Productivity, Output, and Employment. Chapter 3. Copyright 2009 Pearson Education Canada

This Chapter We will now shift from economic measurement to economic analysis In this lecture we will discuss: Production Functions Demand for Labour Introduce Labour Supply Goal: To build a macroeconomic model, that is a general framework to study economic questions from an aggregate perspective. Ch. 3 (Labour Market), Ch. 4 (Goods Market), Ch. 7 (Asset Market) and Ch. 9 puts it all together (IS-LM framework) 1-2

The Production Function How do we describe production in the economy? Factors of production are inputs to the production o process. We will be concerned with three: capital (K) (factories, machines); labour (N) (workers); technology and management. Copyright 2009 Pearson Education Canada 3-3

The Production Function (continued) The effectiveness with which K and N are used may be summarized by a production function A production o function is sa mathematical expression relating the amount of output produced d to quantities of capital and labour utilized. Copyright 2009 Pearson Education Canada 3-4

The Production Function (continued) In its general form, it looks like this: Y = AF(K,N) Y is real output produced A is a number measuring overall productivity K is the quantity of capital used (capital stock) N is the number of workers employed F is a function relating Y to K and N; it tells us how changes in K and N change Y,, for a given value of A Copyright 2009 Pearson Education Canada 3-5

A Very Simple Economy This classroom We have capital: the laptop, MC Hall, and the projector. We have labour: me If we combine the inputs we get the output (from 1pm-4pm): a lecture We can generalize this idea to the whole economy to get Y = A F(K,N) Copyright 2009 Pearson Education Canada 3-6

The Production function (continued) Y = AF(K,N) = AK 1 α This is perhaps the most well-known and well-used (Cobb-Douglas). α N β = AK The exponents (α and β) represent shares in income Because their values are less than unity, we get diminishing returns to factors. F tells us how changes in K and N change Y,, for a given value of A Copyright 2009 Pearson Education Canada 3-7 α N

The Production function (continued) In the real world, there are returns to scale (RS) which can be increasing (IRS), decreasing (DRS), or constant (CRS). We will focus on CRS, i.e. β=1-α, with 0<α<1. This means an increase of an equal percentage in all factors of production causes an increase in output of the same percentage: zy = F(zK, zn) for any z>0. Copyright 2009 Pearson Education Canada 3-8

The Production Function (continued) Total factor productivity (A) is a measure of overall effectiveness with which capital and labour are used. A can be anything else that affects Y An improvement in production technology or just using existing factors more efficiently, allows capital and labour to be utilized more effectively. If A goes up by 10%, Y goes up 10%, for given K, N Copyright 2009 Pearson Education Canada 3-9

The Shape of the Production Function Show it by fixing i two of (A,K,N) KN) and letting the remaining term vary Two properties: Production function slopes upward from left to right, F >0 As K increases, more output can be produced Slope of the production function becomes flatter from left to right, F <0 More K means more Y, but at a decreasing rate Copyright 2009 Pearson Education Canada 3-10

The Marginal Product of Capital The Marginal Product of Capital (MPK) is the increase in output produced resulting from a one-unit increase in the capital stock (other factors held constant). Properties: MPK is positive MPK declines as K increases (i.e. diminishing marginal productivity) Copyright 2009 Pearson Education Canada 3-11

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The Marginal Product of Capital (continued) The MPK equals the slope of the line tangent to the production function at a given point: MPK = ΔY ΔK In calculus, it is the first derivative of Y with respect to (wrt) to K: MPK = dy dk = αak (α-1) N (1-α) > 0 Copyright 2009 Pearson Education Canada 3-13

The Marginal Product of Labour We can apply the same concept to N The Marginal Product of Labour (MPN) is the increase in output produced by each additional unit of labour: MPN = ΔY ΔN It is also a first derivative, of Y wrt N: MPN = dy dn = (1-α)AK α N (-α) > 0 MPN exhibits similar properties as MPK Copyright 2009 Pearson Education Canada 3-14

