Econ 4002.01 Chapter 3
National Saving (Saving)
A nation's income minus consumption and government purchases; the sum of private and public saving. Y-C-G is national saving. Saving equals investment. National saving is the sum of private and public saving.
Cobb-Douglas Production Function
A production function of the form F(K, L)=AK^α L^(1-α) where K is capital, L is labor, and A and are parameters. (A is a parameter greater than zero that measures the productivity of the available technology.) The Cobb-Douglas production function has constant returns to scale. That is, if capital and labor are increased by the same proportion, then output increases by that proportion as well.
Constant Returns to Scale
A property of a production function whereby a proportionate increase in all factors of production leads to an increase in output of the same proportion. A production function has constant returns to scale if an increase of an equal percentage in all factors of production causes an increase in output of the same percentage. If the production function has constant returns to scale, then we get 10 percent more output when we increase both capital and labor by 10 percent. Mathematically, a production function has constant returns to scale if: zY = F(zK, zL) for any positive number z.
Loanable Funds
The flow of resources available to finance capital accumulation. Saving is the supply of loanable funds. Households lend their saving to investors or deposit their saving in a bank that then loans the funds out. Investors borrow from the public directly by selling bonds or indirectly by borrowing from banks. Because investment depends on the interest rate, the quantity of loanable funds demanded also depends on the interest rate.
What Determines Demand? Government Spending
Total government spending includes both government purchases of goods and services and government transfer payments. -Government purchases represent about 20% of expenditures on goods and services. -Transfer payments are not made in exchange for goods and services and, therefore, are counted as expenditures. -Transfer payments do affect spending indirectly. --Transfer payments can be thought of as negative taxes. -- T=net Taxes=Taxes-Transfer Payments We can now consider the government's budget. -If G=T, the budget is in balance. -If G>T, there is a budget deficit and the government must borrow money by issuing debt. -If G<T, there is a budget surplus and existing debt can be repaid. Government purchases and net taxes are determined by the policy makers and will be treated as exogenous variables in the model. - G=Gbar - T=Tbar
Private Saving
Disposable income minus consumption. Y-T-C is disposable income minus consumption, AKA private saving.
What Establishes Equilibrium? Consumption and Saving
Finally, suppose that consumption and saving were dependent on the interest rate too. -Suppose that a higher interest rate causes the households to spend less and save more. -An exogenous change that increases investment will: --Increase investment at the original interest rate. --Raise the interest rate. --Decrease consumption and increase saving by ΔI -Consumption will be replaced by investment. An increase in desired investment raises the interest rate and raises equilibrium investment and saving.
Public Saving
Government receipts minus government spending; the budget surplus. T-G is government revenue minus government spending, AKA public saving. If government spending exceeds government revenue, then the government runs a budget deficit and public saving is negative.
What Establishes Equilibrium? Exogenous Change
Now lets consider an exogenous change that causes an increase in investment expenditures. -A technical innovation that requires the purchase of new capital equipment. -Changes in business taxes providing an incentive for additional investment. Suppose that investment increases by ΔI: -The demand for loanable funds will increase at the original interest rate. -The interest rate will rise. -Investment will fall to its original level. Notice that there is no change in the demand for goods and services. An increase in desired investment raises the interest rate.
Income Inequality
One aspect of the distribution of income that has received attention in recent years is the problem of income inequality. -The Gini coefficient is a measure of income dispersion. --A value of zero means perfect income equality. --A value of one means perfect income inequality. -In 1968 the Gini coefficient reached a low of 0.35. -By 2012 the Gini coefficient had risen to 0.45. Possible explanations: -The changing factor shares between labor and capital because ownership of capital is more concentrated in higher income households. -Within the labor share, the gap between high wage earners and low wage earners has increased substantially. --Golden and Katz argue that the increasing gap is the result of an educational slowdown. --The increase in the supply of high skill labor has been slower than the increase in demand for high skill labor. --A possible solution is to allocate more resources to the development of human capital.
