The material in this chapter is the basis of much of the remaining material in this book. So, the time your students spend mastering this material will pay dividends throughout the semester. New to the 6 th edition, the appendix on the Cobb-Douglas production function is now integrated into the chapter – and into this PowerPoint presentation. Also, if you used the previous edition of these PowerPoints, you will find that I have cleaned up and expanded the returns to scale section and the optional last section on the loanable funds model with an upward-sloping saving curve. As a result of these changes, this PowerPoint presentation is longer. I suggest you look through it before presenting it in class to determine whether there’s any material you might want to cut out or shorten.
It’s useful for students to keep in mind the “big picture” as they learn the individual components of the model in the following slides.
Again, emphasize that “F(Kbar,Lbar)” means we are evaluating the function at a particular combination of capital and labor. The resulting value of output is called “Ybar”.
Recall from chapter 2: the value of output equals the value of income. The income is paid to the workers, capital owners, land owners, and so forth. We now explore a simple theory of income distribution.
It might be worthwhile to refresh students’ memory about nominal and real variables. The nominal wage & rental rate are measured in currency units. The real wage is measured in units of output. To see this, suppose W = $10/hour and P = $2 per unit of output. Then, W/P = ($10/hour) / ($2/unit of output) = 5 units of output per hour of work. It’s true, the firm is paying the workers in money units, not in units of output. But, the real wage is the purchasing power of the wage - the amount of stuff that workers can buy with their wage.
Since the distribution of income depends on factor prices, we need to see how factor prices are determined. Each factor’s price is determined by supply and demand in a market for that factor. For instance, supply and demand for labor determine the wage.
(Figure 3-3 on p.51) It’s straightforward to see that the MPL = the prod function’s slope: The definition of the slope of a curve is the amount the curve rises when you move one unit to the right. On this graph, moving one unit to the right simply means using one additional unit of labor. The amount the curve rises is the amount by which output increases: the MPL.
Tell class: Many production functions have this property. This slide introduces some short-hand notation that will appear throughout the PowerPoint presentations of the remaining chapters : The up and down arrows mean increase and decrease, respectively. The symbol “ ” means “causes” or “leads to.” Hence, the text after “Intuition” should be read as follows: “ An increase in labor while holding capital fixed causes there to be fewer machines per worker, which causes lower productivity.” Many instructors use this type of short-hand (or something very similar), and it’s much easier and quicker for students to write down in their notes.
It’s easy to see that the MPL curve is the firm’s L demand curve. Let L* be the value of L such that MPL = W/P. Suppose L < L*. Then, benefit of hiring one more worker (MPL) exceeds cost (W/P), so firm can increase profits by hiring one more worker. Instead, suppose L > L*. Then, the benefit of the last worker hired (MPL) is less than the cost (W/P), so firm should reduce labor to increase its profits. When L = L*, then firm cannot increase its profits either by raising or lowering L. Hence, firm hires L to the point where MPL = W/P. This establishes that the MPL curve is the firm’s labor demand curve.
The labor supply curve is vertical: We are assuming that the economy has a fixed quantity of labor, Lbar, regardless of whether the real wage is high or low. Combining this labor supply curve with the demand curve we’ve developed in previous slides shows how the real wage is determined.
In our model, it’s easiest to think of firms renting capital from households (the owners of all factors of production). R/P is the real cost of renting a unit of K for one period of time. In the real world, of course, many firms own some of their capital. But, for such a firm, the market rental rate is the opportunity cost of using its own capital instead of renting it to another firm. Hence, R/P is the relevant “price” in firms’ capital demand decisions, whether firms own their capital or rent it.
The previous slide used the same logic behind the labor demand curve to assert that the capital demand curve is the same as the downward-sloping MPK curve. The supply of capital is fixed (by assumption), so the supply curve is vertical. The real rental rate (R/P) is determined by the intersection of the two curves.
When I teach this theory, after saying “accepted by most economists” I append “at least, as a starting point.” This theory is fine for macro models with only one type of labor. But taken literally, it implies that people who earn low wages have low marginal products. Thus, this theory would attribute the entire observed wage gap between white males and minorities to productivity differences, a conclusion that most would find objectionable.
The last equation follows from Euler’s theorem, discussed in text on p. 54.