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Supply Shocks to the Production Function A supply shock (productivity it shock) is a change in an economy s production function and is represented by a change in A. A positive (beneficial) shock (e.g. new technology, innovation) raises the amount of output which h can be produced d with each K-N combination. Positive shocks shift the production function upward. A negative (adverse) shock (e.g. drought, oil price hike) lowers the amount of output which can be produced with each K-N combination. Negative shocks shift the production function downward Copyright 2009 Pearson Education Canada 3-16

What determines the demand for inputs? The two most important are K and N The capital stock is slow to change because it is built up over years and is long lived, so we treat it as fixed in the short run This allows us to focus on labour, which changes fairly quickly and we treat it as variable in the short run. Copyright 2009 Pearson Education Canada 3-17

The Demand for Labour (continued) We also assume that: Workers are all alike. The wage is determined in a competitive market. A firm employs workers to earn the highest possible level of profit (up to MPN equals wage, in real terms). Copyright 2009 Pearson Education Canada 3-18

The MPN and the Labour Demand Curve The MPN measures the benefit of employing an additional worker in terms of the extra output t produced remember the figure on the production function. This is the demand curve for labour. It as well is a first derivative wrt to N. Copyright 2009 Pearson Education Canada 3-19

The MPN and the Labour Demand Curve (continued) The marginal revenue product of labour (MRPN) measures the benefit to the firm of employing an additional worker in terms of the extra revenue produced. MRPN = P MPN P is the price of output. Copyright 2009 Pearson Education Canada 3-20

The MPN and the Labour Demand Curve (continued) To an employer the benefit is MRPN and the cost is the nominal wage (W) (MB=MC MRPN = W) In real terms the benefit e is MPN and the cost is the real wage (w) - the nominal wage (W) )divided d dby the price of output (P) (i.e. w = W/P) Copyright 2009 Pearson Education Canada 3-21

The MPN and the Labour Demand Curve (continued) The w line is horizontal, the wage is constant in a competitive labour market. For profit-maximizing amount of labour input the MPN curve and w line intersect, MPN=w. If MPN>w, MB>MC so hire more If MPN<w, MB<MC so fire more Copyright 2009 Pearson Education Canada 3-22

The MPN and the Labour Demand Curve The relationship between the real wage and the quantity of labour demanded is negative. The MPN curve is downward d sloping due to diminishing MPN. Copyright 2009 Pearson Education Canada 3-23

The Labour Demand Curve Shifters Economists are always interested in the differences between movements along a curve and shifts in a curve. Changes in the real wage are represented as movements along the labour demand curve. The labour demand curve shifts in response to factors that change the amount of labour that firms want to employ at any given level of real wage. Copyright 2009 Pearson Education Canada 3-24

The Labour Demand Curve Shifters (continued) A positive supply (productivity) shock increases the MPN and increases the quantity of labour demanded at each real wage level. Higher capital stock increases the MPN and increases the quantity of labour demanded at each real wage level. All of this is represented by a shift in the labour demand curve. (board) Copyright 2009 Pearson Education Canada 3-25

Aggregate Labour Demand Aggregate labour demand is the sum of the labour demands of all the firms in the economy. The aggregate labour demand d curve looks the same and behaves the same as a labour demand d curve for an individual firm. Copyright 2009 Pearson Education Canada 3-26

The Supply of Labour Demand is determined by firms but supply is determined by individuals. Aggregate supply of labour is the sum of labour supplied by everyone in the economy. Each person must decide how much time to work for income versus how much time to allocate for leisure (off work activities). Copyright 2009 Pearson Education Canada 3-27

The Supply of Labour (continued) When talking about individuals id making choices the concept of utility is helpful. The utility (happiness) from income for one more hour at work is compared to the cost (lost utility) of one less hour of leisure there is a trade-off. Utility is maximized when these values are the same. (MB=MC) MC) Copyright 2009 Pearson Education Canada 3-28

Real Wages and Labour Supply The real wage is the real income received in exchange for giving up a unit of leisure for work. An increase in the real wage affects the labour supply decision two ways: The substitution effect of a higher real wage is the tendency of workers to supply more labour and reduce leisure hours in response to a higher real wage. Copyright 2009 Pearson Education Canada 3-29

