Topic4-Production_AAP_BW - The Production &...

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Unformatted text preview: The Production & Distribution of National Income The Production Function, Productivity, Marginal Products of Capital & Labor, Household Demand, Equilibrium, Growth Accounting. Topic 4 (Text: 3.1, 3.2, 4.2, 4.3) 1 Key Concepts • A macro description of production Combine Capital, labor Combine Capital labor A lot of reality is subsumed in this lot Productivity tells you how well K and L work together Productivity • How decisions to rent capital & labor are made (MPK & MPL & how they turn into “demand”) MPL demand” • The demand for investment & the supply of savings • Equilibrium analysis & “shifts” shifts” • Growth accounting 9 The Production Function The economy’s productive capacity is the economy’ most fundamental determinant of economic well-being well• The production function is a mathematical description of the economy’s productive economy’ capacity 10 1 1 The Production Function (cnt.) cnt.) • A production function relates the amount of output that can be produced to the amount of inputs and the level of productivity General form: Y = A F(K, L) • The inputs are called factors of production. factors e.g. Capital, Labor, possibly Land, Human Capital, & Organization • A commonly used specification of the production function is the Cobb-Douglas Cobb(C-D) function (C11 The Production Function (cnt.) cnt.) • Example of a C-D production function: CY = A K0.3L0.7 K ↑ by 1% L ↑ by 1% Y ↑ by 0.3% (ceteris paribus) Y ↑ by 0.7% (ceteris paribus) • If doubling all inputs doubles output, the all production function is said to exhibit constant constant returns to scale (CRS) If output less than doubles, decreasing returns If decreasing If it more than doubles, increasing returns If increasing • The C-D function exhibits constant returns to Cconstant scale but decreasing returns to each factor decreasing 12 The Production Function (cnt.) cnt.) • K, L, and Y can be in any convenient units, A will have the right units to connect the three • L can be raw labor hours, especially if A includes labor quality, or • L can be effective labor hours, adjusted for labor quality / human capital If K, L, and A are fixed, Y is determined If is Y = A K0.3L0.7 13 2 2 Productivity • “A” in the production function is called the productivity or technology of the economy • Higher productivity means that the same K and L can produce more Y • It is common to take K and L as raw quantities and include quality in A quality • Changes in A are called productivity or productivity supply shocks supply 14 Productivity (cnt.) cnt.) • We are concerned with how A varies over time for a specific country, and over across countries at a given point in time across • Increases in A over the long run are related to economic growth • Short run variations in A (productivity shocks) are related to business cycles 15 Productivity (cnt.) cnt.) U.S. TF Productivity Growth 49 - 59 = 1.76% 60 - 69 = 2.03% 70 - 79 = 0.37% 80 - 89 = 0.99% 90 - 99 = 1.45% 00 - 05 = 0.92% 6.0% 4.0% 2.0% 0.0% 19 -2.0% 49 19 53 19 57 19 61 19 65 19 69 19 73 19 77 19 81 19 85 19 89 19 93 19 97 20 01 20 05 -4.0% 17 3 3 Productivity (concl.) concl.) • “What determines productivity growth?” is critical to economic development and prosperity We’ll return to this issue We’ 18 Marginal Products of Capital & Labor • So far we learned what makes production happen • The next step is to understand how factor inputs are paid i.e., what do K and L receive, or i.e., what do K and L cost? what And WHY? And 19 Marginal Products of Capital & Labor • We are led to the concept of marginal product MPs will give us the demand for factor inputs MP demand MPL↓ with L (diminishing marginal product), and ↑ MPL with K and A MPK↓ with K (diminishing marginal product), and MPK ↑ with L and A 20 4 4 Marginal Product of Labor • The marginal product of labor (MPL) is the extra amount of output which can be extra produced with an extra unit of labor extra MPL = ΔY/ΔL = slope of the production MPL function in the direction of L A, K are fixed In the C-D production function In Cα ⎛K⎞ MPL = (1 − α ) A⎜ ⎟ ⎝L⎠ 21 Marginal Product of Capital • The marginal product of capital (MPK) is the extra amount of output which can be extra produced with an extra unit of capital extra MPK = ΔY/ΔK = slope of the production MPK function in the direction of K A, L are fixed In the C-D production function In C1−α ⎛L⎞ MPK = αA⎜ ⎟ ⎝K⎠ 22 Factor Employment Decision • Assume the typical firm that produces the economy’s output is competitive economy’ competitive • It takes the prices of its output (P) and price of its 2 inputs as given W is the wage rate R is the rental rate of capital • Individual firms’ actions do not affect prices firms’ 23 5 5 Optimal Labor Employed The firm maximizes profits (revenue - costs): Π = PY - WL – RK = P F(K,L) - WL – RK PY • How can the firm maximize profits? • The rule is very simple: • Hire labor as long as: MPL ≥ W/P (the real rental rate of labor) MPL labor) i.e. as your profits increase after you pay the real wage 24 Labor Demand Y MPL --K Fixed 2.5 2.0 K is fixed 1.5 Given Wages 1.0 0.5 0.0 0 5 10 15 20 25 L 25 Maximizing Behavior Profits MPL > W/P Profits ⇑ as L ⇑ MPL < W/P Profits ⇓ as L ⇑ Max Profits K is fixed A is fixed L Profit-Maximizing L 26 6 6 Optimal Capital Employed The firm maximizes profits (revenue - costs): Π = PY - WL – RK = P F(K,L) - WL – RK PY • How can the firm maximize profits? • The rule is very simple: • Hire Capital as long as: MPK ≥ R/P (the real rental rate of capital) MPK capital) i.e. as your profits increase after you pay the real rental rate 27 Optimization (cnt.) cnt.) • How much of each factor does the firm hire? Π = PY - WL – RK = P F(K,L) - WL – RK PY To find optimal amount of L: To ΔΠ = P ΔY - W ΔL = 0 ΔY/ΔL = W/P = MPL MPL To find optimal amount of K: To ΔΠ = P ΔY - R ΔK = 0 ΔY/ΔK = R/P = MPK MPK 29 Labor Demand (cnt.) cnt.) • W/P is called the real wage since it real measures the amount of output the wage can purchase, rather than $s • Since the firm hires up to the point where MPL equals the real wage, the MPL MPL the schedule is the firm’s labor demand curve firm’ or demand schedule or demand 30 7 7 Labor Demand (cnt.) cnt.) • Two critical assumptions allow us to call it the firm’s demand for labor: firm’ The firm is a price-taker in the product and The pricefactor markets The firm maximizes profits The 31 Capital Demand • Follow the same logic for capital to get the firm’s demand for capital: firm’ Firm rents capital to the point where Firm MPK = R/P, the real rental price of capital MPK real This is not the cost of buying capital! This not MPK schedule is the firm’s capital demand MPK firm’ • Real rental price of unit of capital = Interest rate + Depreciation rate 32 Capital Demand • The macro model we are using has one good and therefore one price • If there are more goods (as in real life), then the real rental price also includes the price real appreciation of the capital • Real rental price of unit of capital (R/P) = (R/P Interest rate + Depreciation rate – Capital Gains Think of housing Think 33 8 8 Capital Demand Y MPK --L Fixed 4.0 3.5 3.0 L is fixed 2.5 2.0 CoC 1.5 1.0 0.5 0.0 0 5 10 15 20 25 K 34 Marginal Products Again • Economic Π/P = Y – (W/P)* L - (R/P) * K, All quantities are “real” here All real” In a competitive equilibrium In • Economic Π/P = Y - (MPL * L) - (MPK * K), or Y = (MPL * L) + (MPK * K) + Π/P Payments to labor + Payments to capital + Economic profit • For CRS production functions, Euler’s theorem Euler’ implies: • Y = F(K,L) = (MPK * K) + (MPL * L), which in F( turn implies, Economic profit = 0 Economic 35 Come Again! Zero Profits? • If so, how to explain “profits” that we see profits” all around? • With CRS, payments to factor inputs exhaust output This condition is just saying that all the output This all is paid to the factors that produce it Firm’s “profits” are returns to equity Firm’ profits” Entrepreneurial profit? Entrepreneurial 36 9 9 Example #1 • ACME has the following production function: No. of No. of Widgets MPL $MPL Workers Produced 2 15 3 21 4 26 5 30 • What is the MPL for each level of employment? MPL • If ACME gets $5/widget, how many workers will it hire at $27/worker? 