What Establishes Equilibrium? Government Purchases
Since both government purchases and net taxes are exogenous, we can determine the effects of a change in fiscal policy. -A change in either G or T will potentially affect several variables. --The demand for goods and services --Consumption --Saving --The interest rate --Investment If T is held constant, an increase in government purchases of ΔG will: -Increase the demand for goods and services by ΔG -Reduce saving by ΔG -Increase the interest rate -Reduce investment by ΔG, which reduces the demand for goods and services by ΔG The increase in government spending crowds out private investment spending. A fall in saving raises the interest rate. Suppose, instead, that we hold G constant and decrease net taxes by ΔT. -Disposable income will rise by ΔT. -Consumption will rise by (MPC)ΔT. -Saving will fall by (MPC)ΔT. -The interest rate will rise. -Investment will fall by (MPC)ΔT, and the demand for goods and services will fall by (MPC)ΔT. Again, private investment spending has been crowded out.
Diminishing Marginal Product
A characteristic of a production function whereby the marginal product of a factor falls as the amount of the factor increases while all other factors are held constant. Most production functions have the property of diminishing marginal product: holding the amount of capital fixed, the marginal product of labor decreases as the amount of labor increases.
Competitive Firm
A competitive firm is small relative to the markets in which it trades, so it has little influence on market prices.
Consumption Function
A relationship showing the determinants of consumption; for example, a relationship between consumption and disposable income, C = C (Y - T). We assume that the level of consumption depends directly on the level of disposable income. A higher level of disposable income leads to greater consumption. C=C(Y-T) states that consumption is a function of disposable income.
What Determines Total Production
An economy's output of goods and services depends on two things. -The quantity of factors of production or resources available. -The production function. Assume that we use two factors of production to produce goods and services, labor (L) and capital (K). Further assume that the amounts of K and L are fixed: K=Kbar and L=Lbar. Finally, assume that K and L are fully employed. The production function represents how much output can be produced from given amounts of K and L. -The production function is based on the available technology. -Changing technology changes the production function and, thus, the possible output from the given K and L. -The production function can be expressed as: Y=F(K,L) Many production functions exhibit constant returns to scale. -Constant returns to scale exist when an increase of an equal percentage in all factors of production causes an increase in output of the same percentage. -Mathematically: zY=F(zK, zL) for any z>0. For a given technology, combining the production function with the available resources in our model yields the total output or production: Y=F(Kbar, Lbar)=Ybar
Factors of Production
An input used to produce goods and services; for example, capital or labor. The two most important factors of production are capital and labor. -Capital is the set of tools that workers use. -Labor is the time people spend working.
How Is National Income Distributed?
Because the factors of production and the production function determine the total output of goods and services, they also determine the national income.
The Cobb-Douglas Function: Case Study
Case Study: Labor Productivity and Real Wages -W/P=MPL=(1-α)(Y/L) -Changes in the average productivity of labor should lead to changes in the real wage if our theory is right.
How Is Income Distributed? Case Study
Case Study: The Black Death and Factor Prices -Neoclassical theory says that factor prices are equal to the marginal productivity of the factors. -A change in the supply of a factor alters equilibrium prices and the distribution of income. -In 14th century Europe, the Black Death reduced the population by about 1/3 in few years. --The decrease in the supply of labor increased the MPL. --The real wages for workers increased. --The real rent for land-owners decreased because the reduced supply of labor decreased the marginal product of the land.
What Determines Demand? Consumption
Consumption represents about 67% of spending on goods and services. -Households receive income from their labor and ownership of capital. -Part of that income is used to pay taxes. -The remaining after-tax or disposable income is divided between consumption and private saving. -- Y-T=C+S Consumption is related to the level of the households' disposable income. -The relationship can be expressed in functional form as: -- C=C(Y-T) -The consumption function says that consumption is dependent on disposable income. -The relationship between disposable income and consumption is positive. The amount that consumption changes as disposable income changes is called the marginal propensity to consume or MPC. - 0<MPC<1 -Every $1 increase in disposable income will increase consumption by less than $1. -The MPC is the slope of the consumption function. The marginal propensity to save or MPS is the fraction of the dollar that was not spent. MPC+MPS=1 (The slope of the consumption function is MPC/1)
Economic Profit Vs. Accounting Profit
Economic Profit: The amount of revenue remaining for the owners of a firm after all the factors of production have been compensated. The income that remains after the firms have paid the factors of production is the economic profit of the owners of the firms: Economic Profit=Y-(MPLxL)-(MPKxK). Accounting Profit: The amount of revenue remaining for the owners of a firm after all the factors of production except capital have been compensated. Accounting Profit=Economic Profit+(MPKxK). Read more about this in the textbook.
