

Y = product outputK = capital inputL = 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

PriceSupply

DemandEquilibrium price

Profit Determination

Profit = Revenue – Labor Cost – Capital Cost

П = PY – WL – RK

P = price of outputW = price of labor input = wage rateR = price of capital input = interest rate

Production Function

Output

Labor

F(K,L)

Labor in the variable input

1

1

1

MPL

MPL

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 LaborDemand 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 = CInvestment = IGovernment purchases = G

The Circular Flow on Income and Product

Firms Households

Labor Resources

Income Payments

Products

Saving

Labor Market

Product Market

Government

Financial MarketInvestment

Consumption Expenditures

Government PurchasesTaxes

Consumption Function

Consumption is a function of disposable personal income:

C = C(Y – T)

Y = personal incomeT = 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)

MPC1

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 FunctionReal 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:

Sp = Y – T – C

Public saving: left over government revenue:

Sg = 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

r1

I’(r)

r2

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)

I1I2

r1

r2

I1 I2