Real Wages and Labour Supply (continued) The income effect of a higher real wage is the tendency of workers to supply less labour and increase leisure hours as they enjoy higher income. An important point: The longer an increase in the real wage is expected to last, the larger is the income effect. Copyright 2009 Pearson Education Canada 3-30

Real Wages and Labour Supply (continued) The two effects work in opposite directions. The substitution effect of a higher real wage is an increase in the quantity of labour supplied. The income effect is a decrease in the quantity of labour supplied. Copyright 2009 Pearson Education Canada 3-31

Real Wages and Labour Supply (continued) Because of conflicting effects there is some ambiguity about how labour supply will respond to a real wage change The empirical evidence suggests that: when wages increases are perceived as temporary, the substitution effect dominates; but when permanent, the income effect dominates. Copyright 2009 Pearson Education Canada 3-32

The Labour Supply Curve The labour supply curve is the curve which relates the amount of labour supplied to the current real wage (other factors held constant, including the real wage expected in the future). Copyright 2009 Pearson Education Canada 3-33

The Labour Supply Curve (continued) The labour supply curve is upward sloping. An increase in the current real wage leads to an increase in labour supplied. With the exception of the real wage, any factor which changes the amount of labour supply will shift the labour supply curve. Copyright 2009 Pearson Education Canada 3-34

Aggregate Labour Supply Aggregate labour supply is the total amount of labour supplied in the economy. We can also discuss movements e along and shifts in the aggregate labour supply curve Copyright 2009 Pearson Education Canada 3-36

Aggregate Labour Supply (continued) Moving along the curve. An increase in the current economy- wide real wage raises the aggregate quantity of labour supplied: people already working supply more hours; some people are induced to join the labour force (reservation wage). In this case, the substitution effect dominates the wealth effect Copyright 2009 Pearson Education Canada 3-37

Aggregate Labour Supply (continued) Shifts in the curve: An increase in wealth or future income will shift the curve left, since it increases the amount of leisure workers can afford An increase in the working age population or an increase in the participation rate will shift the curve right, since it increases the amount of labour supplied Suppose you win the lottery (board) Copyright 2009 Pearson Education Canada 3-38

The Labour Market: A Summary Labour Demand Labour Supply Determined by Firms Individuals id Goal Max Profits Max Utility Benefit MPN Real Wage Cost Real Wage Loss of Leisure Copyright 2009 Pearson Education Canada 3-39

Labour Market Equilibrium The classical l model of the labour market assumes that the real wage adjusts quickly to equate labour supply and labour demand. In equilibrium supply and demand are equal. Both sides of the labour market (firms and individuals) are satisfied. If they were not, adjustment would occur. Copyright 2009 Pearson Education Canada 3-40

Labour Market Equilibrium (continued) The equilibrium level of employment after the complete adjustment of wages and prices is full-employment level of employment ( N ). The corresponding market clearing real wage is ( w ). Both workers and employers are balancing off marginal costs with marginal benefits. Copyright 2009 Pearson Education Canada 3-41

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Labour Market Equilibrium (continued) Aggregate labour demand or supply curve shifters affect: the equilibrium real wage; the full-employment level of unemployment. A temporary adverse productivity shock shifts the demand curve (by changing the A in the production function); But, because it is temporary, it is not expected to affect future marginal products or real wages longer run income is unaffected, so labour supply remains unchanged. (board) Copyright 2009 Pearson Education Canada 3-43

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Labour Market Equilibrium (continued) The advantage of the model is that t it can say something about how shocks can affect employment and wages. It is also simple and has micro underpinnings, which was always a criticism of the simple Keynesian model. It is considered a good description of long-run equilibrium. Copyright 2009 Pearson Education Canada 3-45

Labour Market Equilibrium (continued) The model can also be used to answer questions about income distribution. Part of the reason for adverse income distribution can be attributed to skill differentials. The data show that the proportion of skilled workers in the labour force is rising. Consider the effect of a skill-biased technological change, such as the introduction of computers (board) Copyright 2009 Pearson Education Canada 3-46

Full-Employment Output By combining labour market equilibrium and the production function, we can determine how much output firms want to supply Full-employment output (potential output), Y is the level of output that firms in the economy supply when wages and prices are fully adjusted. We can calculate it by substituting full employment labour N into the production f ti function: Y = AF(K, N) Copyright 2009 Pearson Education Canada 3-48