How Is Income Distributed?
Factor prices are the amounts paid to each unit of the factors of production. -Labor earns wages (W). -Capital earns rental income (R). Factor prices are determined by the supply and the demand for each resource. (Slide 14) Since the supply of each factor is fixed, the distribution of income will depend on the demand for each factor of production. To illustrate this, assume that firms are perfectly competitive in both the product market and the factor market. -Firms are small relative to the market. -Firms are price takers. For a given production function, Y=F(K,L), the only way that output can increase is by using additional amounts of one of the factors of production.
FYI: Interest Rates
In macroeconomics we talk about the interest rate as if there is only one rate of interest. There are actually many nominal interest rates that are reported, based on: -Term to Maturity -Risk -Government Tax Incentives However, interest rates tend to move together.
How Is Income Distributed? Marginal Product of Capital
In the same way, the firm decides how much capital to rent by using the marginal product of capital (MPK). -The MPK is the amount of extra output the firm gets from an extra unit of capital, holding the amount of labor constant. -MPK=F(K+1, L)-F(K, L) -MPK diminishes as we use more capital. The increased profit from renting an additional machine is the extra revenue from selling the output of that machine minus the machine's rental price. ΔProfit= ΔRevenue- ΔCost =(PxMPK)-R To maximize profits, the firm rents more capital until the MPK falls to a level equal to the real rental price of capital. -MPK=R/P -The real rental price of capital is the rental price measured in units of goods and services rather than dollars.
Disposable Income
Income remaining after the payment of taxes. The income after the payment of all taxes, Y-T. Households divide their disposable income between consumption and saving.
What Determines Demand? Investment
Investment spending represents about 15% of total spending and includes: -Firms adding to the stock of capital. -Firms replacing capital that has depreciated. -Households purchasing houses. The quantity of goods and services demanded depends on the interest rate. -The interest reflects the cost of funds needed for investment. -For a project to be profitable, the rate of return on the project must be higher than the interest rate. -As interest rates rise, the number of projects that will be profitable decreases and investment falls. -This will be true whether the firm uses borrowed funds or its own funds for the project. When studying the decision to invest, we must distinguish between nominal interest rates and real interest rates. -The nominal rate of interest is the rate of interest investors pay to borrow money; the stated rate. -The real rate of interest is the nominal rate corrected for inflation; the true cost of borrowing. - Real Interest (r)=Nominal Interest (i)-Inflation (π) The investment function shows that investment spending depends on the real rate of interest. - I=I(r) - Investment is negatively related to the real rate of interest.
Chapter 3 Part 1 Slide 4
See Circular Flow Chart
What Determines Demand?
Recall that there are four components that make up the expenditures on goods and services. -Consumption (C) -Investment (I) -Government Purchases (G) -Net Exports (NX) For a closed economy the national income identity is: Y=C+I+G
How Is Income Distributed? Rule
Rule: A competitive, profit-maximizing firm demands each factor of production until that factor's marginal product falls to a level equal to its real factor price.
The Cobb-Douglas Function
The Cobb-Douglas production function is a good approximation of how economies convert capital and labor into output. -If the factors of production always earn their marginal product, the Cobb-Douglas function results in constant factor shares. -F(K, L)=AK^α L^(1-α) --Capital Income=MPK x K=αY --Labor Income=MPK x L=(1-α)Y Properties of the Cobb-Douglas Function -Constant Returns to Scale -MPL=(1-α)AK^α L^(-α)=(1-α)(Y/L) -MPK=αAK^(α-1) L^(1-α)=α(Y/K) What can change the marginal products? -An increase in K will increase the MPL, but reduce the MPK. -An increase in L will increase the MPK, but reduce the MPL. -An increase in technology (A) will increase both MPL and MPK. Notice another important result. -The MPL is proportional to the output per worker or the average labor productivity. -The MPK is proportional to the output per machine or the average capital productivity. Does α really determine how much income goes to labor and how much income goes to capital? -Labor Income=MPLxL=(1-α)Y, so (1-α) is labors' share of income. -Capital Income=MPKxK=αY, so α is capital's share of income. -The ratio of labors' share of income to capitals' share of income, (1-α)/α, is constant. --The amount of labor, capital, or the level of technology do not affect the factor shares of income. The share of income going to labor has remained very stable, but not constant. -Since the 1970s, the share of income going to labor has been slowly decreasing. -One explanation may be that changes in technology (A) may have altered the relative important of labor and capital in the production process; the value of α may have changed.