These formulas can be derived with basic calculus and algebra.
We’ve now completed the supply side of the model.
“ g & s” is short for “goods & services”
Again, we are using the short-hand notation that will appear throughout the remaining PowerPoints: X Y means “an increase in X causes a decrease in Y.” Please feel free to edit slides if you wish to substitute other notation.
It might be useful to remind students of the meaning of the terms “exogenous” and “transfer payments.”
Note the only variable in the equilibrium condition that doesn’t have a “bar” over it is the real interest rate. When the full slide is showing, before you advance to the next one, you might want to note that the interest rate is important in financial markets as well, so we will next develop a simple model of the financial system.
After showing definition of private saving, - give the interpretation of the equation: private saving is disposable income minus consumption spending - explain why private saving is part of the supply of loanable funds: Suppose a person earns $50,000/year, pays $10,000 in taxes, and spends $35,000 on goods and services. There’s $5000 remaining. What happens to that $5000? The person might use it to buy stocks or bonds, or she might put it in her savings account or money market deposit account. In all of these cases, this $5000 becomes part of the supply of loanable funds in the financial system. After displaying public saving, explain the equation’s interpretation: public saving is tax revenue minus government spending. Notice the analogy to private saving – both concepts represent income less spending: for the private household, income is ( Y - T ) and spending is C . For the government, income is T and spending is G .
At the end of this chapter, we will briefly consider how things would be different if Consumption (and therefore Saving) were allowed to depend on the interest rate. For now, though, they do not.
This slide establishes that we can use the loanable funds supply/demand diagram to see how the interest rate that clears the goods market is determined. Explain that the symbol means each one implies the other. The thing on the left implies the thing on the right, and vice versa. More short-hand: “eq’m” is short for “equilibrium” and “LF” for “loanable funds.”
Suggestion: Display these questions and give your students 3-4 minutes, working in pairs, to try to find the answers. Then display the analysis on the next slide.
Week 2a nat income, money & inflation
Week-21. National Income: Where it Comes From and Where it Goes2. Money and Inflation
National Income: Where it Comes Fromand Where it GoesIn this meeting, we will discuss… what determines the economy’s total output/income how the prices of the factors of production are determined how total income is distributed what determines the demand for goods and services how equilibrium in the goods market is achieved
Outline of model A closed economy, market-clearing model Supply side factor markets (supply, demand, price) determination of output/income Demand side determinants of C , I , and G Equilibrium goods market loanable funds market
Production Function: Example Y = Kα L1-α This often-used production function is called the Cobb-Douglas production function. α is any positive fraction. For example, α = 0.3. Y = K0.3 L0.7 If K and L are known, then Y can be calculated.
The distribution of nationalincome determined by factor prices, which are the prices per unit that firms pay for the factors of production wage = price of L rental rate = price of K
Notation W = nominal wage of labor W = nominal wage of labor R = nominal rental rate of capital R = nominal rental rate of capital P = price of output (Y) P = price of output (Y) W /P= real wage (measured in units of output) W /P= real wage (measured in units of output) R /P= real rental rate R /P= real rental rate
How factor prices are determined Factor prices are determined by supply and demand in factor markets. Recall: Supply of each factor is fixed. What about demand?
Demand for labor Assume markets are competitive: each firm takes W, R, and P as given. Basic idea: A firm hires each unit of labor if the cost does not exceed the benefit. cost = real wage benefit = marginal product of labor
Marginal product of labor (MPL ) definition: The extra output the firm can produce using an additional unit of labor (holding other inputs fixed): MPL = F (K, L +1) – F (K, L)
Marginal Product of Labor MPL = F (K, L +1) – F (K, L) For the Cobb-Douglas production function F (K, L) = Kα L1- α, it can be shown that: MPL = (1- α) Kα L- α. Once again, if α, K and L are known, then MPL can be calculated.