Labour Market Equilibrium (continued) Anything that changes N or the production function will change Y Effects of an adverse supply shock now hit output as well: The output is reduced directly by a reduction in the productivity measure A. The MPN falls, employment N falls, full employment output Y falls. Copyright 2009 Pearson Education Canada 3-49

Labour Market Equilibrium (continued) The drawbacks of this model is that it implies that there is zero unemployment, which h we know is not realistic. Possible explanations of unemployment: The real wage could be slow to adjust. Matching people to jobs can be a time consuming process. Copyright 2009 Pearson Education Canada 3-50

Unemployment First some definitions (used by Statistics Canada for anyone over 15 yrs old): An employed person (E) is someone who worked full-time or part-time during the past week. An unemployed person (U) is someone who did not work during the past week, but who had actively sought work in the previous four weeks, and was available for work. Copyright 2009 Pearson Education Canada 3-51

Unemployment (continued) Someone not in the labour force is a person who did not work during the past week and did not look for work during the past four weeks. The rest are in the labour force (LF), which is defined as all employed and unemployed workers (E+U). The working age, or adult population (P) is the sum of those in and not in the labour force. Copyright 2009 Pearson Education Canada 3-52

Unemployment (continued) The unemployment rate is the fraction of the labour force that is unemployed [U/(E+U) = U/LF]. The participation rate is the fraction of the labour force in the working-age population (LF/P). The employment ratio is the fraction of the employed in the working-age population (E/P). Copyright 2009 Pearson Education Canada 3-53

Important definitions: A Summary Labor Force = U + E = 17.9 (million) Unemployment rate = U/LF = 61% 6.1% Participation rate = LF/P = 67.5% Employment ratio = E/P = 63.4% The fraction of those not in the labour force = (1 Part rate) = 32.5% 1-54

Changes in Employment Status Labour markets are very dynamic, they are constantly changing. That s why we study them in the short run. The net numbers reported mask a lot of action. Can have fixed employment rate with 1,000's of people becoming unemployed, and 1,000's becoming employed. Flows are crucial! Discouraged workers: people, who after losing a job, stop looking and leave the labour market. Copyright 2009 Pearson Education Canada 3-55

How Long are People Unemployed? An unemployment spell is the period of time that an individual is constantly unemployed. Its length is called the duration of the unemployment spell. Duration of unemployment spells in Canada have two characteristics: they are short (two months or less) most people who are unemployed on a given date are experiencing spells with long duration Copyright 2009 Pearson Education Canada 3-56

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Why are There Always Unemployed People? There are two types of unemployment that prevent the unemployment rate from ever reaching zero: Frictional unemployment e arises as workers search for suitable jobs and firms search for suitable workers. The search and match process takes time. Copyright 2009 Pearson Education Canada 3-58

Why are There Always Unemployed People? Structural unemployment is longterm and chronic unemployment that exists even when the economy is not in a recession. Unskilled or low skilled workers are unable to find long-term jobs. Reallocation of labour from industries/regions in decline to areas that are growing takes time. Copyright 2009 Pearson Education Canada 3-59

The Natural Rate of Unemployment The natural rate of unemployment ( u ) is the rate of unemployment that prevails when output and employment are at their fullemployment levels. The natural aua rate of unemployment poy exist due to frictional and structural causes. Copyright 2009 Pearson Education Canada 3-60

Cyclical Unemployment Cyclical unemployment is the difference between the actual and natural unemployment rate (u u) Cyclical unemployment is positive whenever the actual unemployment rate is above the natural rate (and vice versa). Copyright 2009 Pearson Education Canada 3-61

Okun s Law Relates output and unemployment Okun's Law: the gap between the economy's full-employment output, and the its actual level e of output increases by 2% for each 1% increase in the unemployment level: Y Y Y = 2(u u) Copyright 2009 Pearson Education Canada 3-62

Okun s Law (continued) Okun's law can be rewritten in a slightly different fashion ΔY Y = 3 2Δu It tells us that there is a negative relationship between output growth and the change in the unemployment rate Copyright 2009 Pearson Education Canada 3-63

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