Markets, Prices, Supply, and Demand

Macroeconomics Chapter 6 1

Chapter 6

Markets in the Macroeconomy

Assuming that households perform all of the functions in the economy.

Each household runs a family business and uses labor, L, and capital, K, to produce goods, Y, through the production function.

Y= A· F( K, L)

Markets in the Macroeconomy

Goods market

Labor market

Rental marketBond market

Households Households(Firms)

The Goods Market

Households sell all the goods they produce on a goods market. Then households buy back from this market the goods that they want.

Household buys goods for consumption. to increase the stock of goods in the form

of capital used for production, called investment.

The Goods Market and Prices

The price in this goods market, denoted by P, expresses the number of dollars that exchange for one unit of goods.

We call P the price level.

The goods Market and Prices

Y= A· F( K, L) Since all of these goods are sold on the

goods market, the variable Y will also represent the

Quantity of goods per year sold and bought on the goods market.

The quantity PY is the dollar value per year of the goods bought and sold on the goods market.

The goods Market and Prices

The expression 1/P is the value of $1 in terms of the goods that it buys.

M dollars exchange for (M) · (1/ P) = M/P An expression like M/P is in real terms,

in units of goods, whereas a quantity like M is in dollar or nominal terms.

Labor Market in the Macroeconomy

Households supply labor on a labor market. Assume that the quantity supplied, Ls,

is a constant, L. Households buy and sell labor in the

labor market at the dollar or nominal wage rate, w.

The real wage rate is w/P.

Rental Markets in the Macroeconomy

Each household rents out all of the capital that it owns on a rental market. We think of the capital offered on the

rental market as the supply of capital services, Ks. Since we have assumed that each household rents out all of its capital, we have Ks = K.

Rental Markets and Prices

Households rent out capital, K, for dollars at the dollar or nominal rental price, R

A household that rents the amount of capital Kd pays the nominal amount RKd per year and then gets to use the capital as an input to production.

The real rental price is R/P.

The Bond Market in the Macroeconomy

A borrowing household receives a loan from another household, whereas a lending household provides a loan to another household.

A household that makes a loan receives a piece of paper called a bond, and we call the market on which households borrow or lend the bond market. The holder of a bond, the lender, has a claim to the amount owed by the borrower.

The bond Market and Prices

Each unit of bonds commits the borrower to repay $1 to the holder of the bond. This $1 is the principal of each bond.

The principal is the initial amount advanced on a loan.

The Bond Markets and Prices

Each unit of bonds commits the borrower to pay the holder a flow of interest payments of $i per year.

The variable i is the interest rate, which is the ratio of the interest payment, $i, to the principal $1.

The interest rate, i, can vary over time.

Money as a Medium of Exchange

We assume that the exchanges on each of these markets use a single form of medium of exchange. A medium of exchange is an object

held, not for its own sake, but rather to trade fairly soon for something else, such as goods and services. We call the medium of exchange in our model money.

Assume that money is just a piece of paper, analogous to a paper currency issued by a government. Money is denominated in an arbitrary

unit, such as a “dollar.” Dollar amounts are in nominal terms. Paper money earns no interest.

The sum of the individual holdings of money equals the aggregate quantity of money in the economy. Assume, for now, that this aggregate

quantity of money is a given constant. The total money held by all households

must end up equaling this constant.

Constructing the Budget Constraint

The quantities and prices determined on the four markets will determine household income. Flows of income are sources of funds Purchases of goods and assets are uses

of funds The total sources of funds must equal

the total uses of funds. This equality is called the household budget constraint.

Income Profits

Households may earn profit—an excess of revenue over costs—from their business activities.

Y= A· F( Kd, Ld ) π = PY − (wLd+ RKd) π = P A· F( Kd, Ld ) − ( wLd+ RKd)

Income Wage income

If households supply the quantity of labor Ls to the labor market, they receive the nominal wage income of wLs per year.

Quantity of labor supplied is the fixed amount L, so nominal wage income is wL.

Income Rental income

If households supply the quantity of capital Ks to the rental market they receive the nominal rental income of RKs per year.