37 Example #2 • Below is GDP, K, L (N), for the US economy GDP Year 1960 1970 1980 1990 Y 2,263 3,398 4,615 6,136 K 2,390 3,525 5,032 6,650 N 65.8 78.7 99.3 118.8 • Assume the Prod. Function is Y = AK0.3L0.7 AK • By what % did the U.S. TFP grow in each decade? 39 Markets • To figure out the equilibrium we need to study The demand The The supply The And find out at what point they are equal • Prices are determined by the requirement that “markets clear” i.e., Demand = Supply i.e., 48 10 10 Markets (cnt.) cnt.) • In this economy there are markets for goods, goods labor, and capital labor capital We’ll show that all the key economic We’ quantities are determined! 49 Markets (cnt.) cnt.) EQUILIBRIUM: • Labor market equilibrium determines wage rate and quantity of labor employed Labor Demanded = Labor Supplied Labor • Capital market equilibrium determines rental rate and quantity of capital and investment Investment = Savings Investment • Goods market equilibrium ensures Goods Produced = Goods Demanded Goods If 2 markets are in equilibrium the 3rd is as well! If 50 Markets (cnt.) cnt.) Labor Markets: • Labor demand is the MPL MPL • Any upward-sloping supply for labor will upwardresult in an equilibrium wage 51 11 11 Markets (cnt.) cnt.) Capital Markets: • How are the equilibrium capital stock and investment determined? The MPK function determines the amount of The MPK desired capital, given the real rental rate R/P desired To achieve their desired capital stock, firms To have to invest 52 Demand For Investment • Firm’s desired capital level is given by the real Firm’ rental price (R/P) and MPK MPK • To get to the desired K, K, the firm invests the Desired I = K + Depreciation – K0 Depreciation (Desired) (Current) where Depreciation = δ K0 K0 is Current K δ is the depreciation rate rate 53 Demand For Investment (cnt.) cnt.) • I is the gross addition to K in each period • The investment vs. interest rate curve (MPK) is downward sloping Recall Recall R/P = r + δ A higher real interest rate increases the user cost higher of capital and thus reduces desired investment Desired I = (Desired) K + δ K0 – K0 > 0 Since K decreases as R/P increases, Since I does the same thing 54 12 12 Figure 4.6 Gross and net investment, 192919292005 55 Supply of Savings • Think about the right hand components of the income-expenditure identity: incomeY = C + I + G + NX NX Assume closed economy initially, so NX = 0 Assume NX Also assume that govt. purchases are Also exogenously given at G, instead of modeling the political process • By definition, Households consume and firms invest Households 56 Supply of Savings (cnt.) cnt.) • Household’s decision to consume is based Household’ on its income and the interest rate Savings = Income - Consumption The consumption and savings decisions are two The sides of the same coin • For now assume that savings are either fixed or ↑ with the interest rate (holding Y constant) Theory of the consumption-savings decision Theory consumptionwill come later Supply of Savings is upward sloping Supply 57 13 13 Equilibrium • The capital market clearing condition is: Sd = Id desired savings = desired investment • The real interest rate adjusts until desired savings equal desired investment The equilibrium real interest rate is where the The Savings and Investment curves intersect Savings Investment 58 Equilibrium (cnt.) cnt.) • Important insight on “equilibrium”: equilibrium” From an individual firm’s point of view, From firm’ prices are given, the firm determines its demand (partial equilibrium) From the economy-wide point of view, From economythe confrontation of the sum of the demands with the sum of the supplies determines prices (general equilibrium) 59 Equilibrium (cnt.) cnt.) • Demand for output in the economy depends on the: 1. Consumption-saving