Chapter 3 AGGREGATE PRODUCTION AND PRODUCTIVITY
MPL and MPK are downward sloping
- as Q of factors increases, diminishing marginal product implies that marginal product for factor falls
Q of factor demanded occurs
- at point where marginal product equals real factor price - indicate Q of input demanded for any given real factor price
long-term equilibrium
- everyone who wants to work can find it - all factories and other capital are utilized so that QS of L and K equals QD
perfect competition
- firms take market prices as given because they are not large or powerful enough to charge more than the market price - firms are not powerful enough to pay their workers less than market wage, nor any groups of workers, such as unions, powerful enough to get wages above market wage
MPK > r MPK = r MPK < r
- marginal product of capital exceeds rental cost of capital, adding more capital raises profits - marginal product of capital equals real rental cost - Firms increase profits by reducing amount of capital since cost is above extra revenue it produces of capital
capital
- quantity of structures and equipment (factories, trucks, computers) - workers use to produce goods and services (K) - measured by value of capital stock in real terms (constant dollars)
explaining real wage growth
- real wages are determined by MPL - real wages are proportional to labor productivity implies that real wages and labor productivity should grow at close to the same rate
labor
- summing numbers of hours people work - person-hours (L)
technology shocks
- tech advances - Development of faster computer chip raise total factor productivity so that A parameter in production function rises
Cobb - Douglas Production Function Characteristics
1) Displays constant returns to scale 2) diminishing marginal product
upward sloping production function
1) as capital increases, output goes up 2) as capital increases, the slope, \change Y / \change K falls
Cobb- Douglas production function
1) efficient developed economy generally produces more with the same quantity of K and L than an inefficient, primitive economy 2) shares of L and K income in US economy have remained relatively constant over time at about 70% labor and 30% capital
two sources of differences in per capita income
1) productivity efficiency of economy A 2) amount of capital per person k
Solow Residual
A = Y / (K^0.3L^0.7)
a positive supply shock causes
Aggregate production to shift upward and raises marginal products of K and L
real economic profits
F(K,L) - ((R/P)K - (W/P)L
real economic profits with r and w
F(K,L) - rK - wL
production function of revenue
P x F(K,L)
nominal economic profits (or cost)
P x F(K,L) - RK - WL
excess supply
QD of factor is less than QS - price falls - as long as factor price remains above equilibrium price, excess supply continues, price continues to fall
National Income
Real Labor Income + Capital Income
aggregate production function equation
Y = F(K,L) F = Function that translates K and L into a quantity of real output
Cobb- Douglas production function equation
Y = F(K,L) = AK^0.3L^0.7
a negative supply shock causes
aggregate production function to shift downward and also causes marginal products of K and L to fall
market equilibrium t a given
amount firms are willing to buy (demand) equals amount owners of factors of production are willing to sell (supply) at a given price
factors of production
amount of inputs
labor productivity
amount of output produced per unit of labor
diminishing marginal product
as amount of one factor input increases, holding other inputs constant, the increased amount of output from an extra unit of input(marginal product) declines
diminishing marginal product of labor
as the amount of labor input increases, the marginal product of labor declines
slope of production function holds that
as the capital stock increases, the marginal product of capital declines
classical framework
assuming economy has perfect competition and is AT its long-term equilibrium level
revenue from selling goods and services
average level of prices of goods and services (P) times amount of goods and services sold (Y)
natural environment shocks
blizzards, droughts, floods, earthquakes, hurricanes slow construction activity to grind, reducing output for given level of K and L (unusually warm winter can have opposite effect)
supply shock
change in output an economy can produce from same amount of capital and labor = change in A
negative (adverse) supply shock
decline in Q of output produced from given Q of K and L
marginal product of labor curve is also
demand curve for labor
aggregate production function
description of how much output (Y) is produced for any given amounts of factor inputs (K,L)
how do economists measure labor productivity
divide measured output by amount of labor input
bars over letter
exogenous taken as given
excess demand
factor price below equilibrium price - QD of factor is above QS - price increases - stops rising when excess demand for factor is eliminated at equilibrium price
profit maximizing conditions
firms demand additional Q of each factor of production until marginal product of that factor falls to its real factor price
Second profits maximization implies
firms will hire an amount of labor that will make the marginal product of labor equal to real wage rate MPL = w
First profits maximization implies
firms will want an amount of capital that will make the marginal product of capital equal to rental price of capital MPK = r
production function
how much is produced from given quantities of the factors of production
given quantities of labor and capital
how much output can economy produce
marginal product of capital (MPK)
how much output increases for each additional unit of capital, holding other inputs constant (slope of production function changeY / changeK)
marginal product of labor (MPL)
how much output increases for each additional unit of labor
Energy shocks
important factor of production energy supplies disrupted, firms use less energy causing amount of output the economy produces to fall for given Q of K and L
constant returns to scale
increase all factor inputs by same percentage, output increases by exactly the same percentage
positive supply shock
increase in quantity of output produced for given combinations of capital and labor
two most important factors of production
labor capital
negative shocks are
less common occur if burdensome gvmt regulations make economy less productive
national income is thus divided between
payments to labor and payments to capital, with the size and quantities of these payments determined by marginal products of labor and capital
cost of L
price of labor = wage rate W W x L
cost of using K
price paid to rent capital = rental price of capital R x K
to make country richer
production function analysis suggests policymakers should increase productivity efficiency and capital per person
capital income share
rK / Y
Real Capital Income
rK = MPK x K
real rental price (cost) of capital
rental price of capital in terms of goods and services = nominal rental price of capital divided by price Level r
economic profit
revenue from selling goods and services minus costs of inputs
if Cobb-douglas production function is correct
shares of labor income and capital income in national income do not change even as the total level of income rises and falls
negative supply shock graph
shifts production function downwards
If A goes up by 5%
then for same amount of K and L, the total amount of goods and services produced in economy increases by 5% under Cobb- Douglas function
A Variable
total factor productivity - how PRODUCTIVE capital and labor are - how much output an economy can produce given one unit of capital and one unit of labor
labor income share
wL / Y
Real Labor Income
wL = MPL x L
real wage rate
wage in terms of goods and services = nominal wage rate divided by price level w
income per worker equals total factor productivity term A multiplied by capital per worker ^0.3
y = {Y\over L} = {AK^{0.3}L^{0.7}\over L} = Ak^{0.3} where k = K/L = capital per worker
