Chapter 3: National Income
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Transcript of Chapter 3: National Income
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Chapter 3: National Income
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Production Function
Output of goods and services as a function of factor inputs
Y = F(K, L)
Y = product outputK = capital inputL = Labor input
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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
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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
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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.
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Input Price Determination
Quantity
PriceSupply
DemandEquilibrium price
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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
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Production Function
Output
Labor
F(K,L)
Labor in the variable input
1
1
1
MPL
MPL
MPL
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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)
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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
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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
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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
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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
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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
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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
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Consumption Function
Consumption is a function of disposable personal income:
C = C(Y – T)
Y = personal incomeT = personal income taxes
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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.
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Consumption Function
Disposable income, Y - T
Consumption, C
C = C(Y – T)
MPC1
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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
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Investment FunctionReal interest rate, r
Quantity of investment, I
I(r)
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Government Role
We assume government purchases of goods and services and resources and personal income taxes are fixed amounts:
G = G T = T
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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
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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
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Components of National Saving
Private saving: left over household income:
Sp = Y – T – C
Public saving: left over government revenue:
Sg = T – G
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Determination of Real Interest Rate
Investment, Saving
I(r)
Real interest rate
S
Equilibrium interest rate
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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
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Classical Saving Function
Saving is positively related to the real interest rate S = S(r)
Quantity of Saving
Real interest rate
S(r)
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Increase in Investment Demand
Quantity of Saving
Real interest rate
S(r)
I1I2
r1
r2
I1 I2