MPL and the production function Youtput F (K , L ) MP 1 L As more labor is MP added, MPL ↓ 1 L MP Slope of the production L function equals MPL 1 L labor
Diminishing marginal returns As a factor input is increased, its marginal product falls (other things equal). Intuition: Suppose ↑L while holding K fixed ⇒ fewer machines per worker ⇒ lower worker productivity
MPL and the demand for labor Units of output Each firm hires labor Each firm hires labor up to the point where up to the point where MPL = W/P. MPL = W/P. Real wage MPL, Labor demand Units of labor, L Quantity of labor demanded
The equilibrium real wage Units of Labor output supply The real wage The real wage adjusts to equate adjusts to equate labor demand with labor demand with supply. supply.equilibriumreal wage MPL, Labor demand L Units of labor, L
Calculating the Real Wage We saw earlier, that if the production function is known, and if K and L are known, then MPL can be calculated. As W/P = MPL, the real wage can also be calculated. The total real income of labor is W/P × L, this can also be calculated.
Determining the rental rateWe have just seen that MPL = W/P.The same logic shows that MPK = R/P : diminishing returns to capital: MPK ↓ as K↑ The MPK curve is the firm’s demand curve for renting capital. Firms maximize profits by choosing K such that MPK = R/P .
The equilibrium real rental rate Units of output Supply of The real rental rate capital The real rental rate adjusts to equate adjusts to equate demand for capital demand for capital with supply. with supply.equilibrium R/P MPK, demand for capital K Units of capital, K
Calculating the Real Rental If the production function is known, and if K and L are known, then MPK can be calculated. As R/P = MPK, the real rental rate can also be calculated. As the total real income of capital is R/P × K, this can also be calculated.
The Neoclassical Theoryof Distribution Our theory of the distribution of total income between labor and capital is called the neoclassical theory of distribution It states that each factor input is paid its marginal product
How income is distributed: Wtotal labor income = L = MPL × L P Rtotal capital income = K = MPK × K PIf production function has constant returns to scale, then Y = MPL × L + MPK × K national labor capital income income income
The Cobb-Douglas ProductionFunction The Cobb-Douglas production function has constant factor shares: α = capital’s share of total income: capital income = MPK x K = α Y labor income = MPL x L = (1 – α )Y The Cobb-Douglas production function is: Y = AK α L1−α where A represents the level of technology.
The Cobb-Douglas ProductionFunction Each factor’s marginal product is proportional to its average product: α −1 1−α αY MPK = α AK L = K α −α (1 − α )Y MPL = (1 − α ) AK L = L
Outline of model A closed economy, market-clearing model Supply sideDONE factor markets (supply, demand, price) DONE determination of output/incomeNext Demand side determinants of C , I , and G Equilibrium goods market loanable funds market
Demand for goods & servicesComponents of aggregate demand: C = consumer demand for g & s I = demand for investment g & s G = government demand for g & s (closed economy: no NX )
Consumption, C def: Disposable income is total income minus total taxes: Y – T. Consumption function: C = C (Y – T ) Shows that ↑(Y – T ) ⇒ ↑C def: Marginal propensity to consume (MPC) is the increase in C caused by a one-unit increase in disposable income.
Consumption Function: Example Assume C (Y – T ) = 10 + 0.8 × (Y – T ) We saw earlier that if K, L, and the production function are known, then Y can be calculated. Therefore, If T, which is an exogenous variable, is known and if the consumption function is known, then C can be calculated.
Consumption Function: Example C (Y – T ) = 10 + 0.8 × (Y – T ) Marginal Propensity to Consume = 0.8 ↑Y ⇒ ↑C ↓T ⇒ ↑C All other factors that can boost C are hidden in the number 10. When there is such a boost, 10 will increase to, say, 12.
Figure 3-6: The consumptionfunction C C (Y –T ) The slope of the MPC consumption function 1 is the MPC. Y–T
Investment, IThe investment function is I = I (r ), where r denotes the real interest rate, the nominal interest rate corrected for inflation.The real interest rate is the cost of borrowing the opportunity cost of using one’s own funds to finance investment spending. So, ↑ r ⇒ ↓ I
Investment I = 100 – 8 × r is a simple investment function. Note that ↑r ⇒ ↓I All other factors that can boost I are hidden in the number 100. When there is such a boost, 100 will increase to, say, 120.
