Econ 313 Chapter 3: Aggregate Production and Productivity

determination of factor prices

- the production function enables us to make some interesting predictions about the level of wages and rental costs of capital. this helps us to see how the economy distributes national income to workers and capital owners. - we conduct this under a classical framework, assuming the economy has perfect competition and is at its long-term equilibrium level.

Summary Slides:

1) The aggregate production function tells us how much output an economy produces for given amounts of factor inputs, capital and labor. The Cobb-Douglas production function, Y = F(K,L) = AK^0.3L^0.7, displays constant returns to scale: when all the factor inputs increase by the same %, aggregate output increases by exactly the same %. The Cobb-Douglas production function also displays diminishing marginal product: as the amount of a specific factor input increases, holding other inputs constant, its marginal product decreases. Positive supply shocks result in an increase in the quantity of output and marginal products of factors for any given combination of capital and labor, while negative shocks do the opposite. 2) Profit maximization indicates that firms demand a quantity of each factor of production (labor and capital) up until the marginal product of that fact falls to its real factor price, that is, MPK = R/P =rc and MPL = W/P = w. Hence, the marginal product curves for each factor. Factor prices are determined at the intersection of the demand and supply curves for each factor. 3) National income is divided b/w payments to capital and payments to labor, with the sizes of these payments determined by the MP of K and L. Capital and labor income shares of national income do not change even as the level of income grows over time.

Cobb Douglas production function has two characteristics that give it it's prominent role in econ

1) it displays constant returns to scale 2) it has diminishing marginal return

types of supply shocks

1) technology shocks: technology advances can raise total factor productivity so that the parameter A in the production function rises 2) natural environment shocks: blizzards, droughts, floods, earthquakes, and hurricanes can slow construction activity to a grind, reducing output for a given level of capital and labor 3) energy shocks: energy is an important factor of production separate from capital or labor

real GDP is determined by

1) the amount of inputs or factors or production that go into the production process 2) the production function, which tells us how much is produced from given quantities of the factor production

demand curve analysis

MPL and MPK curves are downward sloping: as the quantity of the factor increases, diminishing marginal product implies that the marginal product for the factor falls. since the quantity of the factor demanded occurs at the point where the MP = the real factor price, the MP curves indicate the quantity of the input demanded for any given real factor price. sense, MPL curve is also the demand curve for labor and we mark it as both MPL and D^L

nominal economic profits

P x F(K,L) - RK - WL

national income

Y = 0.7Y + 0.3Y = real labor income + capital income national income is thus divided b/w payments to labor and payments to capital, with the size and quantities of these payments determined by the marginal products of labor and capital Labor income share = wL/Y = 0.7Y/Y = 0.7 Capital income share = rcK/Y = 0.3Y/Y = 0.3 the labor income share of 0.7 is the value of the exponent on labor in the Cobb-Douglas production function is correct, then the shares of labor income and capital income in national income do not change even as the total level of income rises and falls Cobb-Douglas production function has the sensible property that aggregate production displays constant returns to scale

Cobb-Douglas production function equation

Y = F(K,L) = AK^0.3L^0.7 A describes productivity/total factor productivity - we can measure y, K and L and then find A via algebra two observations: 1) an efficient, developed economy will generally produce more with the same quantity of capital and labor than an inefficient, primitive economy 2) the shares of labor and capital income in the US economy have remained relatively constant over time at about 70% labor and 30% capital

supply shock

a change in the output an economy can produce from the same amount of capital and labor - production function can shift

aggregate production function

a description of how much output, Y, is produced for any given amounts of factor inputs, such as K and L -answers who much output an economy can produce Y = F(K,L) - F representing the function that translates K and L into a quantity of real output

supply shocks have the following impact:

a negative supply shock causes the aggregate production function to shift downward and also causes the marginal products of capital and labor to fall. reversing the reason, we have the following: a positive supply shock causes the aggregate production to shift upward and raises the marginal products of products of capital and labor

diminishing marginal product

as the amount of one factor input increases, holding other inputs constant, the increased amount of output from an extra unit of the input (its marginal product) declines

bars over letters

assume they are fixed

productive capacity

economy's ability to create goods and services

perfect competition

firms take market prices as given because they are not large or powerful enough to charge more than the market price for their goods or services - firms are not powerful enough to pay their workers less than the market wage, nor are groups of workers, such as unions, powerful enough to get wages above the market wage. - long run equilibrium, everyone who wants to work can find it and all factories and other capital are utilized so that quantity of labor and capital supplies equals quantity demanded