decision of the Consumptionhouseholds, 2. Investment decision of the firms, and 3. Purchases of the government • These demands jointly determine the equilibrium Wages, rental rate, output Wages, 60 14 14 Equilibrium Analysis • A typical definition of equilibrium is: Households maximize utility Households lies behind consumption-savings decision lies consumptiondetermines saving and labor supplied determines Firms maximize profits Firms determines demand for labor and capital, and determines therefore investment Prices adjust such that all markets clear Prices supply = demand in all markets supply “prices” means wages & interest rates prices” 61 How to Ask Questions: a Function “Shift” Shift” • All demand and supply functions are multidimensional or multivariate More than one argument More Univariate y = f (x1) Univariate Multivariate y = f (x1, x2, x3, … xn) Multivariate • A 2-dimensional graph shows the relation of 2y to xi • When xj changes, it is represented as a “shift” shift” 62 Shifts in the Equilibrium • Some factors that shift the savings curve: Changes in G (e.g. increases during wars) Changes A decrease in taxes decrease • Some factors that shift the investment curve: Technological innovation that increases MPK Technological MPK Investment tax credit Investment • In the next few classes, we will delve deeper into how labor supply, consumption-saving, consumptionand investment decisions are made 63 15 15 Growth Accounting • Very often productivity is discussed in terms of growth rates rather than levels • We first need to understand the mechanics of productivity growth; that is, how it is calculated We’ll see this again when we study economic growth We’ • Consider the C-D production function: CY = A K0.3L0.7 • Relation between output growth rate and input & productivity growth rates is: ΔY/Y = ΔA/A + 0.3(ΔK/K) + 0.7(ΔL/L) Gr(Y) means the same thing 65 Growth Accounting (cnt.) cnt.) ΔY/Y = ΔA/A + 0.3(ΔK/K) + 0.7(ΔL/L) or gY = gA + 0.3gK + 0.7gL • This is the growth accounting equation growth • Its purpose is to separate The output growth due to the accumulation of The inputs, and The output growth due to productivity increases The 66 Growth Accounting (cnt.) cnt.) ΔA/A = ΔY/Y - 0.3 (ΔK/K) - 0.7 (ΔL/L) • How is it used? • ΔA/A is the Total Factor Productivity (TFP) growth rate • We have estimates of the growth rates of Y, K, and L We back out an estimate of TFP growth We back 67 16 16 Growth Accounting (cnt.) cnt.) • Another concept is Labor Productivity: AL = Y/L • Therefore, ΔAL/AL = ΔY/Y - ΔL/L ≡ G(AL) This is different from TFP, because it lumps This together increases that come from capital capital and those that come from TFP TFP 68 Growth Accounting in United States (percent per year) 1929-1948 1948-1973 1973-1982 1929-1982 Source of growth labor growth 1.42 1.40 1.13 1.34 capital growth 0.11 0.77 0.69 0.56 total input growth 1.53 2.17 1.82 1.90 productivity growth 1.01 1.53 0.27 1.02 total output growth 2.54 3.70 1.55 2.92 70 Growth of Output and Productivity Around 1973 (percent per year) output growth productivity growth 1960-1973 1973-1990 1960-1973 1973-1990 United States 4.0 2.5 1.6 Japan 10.0 4.0 5.9 0.0 1.8 Europe 4.9 2.3 3.2 1.3 OECD 5.3 2.7 2.8 0.7 71 17 17 Example #4 • The observed growth rates in the economy are: Y = 8.2%, K = 10%, L = 1% 1. What is the growth rate of TFP? 2. What is the growth rate of AL? 72 Glossary of Terms Y A K L P W, W/P R, R/P δ Π MPK MPL C, I, G, NX NX Total output (connect to GDP) GDP Economy-wide productivity (technology) EconomyPhysical capital Labor Output price (general price level) Wage rate (nominal & real) Capital rental rate (nominal & real) Depreciation rate Profits Marginal product of capital Marginal product of labor As in topic 3 (superscript d stands for desired) 74 THE END 75 18 18 ...
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This note was uploaded on 03/02/2010 for the course BUAD 350 taught by Professor Safarzadeh during the Spring '07 term at USC.

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