chapter 6 markets, prices, supply, and demand. objective: understand short-run economic...
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Chapter 6 Markets, Prices, Supply, and Demand
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Objective: understand short-run economic fluctuations.
Micro foundations: the choices made by consumers and firms.Supply and demand behavior.
The neoclassical way: the market clears.
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Timing
States: Bt-1, Kt-1, Pt-1, Mt-1
They are values at the end of period t-1, or at the beginning of period t.
They are real or nominal assets at the end of period t.
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Timing Economic agents (period t)
Firm: Yt=AtF(Kt-1, Lt);Consumer: U(Ct, 1-Lt);Both are price-takers.
Markets (period t)Rental market: Rt-1;Bonds market: it-1;Labor market: wt;Money market: Pt.
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Timing Controls: Ct, Lt, Bt, Kt,
They are household’s decisions based on observed prices and real assets;
Real assets include interest and rental income paid in period t.
States at the end of period t: Bt, Kt, Pt, Mt
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Markets in the Macroeconomy Direct ownership of firms: no stock market. The goods market: nothing peculiar. The labor market
Inelastic supply of labor: Ls=Lt;
Ld determined by firms’ behavior. The rental market
Inelastic supply of capital: Ks=Kt-1;
Kd determined by firms’ behavior.
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Markets in the Macroeconomy The bond market: borrowing between househo
lds. The money market
Inelastic supply of money: Ms=Mt;
Household demands md=Md/Pt.
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Money as a Medium of Exchange All exchange uses money. Dollar amounts are nominal terms. Money earns no interest.
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Markets and Prices The money market
The general price level: Pt.
The labor marketNominal wage: wt.
Real wage: wt/Pt.
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Markets and Prices The rental market
Nominal rental price: Rt-1.
Real rental price: Rt-1/Pt.
Nominal rental income (payment): Rt-1Kt-1.
The bond marketNominal interest rate: it-1.
Nominal interest income: it-1Bt-1.
In aggregation, the net borrowing must be zero.
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The Budget Constraint Nominal income
Profit: t=PtAtF(Kt-1, Lt)-(wtLt+Rt-1Kt-1)
Wage income: wtLt.
Rental income: Rt-1Kt-1. Net nominal rental income: Rt-1Kt-1-PtKt-1. Rate of return: Rt-1/Pt-.
Interest income: it-1Bt-1.
Total income: t+wtLt+(Rt-1/Pt-)PtKt-1+it-1Bt-1.
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The Budget Constraint Nominal rates of return from t-1 to t:
On bonds: it-1;
On capital: ;
Real rates of return from t-1 to t:
On bonds: ;
The Fischer equation:
On capital: .
1 1 1 1
1 1 1
t t t t t t
t t t t
R K PK R P
P K P P
11 1(1 ) 1t
t tt
Pr i
P
1t
t
R
P
11 1 1 1
1
11
1t
t t t tt
ir r i
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The Budget Constraint Nominal consumption: PtCt. Assets
Capital, bonds, and money.Nominal income from holding money: zero.Capital and bonds must yield the same real rates of
return.
The nominal income can be put as
t+wtLt+rt-1PtKt-1+it-1Bt-1=t+wtLt+rt-1PtKt-1+((1+rt-1)Pt/Pt-1-1)Bt-1
11
tt
t
Rr
P
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The Budget Constraint Household budget constraint
Nominal value of assets: Mt-1+Bt-1+PtKt-1.
Nominal saving: Mt+Bt+PtKtBudget constraint in nominal terms:
PtCt+Bt+PtKt+Mt=t+wtLt+it-1Bt-1+rt-1PtKt-1Budget constraint in real terms:
11 1 1
t t t t tt t t t t t
t t t t t
B M w BC K L i r K
P P P P P
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The Budget Constraint The budget line
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Market Clearing Profit maximization
The firm tries to maximize the real profit:
Assuming competitive behavior: price taker.Maximize profit by choosing over Kd and Ld.
1( , )d d d dt t tt
t t t
w RAF K L L K
P P P
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Market Clearing The labor market
Demand for labor: The production function exhibits diminishing marginal
productivity in labor; The labor demand curve is downward sloping.
Supply of labor: Ls=Lt.
Market clearing:
1( , )dt t
wAF K L
L P
1( , ) tt t
t
wAF K L
L P
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Market Clearing Labor market clears
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Market Clearing The Market for capital services
Demand for capital: The production function exhibits diminishing marginal
productivity in capital; The demand curve for capital is downward sloping.
Supply of capital: Ks=Kt-1.
Market clearing:
The real interest rate:
( , )dt
RAF K L
K P
11( , ) t
t tt
RAF K L
K P
11 1( , )t
t t t tt
Rr A F K L
P K
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Market Clearing Market of capital services clears
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Market Clearing Zero profit at equilibrium
11 1( , )t t t
t t t t tt t t
w RAF K L L K
P P P
11 1( , ) ( , )t t
t t t t t tt t
w RAF K L AF K L
P L P K
1 11 1
( , ) ( , )( , )
0
t t t t tt t t t t
t
F K L F K LA F K L L K
P L K
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The budget constraint Budget constraint in nominal terms:
PtCt+Bt+PtKt+Mt=wtLt+it-1Bt-1+rt-1PtKt-1PtCt+Bt+PtKt+Mt=wtLt+(1+it-1)Bt-1+(1+rt-1)PtKt-1+Mt-
1
PtCt+Bt+PtKt+Mt=wtLt+(1+it-1)Bt-1+(Rt-1/Pt+1-)PtKt-1+Mt-1
PtCt+Bt+PtKt+Mt=PtAtF(Kt-1, Lt)+(1+it-1)Bt-1+(1-)PtKt-1+Mt-1
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The budget constraint Budget constraint in real terms:
11 1 1
t t t tt t t t t t
t t t t
B M w BC K L i r K
P P P P
1 11 1 1(1 ) (1 )t t t t t
t t t t t tt t t t t
B M w B MC K L i r K
P P P P P
1 1
1 11
( , ) (1 )
(1 )
t tt t t t t t
t t
t tt
t t
B MC K AF K L K
P P
B Mi
P P
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Choice of future assets Future rates of return: it and Rt
They are determined by future market conditions; Future price level: Pt+1
It is determined by future market conditions; Real rates of return:
(1+it)Pt/Pt+1-1 and Rt/Pt+1-; The choice of Bt and Kt is based on expectation
s on future rates of return and future price level.
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Real Business Cycle Money is left untreated:
Assume that Mt=M;
Assume that Pt=P;
It follows that it-1=rt-1.
Household budget constraint:PCt+Bt+PKt=wtLt+it-1Bt-1+rt-1PKt-1PCt+Bt+PKt=PAtF(Kt-1, Lt)+(1+it-1)Bt-1+(1-)PKt-1
11 1 1( , ) (1 ) (1 )t t
t t t t t t t
B BC K AF K L K i
P P
11 1 1
t t tt t t t t t
B w BC K L i r K
P P P