Equilibrium in the market

for labor D^L = S^L for capital D^K = S^K

constant returns to scale

if you increase all the factor inputs by the same percentage, then output increases by exactly the same percentage - double inputs, double outputs

income per worker

income per worker (y) y = Y = AK^0.3L^0.7 = AK^0.3 --- ------------ -------- = Ak^0.3 L L L^0.3 where k=K/L = cap per worker this equation tells us the income per worker equals the total factor productivity term A multiplied by the capital per worker raised to the power 0.3 the production function indicates that there are two sources of differences in per capita income: 1) the productive efficiency of the economy, represented by the total factor productivity term A 2) the amount of capital per person, represented by k to make a country richer, production-function analysis suggests that policymakers should increase productive efficiency and capital per person The short-fall of per capita income in other countries relative to the US is due more to lower productivity that it is lower amounts of capital per person

two most important factors of production

labor and capital

real economic profits

pi = F(K,L) - (R/P)K - (W/P)L

real economic profits

pi = F(K,L) - rcK - wL

profit maximization

profit maximization implies first that firms will want an amount of capital that will make the marginal product of capital equal to the real rental price of capital MPK = rc (11) Maximizing profits also implies that firms will hire an amount of labor that will make the marginal product of labor equal to the real wage rate MPL = w (12) 11/12 --> firms demand additional quantities of each factor in production (labor and capital) until the marginal product of that factor falls to its real factor price

supply curve

shows relationship b/w quantity of factor supplied and any given real factor price

negative (or adverse) supply shocks

supply shocks that lead to a decline in the quantity of output produced from given quantities of capital and labor - negative shocks are less common but can occur if burdensome gov regulations make the economy less productive

positive (or favorable) supply shocks

supply shocks that result in an increase in the quantity of output produced for given combinations of capital and labor

total factor productivity

tells us how much output an economy can produce given one unit of capital and one unit of labor

oil shocks, real wages and the stock market -- application

the US economy has experienced 3 oil price shocks in the salt 40 years. after each, both real wages and stock prices fell. our supply and demand analysis of factor prices can help explain why a sudden rise in oil prices could trigger these outcomes. negative supply shocks also reduce the marginal product of capital, so the demand curve for capital shifts down and to the left

factors of production

the amount of inputs that go into the production process

labor productivity

the amount of output produced per unit of labor - divide measure output by the amount of labor input

real labor income

the income paid to labor in real terms (real labor income) is the real wage times the quantity of labor real labor income = wL = MPL * L

real capital income

the income paid to owners of capital in real terms is the real rental price of capital times the quantity of capital rock real capital income = rock = MPK*K

demand for capital and labor

the more capital and labor employed by firms, the more they can produce and sell, but adding capital and labor adds costs, reducing profit

wage rate (W)

the price of labor

real rental price (or cost) of capital (rc)

the price paid to rent the capital in terms of goods and services which is the nominal rental price of capital divided by the price level rc = R/P

capital (K)

the quantity of structures and equipment--such as factories trucks and computers--that workers use to produce goods and services - measured by the value of the capital stock in real terms, constant dollars

Explaining real wage growth

the rate of change has varied quite considerably over time the term Y/L, output per unit of labor, is labor productivity, and the fact that real wages are proportional to labor productivity implies that real wages and labor productivity should grow at close to the same rate causes of labor productivity growth slowdown after 1973 - one possible factor is the sharp rise in energy prices that occurred around that time

economic profits

the revenue from selling goods and services minus the costs of the inputs key components: - the revenue from selling goods and services : average price level of the prices of goods and services (P) times the amount of goods and services sold, Y: using the production function, the revenue P x Y is P x F(K,L) - the cost of using capital is the price paid to rent the capital (R) times the amount of capital (K) ... R*K - the cost of labor is the price of labor, the wage rate, W, times the amount of labor, L, ... W*L

excess demand

the situation where the quantity demanded of a factor is above the quantity supplied -firms want to buy more of the factor that owners of the factors want to sell, driving up the price of the factors

excess supply

the situation where the quantity demanded of a factor is less than the quantity supplied

marginal product of capital (MPK)

the slope of the production function ∆Y / ∆K that indicates how much output increases for each additional unit of capital, holding other inputs constant - slope of production function: as capital stock increases, the marginal produce of capital declines MPK = 0.3Y ---- K

marginal product of labor (MPL)

the slope of the production function, ∆Y / ∆L, that indicates how much output increases for each additional unit of labor, holding capital constant at $10 trillion - as the amount of labor input increases, the marginal product of labor declines. while holding the other one constant, its marginal product decreases. MPL = 0.7Y ----- L

labor (L)

the sum of the numbers of hours people work (also known as "person-hours")

real wage rate

the wage in terms of goods and services, which can be written as the nominal wage rate divided by the price level w=W/P