How Is Income Distributed? The Neoclassical Theory of Income Distribution
The Neoclassical Theory of Income Distribution: -Prices adjust to supply and demand. -The demand for each factor of production depends on the marginal productivity of that factor. -Each factor's share of national income will depend on the combination of these two ideas.
Marginal Propensity to Consume (MPC)
The amount by which consumption changes when disposable income increases by one dollar. The MPC is between zero and one: an extra dollar of income increases consumption, but by less than one dollar. Thus, if households obtain an extra dollar of income, they save a portion of it.
Marginal Product of Capital (MPK)
The amount of extra output produced when the capital input is increased by one unit. The marginal product of capital is the amount of extra output the firm gets from an extra unit of capital, holding the amount of labor constant: MPK=F(K+1, L)-F(K,L). Thus, the marginal product of capital is the difference between the amount of output produced with K+1 units of capital and that produced with only K units of capital. Like labor, capital is subject to diminishing marginal product.
Marginal Product of Labor (MPL)
The amount of extra output produced when the labor input is increased by one unit. The extra amount of output the firm gets from one extra unit of labor, holding the amount of capital fixed. We can express this using the production function: MPL=F(K, L+1)-F(K, L).
Factor Prices
The amount paid for one unit of a factor of production. In an economy where the two factors of production are capital and labor, the two factor prices are the wage workers earn and the rent the owners of capital collect.
How Is Income Distributed? Decision To Increase Labor
The decision to use another unit of labor requires a comparison of the extra revenue from the increased production with the extra cost of hiring the additional unit of labor. ΔProfit= ΔRevenue- ΔCost =(PxMPL)-W Assuming that there is a diminishing marginal product of labor, should the firm hire an additional unit of labor? -If PxMPL>W, profits will rise when one more unit of labor is hired. -If PxMPL<W, profits will fall when one more unit of labor is hired. -A profit maximizing firm will hire workers up to the point where PxMPL=W. Rewriting the last equation yields: MPL=W/P -W/P is known as the real wage. -The real wage is the payment to labor measured in units of output. -Therefore, *firms will hire workers up to the point where the MPL is equal to the real wage.* The MPL represents the demand for labor.
Profit
The income of firm owners; firm revenue minus firm costs. Profit equals revenue minus costs; is it what the owners of the firm keep after paying for the costs of production. Profit=Revenue-Labor Costs-Capital Costs Profit=PY-WL-RK Where revenue equals P × Y, the selling price of the good P multiplied by the amount of the good the firm produces Y. Costs include labor and capital costs. Labor costs equal W × L, the wage W times the amount of labor L. Capital costs equal R × K, the rental price of capital R times the amount of capital K. To see how profit depends on the factors of production, we use the production function Y=F(K, L) to substitute for Y to obtain: Profit=PF(K,L)-WL-RK.
What Establishes Equilibrium? Interest Rate
The interest rate must adjust to ensure that the demand for goods and services is equal to the supply. -If the interest rate is too high, supply will exceed demand. -If the interest rate is too low, demand will exceed supply. -At the equilibrium real rate of interest, the demand for goods and services will be equal to the supply. To see how this happens, we will examine the market for loanable funds. -National Saving (S)=private saving+public saving --Private saving=Y-T-C --Public saving=T-G - S=(Y-T-C)+(T-G)=Y-C-G -But, from the national income identity Y-C-G=I -Therefore, S=I What flows into the market for loanable funds must flow back out. Now, substitute the exogenous and endogenous variables into this equation. - S=Y-C(Y-T)-G=I(r) and - Sbar=Ybar-C(Ybar-Tbar)-Gbar=I(r) The supply of loanable funds is fixed, so the interest rate will have to adjust to balance the demand for loanable funds with the supply.