Since households supply all of their available capital, K, to the rental market, so that Ks = K, the nominal rental income is RK.

Rental income The quantity δK of capital disappears each year.

The dollar value of this lost capital is P·δK. net nominal rental income= nominal rental

income− value of depreciation net nominal rental income = RK−δPK net nominal rental income = (R/P)·PK−δPK net nominal rental income= (R/P−δ)·PK

Rate of return on owning capital= R/P−δ

Interest Income If a household’s nominal bond holdings

are B, the flow of nominal interest income received is iB per year.

Since B equals zero for the whole economy, we have that the total of interest income equals zero.

Total income Household nominal income= nominal

profit + nominal wage income + nominal net rental income+ nominal interest income

Household nominal income =π+wL+(R/P−δ)·PK+iB

Consumption

Households consume goods in the quantity C per year at price P

Household nominal consumption= P C

Assets Households hold assets in three forms:

money, M; bonds, B; ownership of capital, K.

Assets We assume that households hold a

fixed amount of money in dollar terms; that is, we assume that the change over time of a household’s nominal money holdings is zero

∆M=0

Assets In considering whether to hold assets

as bonds or capital, households would compare the rate of return on bonds, the interest rate, i, with the rate of return on ownership of capital, R/P −δ.

Rate of return on bonds= rate of return on ownership

i = R/P − δ

Household nominal income = π + wL + i · ( B+ PK )

Household Budget Constraint nominal value of assets= M+ B+ P K nominal saving to be the change over

time in the nominal value of assets. nominal saving= (∆nominal assets) = ∆M + ∆B + P·∆K

Household Budget Constraint nominal saving= nominal income−

nominal consumption nominal saving= π + wL + i · ( B+ P K )

− P C ∆B + P ·∆K = π + wL + i·( B+ PK)−PC

Household Budget Constraint in Nominal Terms PC + ∆B + P·∆K = π + wL + i·( B+ PK ) nominal consumption + nominal saving

= nominal income

Household Budget Constraint real terms C + (1/P)·∆B+ ∆K = π/P + (w/P)·L +

i·(B/P+K) consumption + real saving = real

income

Profit Maximization

Real Profit π/P = A·F(Kd,Ld) − (w/P) · Ld − (R/P) · Kd

real profit= output − real wage payments − real rental

payments

Clearing of the Markets for Labor and Capital Services

The Labor Market Demand for labor

∆(π/P) = ∆[ A·F( Kd, Ld) ] − w/P = MPL − w/P change in real profit= marginal product of

labor− real wage rate

Supply of labor We are assuming that each household

supplies a fixed quantity of labor to the labor market.

Therefore, the aggregate or market supply of labor, Ls, is the given amount L.

Clearing of the labor market w/P is determined to equate the

aggregate quantity of labor demanded, Ld, to the aggregate quantity supplied, L.

(w/P)* = MPL ( evaluated at L)

The Market for Capital Services Demand for capital services

∆(π/P) = ∆[ A·F(Kd, Ld) ] − R/P = MPK − R/P

change in real profit= marginal product of capital− real rental

The Market for Capital Services Supply of capital services

For the economy as a whole, the aggregate quantity of capital, K, is given from past flows of investment.

In the short run, the aggregate or market quantity of capital services supplied, Ks, equals K.

The Market for Capital Services Clearing of the market for capital

services R/P will be determined to clear the market

—that is, so that the aggregate quantity of capital services supplied, K, equals the aggregate quantity demanded, Kd

(R/P)* = MPK( evaluated at K)

The Market for Capital Services The interest rate

i = R/P − δ rate of return on bonds= rate of return on ownership of capital

i = MPK ( evaluated at K) − δ

Profit in Equilibrium π/P = A· F(K,L) − (w/P)·L − ( R/P)· K

w/P = MPL R/P = MPK

π/P = A· F(K, L) − MPL· L − MPK· K

Zero Profit in Equilibrium

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Markets, Prices, Supply, and Demand

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household buys goods

thequantity of goods

units of goods

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bond markets

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