The investment function r Spending on investment goods depends negatively on the real interest rate. I (r ) I
Government spending, G G = government spending on goods and services. G excludes transfer payments (e.g., social security benefits, unemployment insurance benefits). Assume government spending and total taxes are exogenous: G =G and T =T
The market for goods & services Aggregate demand: C (Y − T ) + I (r ) + G Aggregate supply: Y = F (K , L ) Equilibrium: Y = C (Y − T ) + I (r ) + G The real interest rate adjusts to equate demand with supply.
The loanable funds market A simple supply-demand model of the financial system. One asset: “loanable funds” demand for funds: investment supply of funds: saving “price” of funds: real interest rate
Demand for funds: InvestmentThe demand for loanable funds… comes from investment: Firms borrow to finance spending on plant & equipment, new office buildings, etc. Consumers borrow to buy new houses. depends negatively on r, the “price” of loanable funds (cost of borrowing).
Loanable funds demand curve r The investment The investment curve is also the curve is also the demand curve for demand curve for loanable funds. loanable funds. I (r ) I
Supply of funds: Saving The supply of loanable funds comes from saving: Households use their saving to make bank deposits, purchase bonds and other assets. These funds become available to firms to borrow to finance investment spending. The government may also contribute to saving if it does not spend all the tax revenue it receives.
Types of savingprivate saving = (Y – T ) – Cpublic saving = T – Gnational saving, S = private saving + public saving = (Y –T ) – C + T–G = Y – C – G
Saving If K, L, and the production function are known, then Y can be calculated. If T and the consumption function are also known, then C can be calculated. Finally, if G, which is exogenous, is known, then S = Y – C – G can be calculated.
Loanable funds supply curve r S = Y − C (Y −T ) − GNational savingNational savingdoes notdoes notdepend on r,depend on r,so the supplyso the supplycurve is vertical.curve is vertical. S, I
Loanable funds market equilibrium r S = Y − C (Y −T ) − GEquilibrium realinterest rate I (r ) Equilibrium level S, I of investment
Equilibrium in the Loanable FundsMarket Recall: Equilibrium in the goods market requires Y = C + I + G . Therefore, Y – C – G = I. Therefore, S = I. This condition determines the real interest rate.
Investment and Interest Rate We saw earlier how S can be calculated. S = I means that investment can be calculated. If, further, the investment function is known to be, say, I = 100 – 8 × r, then I = 100 – 8 × r can be used to calculate r.
The special role of rr adjusts to equilibrate the goods market and the r adjusts to equilibrate the goods market and theloanable funds market simultaneously: loanable funds market simultaneously: If L.F. market is in equilibrium, then If L.F. market is in equilibrium, then Y – C – G = II Y –C –G = Add (C +G ) to both sides to get Add (C +G ) to both sides to get Y = C + II + G (goods market eq’m) Y = C + + G (goods market eq’m)Thus,Thus, Eq’m in Loanable ⇔ Eq’m in goods market Funds market
Effects of deficit Gov. Budget increases in defense spending: ∆G > 0 big tax cuts: ∆T < 0 Both policies reduce national saving: S = Y − C (Y − T ) − G ↑G ⇒ ↓ S ↓T ⇒ ↑ C ⇒ ↓ S
Effects of deficit Gov. Budget r S2 S11. The increase in1. The increase in the deficit the deficit reduces saving… reduces saving… r22. …which causes2. …which causes the real interest the real interest r1 rate to rise… rate to rise…3. …which reduces3. …which reduces the level of the level of I (r ) investment. investment. I2 I1 S, I
An increase in investmentdemand r S …raises the interest rate. An increase r2 in desired investment… r1 I2But the equilibrium I1level of investmentcannot increasebecause thesupply of loanable S, Ifunds is fixed.
A Jump in Consumption If there is a boom in real- estate prices or in the stock market, people feel C wealthier. They feel a CA reduced need to save. Therefore, CB There is a jump in consumption How will this affect the Y–T market for loanable funds?
Saving and the interest rate Why might saving depend on r ? How would the results of an increase in investment demand be different? Would r rise as much? Would the equilibrium value of I change?
An increase in investment demandwhen saving depends on r r S (r )An increase in An increase ininvestment investmentdemand raises r, demand raises r,which induces an which induces an r2increase in the increase in thequantity of saving, quantity of saving, r1which allows II which allowsto increase. to increase. I(r)2 I(r) I1 I2 S, I