Interest Rate
The market price at which resources are transferred between the present and the future; the return to saving and the cost of borrowing. The interest rate measures the cost of the funds used to finance investment. For an investment project to be profitable, its return (the revenue from increased future production of goods and services) must exceed its cost (the payments for borrowed funds). If the interest rate rises, fewer investment projects are profitable, and the quantity of investment goods demanded falls.
Production Function
The mathematical relationship showing how the quantities of the factors of production determine the quantity of goods and services produced; for example, Y = F(K, L). This equation states that output is a function of the amount of capital and the amount of labor. The production function reflects the available technology for turning capital and labor into output. If someone invents a better way to produce a good, the result is more output from the same amounts of capital and labor. Thus, technological change alters the production function.
What Determines Demand? Endogenous Variables
The model has three endogenous variables; C, I, and r. -We want to understand how changes in an exogenous variable will effect the endogenous variables in our model.
Real Rental Price of Capital
The real rental price of capital is the rental price measured in units of goods rather than in dollars (R/P).
Crowding Out
The reduction in investment that results when expansionary fiscal policy raises the interest rate. Government purchases are said to crowd out investment. (Increasing government purchases, increases the interest rate, which decreases investment.)
Real Interest Rate
The return to saving and the cost of borrowing after adjustment for inflation. The nominal interest rate corrected for the effects of inflation. The real interest rate measures the true cost of borrowing and thus determines the quantity of investment. Equation relating investment (I) to the real interest rate (r): I=I(r)
Nominal Interest Rate
The return to saving and the cost of borrowing without adjustment for inflation. The rate of interest that investors pay to borrow money.
How Is Income Distributed? The Economy's Total Income
We can now explain how markets for the factors of production distribute the economy's total income. -If all firms in the economy are competitive and profit maximizing, then each factor of production is paid its marginal contribution to the production process. -WL=MPLxL is the total real wages paid to labor. -RK=MPKxK is the total real return paid to the owners of capital. -Any income remaining after the firms have paid the factors of production is the profit for the owners of the firm. --Economic Profit=Y-(MPLxL)-(MPKxK) If the production function has the property of constant returns to scale, the economic profit must be zero. -Euler's theorem says that when there are constant returns to scale: F(K, L)=(MPKxK)+(MPLxL). However, accounting profits will be greater than zero: -Accounting Profits=Economic Profit+(MPKxK). Total output is divided between the payments to capital and the payments to labor which, in turn, depend on their marginal productivity.
Closed Economy Circular Flow
We can use the circular flow model to begin thinking about the four questions being posed. An important point to note is that national saving is composed of both private saving and public saving: National Saving=Private Saving+Public Saving Private Saving=Y-C Public Saving=T-(G+Tr)
Conclusion
We have created a model of general equilibrium for the economy based on the classical assumption that prices will adjust to balance the supply and demand in the factor markets and the loanable funds market. This model will be a foundation for analysis as we move forward.
Income and Its Distribution
We have examined how income is generated and how it is distributed. Next we look at the demand for goods and services and how the two sides of the circular flow are balanced.
How Is Income Distributed? Maximizing Profits
We will further assume that each firm is a profit maximizer. Profit=Revenue-Cost =Revenue-Labor Cost-Capital Cost =PY-WL-RK =(P)(F(K, L))-WL-RK What quantities of labor and capital will maximize profits? -The marginal product of labor (MPL) is the extra output a firm gets from using one extra unit of labor holding the amount of capital fixed. -MPL=F(K, L+1)-F(K, L) -In most production functions, the MPL diminishes with each additional unit of labor used. The slope of the production function equals the marginal product of labor. As more labor is added, the marginal product of labor declines.
What Establishes Equilibrium?
What guarantees that the sum of consumption, investment, and government purchases will be equal to the amount produced? -In the classical model, the interest rate has the key role in balancing the supply and demand. -The interest rate effects the supply and demand for goods and services. -As the same time, the interest rate also effects the supply and demand for loanable funds. Our model can be summarized as follows: Y=C+I+G C=C(Y-T) I=I(r) G=Gbar T=Tbar Y=Y(Kbar, Lbar)=Ybar Substituting exogenous variables into the national income identity: Ybar=C(Ybar-Tbar)+I(r)+Gbar Notice that r is the only variable not predetermined in this equation.
